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www.allsyllabus.com www.allsyllabus.com EC2353 -Antenna and wave propagation Introduction An antenna is an electrical conductor or system of conductors Transmission - radiates electromagnetic energy into space Reception - collects electromagnetic energy from space In two-way communication, the same antenna can be used for transmission and reception An antenna is a circuit element that provides a transition form a guided wave on a transmission line to a free space wave and it provides for the collection of electromagnetic energy. In transmit systems the RF signal is generated, amplified, modulated and applied to the antenna In receive systems the antenna collects electromagnetic waves that are ―cutting‖ through the antenna and induce alternating currents that are used by the receiver CONCEPT OF VECTOR POTENTIAL
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Page 1: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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EC2353 -Antenna and wave propagation

Introduction

An antenna is an electrical conductor or system of conductors

Transmission - radiates electromagnetic energy into space

Reception - collects electromagnetic energy from space

In two-way communication the same antenna can be used for transmission and

reception

An antenna is a circuit element that provides a transition form a guided wave on a

transmission line to a free space wave and it provides for the collection of

electromagnetic energy

In transmit systems the RF signal is generated amplified modulated and applied

to the antenna

In receive systems the antenna collects electromagnetic waves that are ―cutting

through the antenna and induce alternating currents that are used by the receiver

CONCEPT OF VECTOR POTENTIAL

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Hertzian dipole

A simple practical antenna is a doublet or Hertzian dipole (see a figure below) It

is very short length of wire over which the current distribution can be assumed uniform

Maxwellrsquos equations show that such an antenna when energized by a high frequency

current is associated with an induction field which decreases inversely as square of the

distance and a radiation field which decreases inversely as distance only The later is still

measurable at large distances from the doublet and is well-known radiation field used in

radio communications

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DEFINITIONS

Radiation Intensity In a given direction the power radiated form an antenna per

unit solid angle

Directive Gain In a given direction 4eth times the ratio of theradiation intensity in

that direction to the total power radiated by the antenna

Directivity The value of the directive gain in the direction of its maximum value

Power Gain In a given direction 4eth times the ratio of the radiationintensity in

that direction to the net power accepted by the antenna from the connected

transmitter NOTES (1) When thedirection is not stated the power gain is usually

taken to be thepower gain in the direction of its maximum value (2) Power gain

does not include reflection losses arising from mismatchof impedance

Beamwidth is the angular separation of the half-power points of the radiated

pattern

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Bandwidth is the difference between the upper and lower cutoff frequencies

offor example a filter a communication channel or a signal spectrum and is

typically measured in hertz In case of a baseband channel or signal the andwidth

is equal to its upper cutoff frequency Bandwidth in hertz is a centralconcept in

many fields including electronics information theory radio communications

signal processing and spectroscopy

GAIN Gain is an antenna property dealing with an antennas ability to

direct its radiated power in a desired direction or to receive

energy preferentially from a desired direction However gain is

not a quantity which can be defined in terms of physical quantities

such as the Watt ohm or joule but is a dimensionless ratio

As a consequence antenna gain results from the interaction of

all other antenna characteristicsAntenna characteristics of gain

beamwidth and efficiency areindependent of the antennas use for

either transmitting or receiving Generally these characteristics are

more easilydescribed for the transmitting case however the

properties apply as well to receiving applications

Radiation resistance

An important property of a transmitting antenna is its radiation resistance which is

associated with power radiated by the antenna If I is the rms (root mean square)

antenna current and Rr is its radiation resistance then the power radiated is I2Rr

watts where Rr is a fictitious resistance which accounts for the radiated power

somewhat like a circuit resistance which dissipates heat The larger the radiation

resistance the larger the power radiated by the antenna In contrast for receiving

antenna its input impedance is important The input impedance is defined as the ratio

of voltage to current at its input and it must be generally matched to the connecting

line or cable The input impedance may or may not be equal to radiation resistance

though very often it does In most case Rr may be calculated or it can be determined

experimentally

Half-wavelength dipole

This type of antenna is a special case where each wire is exactly one-quarter of

the wavelength for a total of a half wavelength The radiation resistance is about 73

ohms if wire diameter is ignored making it easily matched to a coaxial transmission

line The directivity is a constant 164 or 215 dB Actual gain will be a little less due

to ohmic losses

Folded dipole

A folded dipole is a dipole where an additional wire (λ2) links the two ends of the

(λ2) half wave dipole The folded dipole works in the same way as a normal dipole

but the radiation resistance is about 300 ohms rather than the 75 ohms which is

expected for a normal dipole The increase in radiation resistance allows the antenna

to be driven from a 300 ohm balanced line

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RECIPROCITY

An antenna ability to transfer energy form the atmosphere to its receiver with the

same efficiency with which it transfers energy from the transmitter into the

atmosphere

Antenna characteristics are essentially the same regardless of whether an antenna

is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered

as having a shorter effective length Le over which the current is assumed to be uniform

and equal to its peak The relationship between Le and L is given by

Effective aperture

The power received by an antenna can be associated with collecting area Every

antenna may be considered to have such a collecting area which is called its effective

aperture A If Pd is a power density at the antenna and Pr is received power then

Polarization is the direction of the electric field and is the same as the physical

attitude of the antenna

A vertical antenna will transmit a vertically polarized wave

The receive and transmit antennas need to possess the same polarization

Antenna Gain

Relationship between antenna gain and effective area

G = antenna gain

Ae = effective area

f = carrier frequency

c = speed of light (raquo 3 acute 108 ms)

= carrier wavelength

Radiation Pattern

Radiation pattern is an indication of radiated field strength around the antenna

Power radiated from a 2 dipole occurs at right angles to the antenna with no

power emitting from the ends of the antenna Optimum signal strength occurs at

right angles or 180deg from opposite the antenna

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Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section

Beam width (or half-power beam width)

Measure of directivity of antenna

Reception pattern

Receiving antennarsquos equivalent to radiation pattern

Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment This temperature is not the physical temperature of the antenna Moreover

an antenna does not have an intrinsic antenna temperature associated with it rather the

temperature depends on its gain pattern and the thermal environment that it is placed in

To define the environment well introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates For

instance the night sky is roughly 4 Kelvin the value of the temperature pattern in the

direction of the Earths ground is the physical temperature of the Earths ground This

temperature distribution will be written as Hence an antennas temperature will

vary depending on whether it is directional and pointed into space or staring into the sun

For an antenna with a radiation pattern given by the noise temperature is

mathematically defined as

This states that the temperature surrounding the antenna is integrated over the entire

sphere and weighted by the antennas radiation pattern Hence an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna for a perfectly directional antenna (with a pencil beam) the antenna temperature

will only depend on the temperature in which the antenna is looking

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over

In the above K is Boltzmanns constant (138 10^-23 [JoulesKelvin = JK]) The

receiver also has a temperature associated with it ( ) and the total system temperature

(antenna plus receiver) has a combined temperature given by This

temperature can be used in the above equation to find the total noise power of the system

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics because the resulting systems very much depend on each other

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 2: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Hertzian dipole

A simple practical antenna is a doublet or Hertzian dipole (see a figure below) It

is very short length of wire over which the current distribution can be assumed uniform

Maxwellrsquos equations show that such an antenna when energized by a high frequency

current is associated with an induction field which decreases inversely as square of the

distance and a radiation field which decreases inversely as distance only The later is still

measurable at large distances from the doublet and is well-known radiation field used in

radio communications

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DEFINITIONS

Radiation Intensity In a given direction the power radiated form an antenna per

unit solid angle

Directive Gain In a given direction 4eth times the ratio of theradiation intensity in

that direction to the total power radiated by the antenna

Directivity The value of the directive gain in the direction of its maximum value

Power Gain In a given direction 4eth times the ratio of the radiationintensity in

that direction to the net power accepted by the antenna from the connected

transmitter NOTES (1) When thedirection is not stated the power gain is usually

taken to be thepower gain in the direction of its maximum value (2) Power gain

does not include reflection losses arising from mismatchof impedance

Beamwidth is the angular separation of the half-power points of the radiated

pattern

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Bandwidth is the difference between the upper and lower cutoff frequencies

offor example a filter a communication channel or a signal spectrum and is

typically measured in hertz In case of a baseband channel or signal the andwidth

is equal to its upper cutoff frequency Bandwidth in hertz is a centralconcept in

many fields including electronics information theory radio communications

signal processing and spectroscopy

GAIN Gain is an antenna property dealing with an antennas ability to

direct its radiated power in a desired direction or to receive

energy preferentially from a desired direction However gain is

not a quantity which can be defined in terms of physical quantities

such as the Watt ohm or joule but is a dimensionless ratio

As a consequence antenna gain results from the interaction of

all other antenna characteristicsAntenna characteristics of gain

beamwidth and efficiency areindependent of the antennas use for

either transmitting or receiving Generally these characteristics are

more easilydescribed for the transmitting case however the

properties apply as well to receiving applications

Radiation resistance

An important property of a transmitting antenna is its radiation resistance which is

associated with power radiated by the antenna If I is the rms (root mean square)

antenna current and Rr is its radiation resistance then the power radiated is I2Rr

watts where Rr is a fictitious resistance which accounts for the radiated power

somewhat like a circuit resistance which dissipates heat The larger the radiation

resistance the larger the power radiated by the antenna In contrast for receiving

antenna its input impedance is important The input impedance is defined as the ratio

of voltage to current at its input and it must be generally matched to the connecting

line or cable The input impedance may or may not be equal to radiation resistance

though very often it does In most case Rr may be calculated or it can be determined

experimentally

Half-wavelength dipole

This type of antenna is a special case where each wire is exactly one-quarter of

the wavelength for a total of a half wavelength The radiation resistance is about 73

ohms if wire diameter is ignored making it easily matched to a coaxial transmission

line The directivity is a constant 164 or 215 dB Actual gain will be a little less due

to ohmic losses

Folded dipole

A folded dipole is a dipole where an additional wire (λ2) links the two ends of the

(λ2) half wave dipole The folded dipole works in the same way as a normal dipole

but the radiation resistance is about 300 ohms rather than the 75 ohms which is

expected for a normal dipole The increase in radiation resistance allows the antenna

to be driven from a 300 ohm balanced line

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RECIPROCITY

An antenna ability to transfer energy form the atmosphere to its receiver with the

same efficiency with which it transfers energy from the transmitter into the

atmosphere

Antenna characteristics are essentially the same regardless of whether an antenna

is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered

as having a shorter effective length Le over which the current is assumed to be uniform

and equal to its peak The relationship between Le and L is given by

Effective aperture

The power received by an antenna can be associated with collecting area Every

antenna may be considered to have such a collecting area which is called its effective

aperture A If Pd is a power density at the antenna and Pr is received power then

Polarization is the direction of the electric field and is the same as the physical

attitude of the antenna

A vertical antenna will transmit a vertically polarized wave

The receive and transmit antennas need to possess the same polarization

Antenna Gain

Relationship between antenna gain and effective area

G = antenna gain

Ae = effective area

f = carrier frequency

c = speed of light (raquo 3 acute 108 ms)

= carrier wavelength

Radiation Pattern

Radiation pattern is an indication of radiated field strength around the antenna

Power radiated from a 2 dipole occurs at right angles to the antenna with no

power emitting from the ends of the antenna Optimum signal strength occurs at

right angles or 180deg from opposite the antenna

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Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section

Beam width (or half-power beam width)

Measure of directivity of antenna

Reception pattern

Receiving antennarsquos equivalent to radiation pattern

Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment This temperature is not the physical temperature of the antenna Moreover

an antenna does not have an intrinsic antenna temperature associated with it rather the

temperature depends on its gain pattern and the thermal environment that it is placed in

To define the environment well introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates For

instance the night sky is roughly 4 Kelvin the value of the temperature pattern in the

direction of the Earths ground is the physical temperature of the Earths ground This

temperature distribution will be written as Hence an antennas temperature will

vary depending on whether it is directional and pointed into space or staring into the sun

For an antenna with a radiation pattern given by the noise temperature is

mathematically defined as

This states that the temperature surrounding the antenna is integrated over the entire

sphere and weighted by the antennas radiation pattern Hence an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna for a perfectly directional antenna (with a pencil beam) the antenna temperature

will only depend on the temperature in which the antenna is looking

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over

In the above K is Boltzmanns constant (138 10^-23 [JoulesKelvin = JK]) The

receiver also has a temperature associated with it ( ) and the total system temperature

(antenna plus receiver) has a combined temperature given by This

temperature can be used in the above equation to find the total noise power of the system

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics because the resulting systems very much depend on each other

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

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The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 3: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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DEFINITIONS

Radiation Intensity In a given direction the power radiated form an antenna per

unit solid angle

Directive Gain In a given direction 4eth times the ratio of theradiation intensity in

that direction to the total power radiated by the antenna

Directivity The value of the directive gain in the direction of its maximum value

Power Gain In a given direction 4eth times the ratio of the radiationintensity in

that direction to the net power accepted by the antenna from the connected

transmitter NOTES (1) When thedirection is not stated the power gain is usually

taken to be thepower gain in the direction of its maximum value (2) Power gain

does not include reflection losses arising from mismatchof impedance

Beamwidth is the angular separation of the half-power points of the radiated

pattern

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Bandwidth is the difference between the upper and lower cutoff frequencies

offor example a filter a communication channel or a signal spectrum and is

typically measured in hertz In case of a baseband channel or signal the andwidth

is equal to its upper cutoff frequency Bandwidth in hertz is a centralconcept in

many fields including electronics information theory radio communications

signal processing and spectroscopy

GAIN Gain is an antenna property dealing with an antennas ability to

direct its radiated power in a desired direction or to receive

energy preferentially from a desired direction However gain is

not a quantity which can be defined in terms of physical quantities

such as the Watt ohm or joule but is a dimensionless ratio

As a consequence antenna gain results from the interaction of

all other antenna characteristicsAntenna characteristics of gain

beamwidth and efficiency areindependent of the antennas use for

either transmitting or receiving Generally these characteristics are

more easilydescribed for the transmitting case however the

properties apply as well to receiving applications

Radiation resistance

An important property of a transmitting antenna is its radiation resistance which is

associated with power radiated by the antenna If I is the rms (root mean square)

antenna current and Rr is its radiation resistance then the power radiated is I2Rr

watts where Rr is a fictitious resistance which accounts for the radiated power

somewhat like a circuit resistance which dissipates heat The larger the radiation

resistance the larger the power radiated by the antenna In contrast for receiving

antenna its input impedance is important The input impedance is defined as the ratio

of voltage to current at its input and it must be generally matched to the connecting

line or cable The input impedance may or may not be equal to radiation resistance

though very often it does In most case Rr may be calculated or it can be determined

experimentally

Half-wavelength dipole

This type of antenna is a special case where each wire is exactly one-quarter of

the wavelength for a total of a half wavelength The radiation resistance is about 73

ohms if wire diameter is ignored making it easily matched to a coaxial transmission

line The directivity is a constant 164 or 215 dB Actual gain will be a little less due

to ohmic losses

Folded dipole

A folded dipole is a dipole where an additional wire (λ2) links the two ends of the

(λ2) half wave dipole The folded dipole works in the same way as a normal dipole

but the radiation resistance is about 300 ohms rather than the 75 ohms which is

expected for a normal dipole The increase in radiation resistance allows the antenna

to be driven from a 300 ohm balanced line

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RECIPROCITY

An antenna ability to transfer energy form the atmosphere to its receiver with the

same efficiency with which it transfers energy from the transmitter into the

atmosphere

Antenna characteristics are essentially the same regardless of whether an antenna

is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered

as having a shorter effective length Le over which the current is assumed to be uniform

and equal to its peak The relationship between Le and L is given by

Effective aperture

The power received by an antenna can be associated with collecting area Every

antenna may be considered to have such a collecting area which is called its effective

aperture A If Pd is a power density at the antenna and Pr is received power then

Polarization is the direction of the electric field and is the same as the physical

attitude of the antenna

A vertical antenna will transmit a vertically polarized wave

The receive and transmit antennas need to possess the same polarization

Antenna Gain

Relationship between antenna gain and effective area

G = antenna gain

Ae = effective area

f = carrier frequency

c = speed of light (raquo 3 acute 108 ms)

= carrier wavelength

Radiation Pattern

Radiation pattern is an indication of radiated field strength around the antenna

Power radiated from a 2 dipole occurs at right angles to the antenna with no

power emitting from the ends of the antenna Optimum signal strength occurs at

right angles or 180deg from opposite the antenna

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Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section

Beam width (or half-power beam width)

Measure of directivity of antenna

Reception pattern

Receiving antennarsquos equivalent to radiation pattern

Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment This temperature is not the physical temperature of the antenna Moreover

an antenna does not have an intrinsic antenna temperature associated with it rather the

temperature depends on its gain pattern and the thermal environment that it is placed in

To define the environment well introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates For

instance the night sky is roughly 4 Kelvin the value of the temperature pattern in the

direction of the Earths ground is the physical temperature of the Earths ground This

temperature distribution will be written as Hence an antennas temperature will

vary depending on whether it is directional and pointed into space or staring into the sun

For an antenna with a radiation pattern given by the noise temperature is

mathematically defined as

This states that the temperature surrounding the antenna is integrated over the entire

sphere and weighted by the antennas radiation pattern Hence an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna for a perfectly directional antenna (with a pencil beam) the antenna temperature

will only depend on the temperature in which the antenna is looking

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over

In the above K is Boltzmanns constant (138 10^-23 [JoulesKelvin = JK]) The

receiver also has a temperature associated with it ( ) and the total system temperature

(antenna plus receiver) has a combined temperature given by This

temperature can be used in the above equation to find the total noise power of the system

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics because the resulting systems very much depend on each other

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 4: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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DEFINITIONS

Radiation Intensity In a given direction the power radiated form an antenna per

unit solid angle

Directive Gain In a given direction 4eth times the ratio of theradiation intensity in

that direction to the total power radiated by the antenna

Directivity The value of the directive gain in the direction of its maximum value

Power Gain In a given direction 4eth times the ratio of the radiationintensity in

that direction to the net power accepted by the antenna from the connected

transmitter NOTES (1) When thedirection is not stated the power gain is usually

taken to be thepower gain in the direction of its maximum value (2) Power gain

does not include reflection losses arising from mismatchof impedance

Beamwidth is the angular separation of the half-power points of the radiated

pattern

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Bandwidth is the difference between the upper and lower cutoff frequencies

offor example a filter a communication channel or a signal spectrum and is

typically measured in hertz In case of a baseband channel or signal the andwidth

is equal to its upper cutoff frequency Bandwidth in hertz is a centralconcept in

many fields including electronics information theory radio communications

signal processing and spectroscopy

GAIN Gain is an antenna property dealing with an antennas ability to

direct its radiated power in a desired direction or to receive

energy preferentially from a desired direction However gain is

not a quantity which can be defined in terms of physical quantities

such as the Watt ohm or joule but is a dimensionless ratio

As a consequence antenna gain results from the interaction of

all other antenna characteristicsAntenna characteristics of gain

beamwidth and efficiency areindependent of the antennas use for

either transmitting or receiving Generally these characteristics are

more easilydescribed for the transmitting case however the

properties apply as well to receiving applications

Radiation resistance

An important property of a transmitting antenna is its radiation resistance which is

associated with power radiated by the antenna If I is the rms (root mean square)

antenna current and Rr is its radiation resistance then the power radiated is I2Rr

watts where Rr is a fictitious resistance which accounts for the radiated power

somewhat like a circuit resistance which dissipates heat The larger the radiation

resistance the larger the power radiated by the antenna In contrast for receiving

antenna its input impedance is important The input impedance is defined as the ratio

of voltage to current at its input and it must be generally matched to the connecting

line or cable The input impedance may or may not be equal to radiation resistance

though very often it does In most case Rr may be calculated or it can be determined

experimentally

Half-wavelength dipole

This type of antenna is a special case where each wire is exactly one-quarter of

the wavelength for a total of a half wavelength The radiation resistance is about 73

ohms if wire diameter is ignored making it easily matched to a coaxial transmission

line The directivity is a constant 164 or 215 dB Actual gain will be a little less due

to ohmic losses

Folded dipole

A folded dipole is a dipole where an additional wire (λ2) links the two ends of the

(λ2) half wave dipole The folded dipole works in the same way as a normal dipole

but the radiation resistance is about 300 ohms rather than the 75 ohms which is

expected for a normal dipole The increase in radiation resistance allows the antenna

to be driven from a 300 ohm balanced line

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RECIPROCITY

An antenna ability to transfer energy form the atmosphere to its receiver with the

same efficiency with which it transfers energy from the transmitter into the

atmosphere

Antenna characteristics are essentially the same regardless of whether an antenna

is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered

as having a shorter effective length Le over which the current is assumed to be uniform

and equal to its peak The relationship between Le and L is given by

Effective aperture

The power received by an antenna can be associated with collecting area Every

antenna may be considered to have such a collecting area which is called its effective

aperture A If Pd is a power density at the antenna and Pr is received power then

Polarization is the direction of the electric field and is the same as the physical

attitude of the antenna

A vertical antenna will transmit a vertically polarized wave

The receive and transmit antennas need to possess the same polarization

Antenna Gain

Relationship between antenna gain and effective area

G = antenna gain

Ae = effective area

f = carrier frequency

c = speed of light (raquo 3 acute 108 ms)

= carrier wavelength

Radiation Pattern

Radiation pattern is an indication of radiated field strength around the antenna

Power radiated from a 2 dipole occurs at right angles to the antenna with no

power emitting from the ends of the antenna Optimum signal strength occurs at

right angles or 180deg from opposite the antenna

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Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section

Beam width (or half-power beam width)

Measure of directivity of antenna

Reception pattern

Receiving antennarsquos equivalent to radiation pattern

Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment This temperature is not the physical temperature of the antenna Moreover

an antenna does not have an intrinsic antenna temperature associated with it rather the

temperature depends on its gain pattern and the thermal environment that it is placed in

To define the environment well introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates For

instance the night sky is roughly 4 Kelvin the value of the temperature pattern in the

direction of the Earths ground is the physical temperature of the Earths ground This

temperature distribution will be written as Hence an antennas temperature will

vary depending on whether it is directional and pointed into space or staring into the sun

For an antenna with a radiation pattern given by the noise temperature is

mathematically defined as

This states that the temperature surrounding the antenna is integrated over the entire

sphere and weighted by the antennas radiation pattern Hence an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna for a perfectly directional antenna (with a pencil beam) the antenna temperature

will only depend on the temperature in which the antenna is looking

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over

In the above K is Boltzmanns constant (138 10^-23 [JoulesKelvin = JK]) The

receiver also has a temperature associated with it ( ) and the total system temperature

(antenna plus receiver) has a combined temperature given by This

temperature can be used in the above equation to find the total noise power of the system

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics because the resulting systems very much depend on each other

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

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Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

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The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 5: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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DEFINITIONS

Radiation Intensity In a given direction the power radiated form an antenna per

unit solid angle

Directive Gain In a given direction 4eth times the ratio of theradiation intensity in

that direction to the total power radiated by the antenna

Directivity The value of the directive gain in the direction of its maximum value

Power Gain In a given direction 4eth times the ratio of the radiationintensity in

that direction to the net power accepted by the antenna from the connected

transmitter NOTES (1) When thedirection is not stated the power gain is usually

taken to be thepower gain in the direction of its maximum value (2) Power gain

does not include reflection losses arising from mismatchof impedance

Beamwidth is the angular separation of the half-power points of the radiated

pattern

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Bandwidth is the difference between the upper and lower cutoff frequencies

offor example a filter a communication channel or a signal spectrum and is

typically measured in hertz In case of a baseband channel or signal the andwidth

is equal to its upper cutoff frequency Bandwidth in hertz is a centralconcept in

many fields including electronics information theory radio communications

signal processing and spectroscopy

GAIN Gain is an antenna property dealing with an antennas ability to

direct its radiated power in a desired direction or to receive

energy preferentially from a desired direction However gain is

not a quantity which can be defined in terms of physical quantities

such as the Watt ohm or joule but is a dimensionless ratio

As a consequence antenna gain results from the interaction of

all other antenna characteristicsAntenna characteristics of gain

beamwidth and efficiency areindependent of the antennas use for

either transmitting or receiving Generally these characteristics are

more easilydescribed for the transmitting case however the

properties apply as well to receiving applications

Radiation resistance

An important property of a transmitting antenna is its radiation resistance which is

associated with power radiated by the antenna If I is the rms (root mean square)

antenna current and Rr is its radiation resistance then the power radiated is I2Rr

watts where Rr is a fictitious resistance which accounts for the radiated power

somewhat like a circuit resistance which dissipates heat The larger the radiation

resistance the larger the power radiated by the antenna In contrast for receiving

antenna its input impedance is important The input impedance is defined as the ratio

of voltage to current at its input and it must be generally matched to the connecting

line or cable The input impedance may or may not be equal to radiation resistance

though very often it does In most case Rr may be calculated or it can be determined

experimentally

Half-wavelength dipole

This type of antenna is a special case where each wire is exactly one-quarter of

the wavelength for a total of a half wavelength The radiation resistance is about 73

ohms if wire diameter is ignored making it easily matched to a coaxial transmission

line The directivity is a constant 164 or 215 dB Actual gain will be a little less due

to ohmic losses

Folded dipole

A folded dipole is a dipole where an additional wire (λ2) links the two ends of the

(λ2) half wave dipole The folded dipole works in the same way as a normal dipole

but the radiation resistance is about 300 ohms rather than the 75 ohms which is

expected for a normal dipole The increase in radiation resistance allows the antenna

to be driven from a 300 ohm balanced line

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RECIPROCITY

An antenna ability to transfer energy form the atmosphere to its receiver with the

same efficiency with which it transfers energy from the transmitter into the

atmosphere

Antenna characteristics are essentially the same regardless of whether an antenna

is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered

as having a shorter effective length Le over which the current is assumed to be uniform

and equal to its peak The relationship between Le and L is given by

Effective aperture

The power received by an antenna can be associated with collecting area Every

antenna may be considered to have such a collecting area which is called its effective

aperture A If Pd is a power density at the antenna and Pr is received power then

Polarization is the direction of the electric field and is the same as the physical

attitude of the antenna

A vertical antenna will transmit a vertically polarized wave

The receive and transmit antennas need to possess the same polarization

Antenna Gain

Relationship between antenna gain and effective area

G = antenna gain

Ae = effective area

f = carrier frequency

c = speed of light (raquo 3 acute 108 ms)

= carrier wavelength

Radiation Pattern

Radiation pattern is an indication of radiated field strength around the antenna

Power radiated from a 2 dipole occurs at right angles to the antenna with no

power emitting from the ends of the antenna Optimum signal strength occurs at

right angles or 180deg from opposite the antenna

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Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section

Beam width (or half-power beam width)

Measure of directivity of antenna

Reception pattern

Receiving antennarsquos equivalent to radiation pattern

Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment This temperature is not the physical temperature of the antenna Moreover

an antenna does not have an intrinsic antenna temperature associated with it rather the

temperature depends on its gain pattern and the thermal environment that it is placed in

To define the environment well introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates For

instance the night sky is roughly 4 Kelvin the value of the temperature pattern in the

direction of the Earths ground is the physical temperature of the Earths ground This

temperature distribution will be written as Hence an antennas temperature will

vary depending on whether it is directional and pointed into space or staring into the sun

For an antenna with a radiation pattern given by the noise temperature is

mathematically defined as

This states that the temperature surrounding the antenna is integrated over the entire

sphere and weighted by the antennas radiation pattern Hence an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna for a perfectly directional antenna (with a pencil beam) the antenna temperature

will only depend on the temperature in which the antenna is looking

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over

In the above K is Boltzmanns constant (138 10^-23 [JoulesKelvin = JK]) The

receiver also has a temperature associated with it ( ) and the total system temperature

(antenna plus receiver) has a combined temperature given by This

temperature can be used in the above equation to find the total noise power of the system

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics because the resulting systems very much depend on each other

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 6: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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DEFINITIONS

Radiation Intensity In a given direction the power radiated form an antenna per

unit solid angle

Directive Gain In a given direction 4eth times the ratio of theradiation intensity in

that direction to the total power radiated by the antenna

Directivity The value of the directive gain in the direction of its maximum value

Power Gain In a given direction 4eth times the ratio of the radiationintensity in

that direction to the net power accepted by the antenna from the connected

transmitter NOTES (1) When thedirection is not stated the power gain is usually

taken to be thepower gain in the direction of its maximum value (2) Power gain

does not include reflection losses arising from mismatchof impedance

Beamwidth is the angular separation of the half-power points of the radiated

pattern

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Bandwidth is the difference between the upper and lower cutoff frequencies

offor example a filter a communication channel or a signal spectrum and is

typically measured in hertz In case of a baseband channel or signal the andwidth

is equal to its upper cutoff frequency Bandwidth in hertz is a centralconcept in

many fields including electronics information theory radio communications

signal processing and spectroscopy

GAIN Gain is an antenna property dealing with an antennas ability to

direct its radiated power in a desired direction or to receive

energy preferentially from a desired direction However gain is

not a quantity which can be defined in terms of physical quantities

such as the Watt ohm or joule but is a dimensionless ratio

As a consequence antenna gain results from the interaction of

all other antenna characteristicsAntenna characteristics of gain

beamwidth and efficiency areindependent of the antennas use for

either transmitting or receiving Generally these characteristics are

more easilydescribed for the transmitting case however the

properties apply as well to receiving applications

Radiation resistance

An important property of a transmitting antenna is its radiation resistance which is

associated with power radiated by the antenna If I is the rms (root mean square)

antenna current and Rr is its radiation resistance then the power radiated is I2Rr

watts where Rr is a fictitious resistance which accounts for the radiated power

somewhat like a circuit resistance which dissipates heat The larger the radiation

resistance the larger the power radiated by the antenna In contrast for receiving

antenna its input impedance is important The input impedance is defined as the ratio

of voltage to current at its input and it must be generally matched to the connecting

line or cable The input impedance may or may not be equal to radiation resistance

though very often it does In most case Rr may be calculated or it can be determined

experimentally

Half-wavelength dipole

This type of antenna is a special case where each wire is exactly one-quarter of

the wavelength for a total of a half wavelength The radiation resistance is about 73

ohms if wire diameter is ignored making it easily matched to a coaxial transmission

line The directivity is a constant 164 or 215 dB Actual gain will be a little less due

to ohmic losses

Folded dipole

A folded dipole is a dipole where an additional wire (λ2) links the two ends of the

(λ2) half wave dipole The folded dipole works in the same way as a normal dipole

but the radiation resistance is about 300 ohms rather than the 75 ohms which is

expected for a normal dipole The increase in radiation resistance allows the antenna

to be driven from a 300 ohm balanced line

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RECIPROCITY

An antenna ability to transfer energy form the atmosphere to its receiver with the

same efficiency with which it transfers energy from the transmitter into the

atmosphere

Antenna characteristics are essentially the same regardless of whether an antenna

is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered

as having a shorter effective length Le over which the current is assumed to be uniform

and equal to its peak The relationship between Le and L is given by

Effective aperture

The power received by an antenna can be associated with collecting area Every

antenna may be considered to have such a collecting area which is called its effective

aperture A If Pd is a power density at the antenna and Pr is received power then

Polarization is the direction of the electric field and is the same as the physical

attitude of the antenna

A vertical antenna will transmit a vertically polarized wave

The receive and transmit antennas need to possess the same polarization

Antenna Gain

Relationship between antenna gain and effective area

G = antenna gain

Ae = effective area

f = carrier frequency

c = speed of light (raquo 3 acute 108 ms)

= carrier wavelength

Radiation Pattern

Radiation pattern is an indication of radiated field strength around the antenna

Power radiated from a 2 dipole occurs at right angles to the antenna with no

power emitting from the ends of the antenna Optimum signal strength occurs at

right angles or 180deg from opposite the antenna

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Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section

Beam width (or half-power beam width)

Measure of directivity of antenna

Reception pattern

Receiving antennarsquos equivalent to radiation pattern

Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment This temperature is not the physical temperature of the antenna Moreover

an antenna does not have an intrinsic antenna temperature associated with it rather the

temperature depends on its gain pattern and the thermal environment that it is placed in

To define the environment well introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates For

instance the night sky is roughly 4 Kelvin the value of the temperature pattern in the

direction of the Earths ground is the physical temperature of the Earths ground This

temperature distribution will be written as Hence an antennas temperature will

vary depending on whether it is directional and pointed into space or staring into the sun

For an antenna with a radiation pattern given by the noise temperature is

mathematically defined as

This states that the temperature surrounding the antenna is integrated over the entire

sphere and weighted by the antennas radiation pattern Hence an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna for a perfectly directional antenna (with a pencil beam) the antenna temperature

will only depend on the temperature in which the antenna is looking

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over

In the above K is Boltzmanns constant (138 10^-23 [JoulesKelvin = JK]) The

receiver also has a temperature associated with it ( ) and the total system temperature

(antenna plus receiver) has a combined temperature given by This

temperature can be used in the above equation to find the total noise power of the system

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics because the resulting systems very much depend on each other

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 7: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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DEFINITIONS

Radiation Intensity In a given direction the power radiated form an antenna per

unit solid angle

Directive Gain In a given direction 4eth times the ratio of theradiation intensity in

that direction to the total power radiated by the antenna

Directivity The value of the directive gain in the direction of its maximum value

Power Gain In a given direction 4eth times the ratio of the radiationintensity in

that direction to the net power accepted by the antenna from the connected

transmitter NOTES (1) When thedirection is not stated the power gain is usually

taken to be thepower gain in the direction of its maximum value (2) Power gain

does not include reflection losses arising from mismatchof impedance

Beamwidth is the angular separation of the half-power points of the radiated

pattern

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Bandwidth is the difference between the upper and lower cutoff frequencies

offor example a filter a communication channel or a signal spectrum and is

typically measured in hertz In case of a baseband channel or signal the andwidth

is equal to its upper cutoff frequency Bandwidth in hertz is a centralconcept in

many fields including electronics information theory radio communications

signal processing and spectroscopy

GAIN Gain is an antenna property dealing with an antennas ability to

direct its radiated power in a desired direction or to receive

energy preferentially from a desired direction However gain is

not a quantity which can be defined in terms of physical quantities

such as the Watt ohm or joule but is a dimensionless ratio

As a consequence antenna gain results from the interaction of

all other antenna characteristicsAntenna characteristics of gain

beamwidth and efficiency areindependent of the antennas use for

either transmitting or receiving Generally these characteristics are

more easilydescribed for the transmitting case however the

properties apply as well to receiving applications

Radiation resistance

An important property of a transmitting antenna is its radiation resistance which is

associated with power radiated by the antenna If I is the rms (root mean square)

antenna current and Rr is its radiation resistance then the power radiated is I2Rr

watts where Rr is a fictitious resistance which accounts for the radiated power

somewhat like a circuit resistance which dissipates heat The larger the radiation

resistance the larger the power radiated by the antenna In contrast for receiving

antenna its input impedance is important The input impedance is defined as the ratio

of voltage to current at its input and it must be generally matched to the connecting

line or cable The input impedance may or may not be equal to radiation resistance

though very often it does In most case Rr may be calculated or it can be determined

experimentally

Half-wavelength dipole

This type of antenna is a special case where each wire is exactly one-quarter of

the wavelength for a total of a half wavelength The radiation resistance is about 73

ohms if wire diameter is ignored making it easily matched to a coaxial transmission

line The directivity is a constant 164 or 215 dB Actual gain will be a little less due

to ohmic losses

Folded dipole

A folded dipole is a dipole where an additional wire (λ2) links the two ends of the

(λ2) half wave dipole The folded dipole works in the same way as a normal dipole

but the radiation resistance is about 300 ohms rather than the 75 ohms which is

expected for a normal dipole The increase in radiation resistance allows the antenna

to be driven from a 300 ohm balanced line

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RECIPROCITY

An antenna ability to transfer energy form the atmosphere to its receiver with the

same efficiency with which it transfers energy from the transmitter into the

atmosphere

Antenna characteristics are essentially the same regardless of whether an antenna

is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered

as having a shorter effective length Le over which the current is assumed to be uniform

and equal to its peak The relationship between Le and L is given by

Effective aperture

The power received by an antenna can be associated with collecting area Every

antenna may be considered to have such a collecting area which is called its effective

aperture A If Pd is a power density at the antenna and Pr is received power then

Polarization is the direction of the electric field and is the same as the physical

attitude of the antenna

A vertical antenna will transmit a vertically polarized wave

The receive and transmit antennas need to possess the same polarization

Antenna Gain

Relationship between antenna gain and effective area

G = antenna gain

Ae = effective area

f = carrier frequency

c = speed of light (raquo 3 acute 108 ms)

= carrier wavelength

Radiation Pattern

Radiation pattern is an indication of radiated field strength around the antenna

Power radiated from a 2 dipole occurs at right angles to the antenna with no

power emitting from the ends of the antenna Optimum signal strength occurs at

right angles or 180deg from opposite the antenna

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Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section

Beam width (or half-power beam width)

Measure of directivity of antenna

Reception pattern

Receiving antennarsquos equivalent to radiation pattern

Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment This temperature is not the physical temperature of the antenna Moreover

an antenna does not have an intrinsic antenna temperature associated with it rather the

temperature depends on its gain pattern and the thermal environment that it is placed in

To define the environment well introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates For

instance the night sky is roughly 4 Kelvin the value of the temperature pattern in the

direction of the Earths ground is the physical temperature of the Earths ground This

temperature distribution will be written as Hence an antennas temperature will

vary depending on whether it is directional and pointed into space or staring into the sun

For an antenna with a radiation pattern given by the noise temperature is

mathematically defined as

This states that the temperature surrounding the antenna is integrated over the entire

sphere and weighted by the antennas radiation pattern Hence an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna for a perfectly directional antenna (with a pencil beam) the antenna temperature

will only depend on the temperature in which the antenna is looking

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over

In the above K is Boltzmanns constant (138 10^-23 [JoulesKelvin = JK]) The

receiver also has a temperature associated with it ( ) and the total system temperature

(antenna plus receiver) has a combined temperature given by This

temperature can be used in the above equation to find the total noise power of the system

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics because the resulting systems very much depend on each other

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

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Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

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The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 8: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Bandwidth is the difference between the upper and lower cutoff frequencies

offor example a filter a communication channel or a signal spectrum and is

typically measured in hertz In case of a baseband channel or signal the andwidth

is equal to its upper cutoff frequency Bandwidth in hertz is a centralconcept in

many fields including electronics information theory radio communications

signal processing and spectroscopy

GAIN Gain is an antenna property dealing with an antennas ability to

direct its radiated power in a desired direction or to receive

energy preferentially from a desired direction However gain is

not a quantity which can be defined in terms of physical quantities

such as the Watt ohm or joule but is a dimensionless ratio

As a consequence antenna gain results from the interaction of

all other antenna characteristicsAntenna characteristics of gain

beamwidth and efficiency areindependent of the antennas use for

either transmitting or receiving Generally these characteristics are

more easilydescribed for the transmitting case however the

properties apply as well to receiving applications

Radiation resistance

An important property of a transmitting antenna is its radiation resistance which is

associated with power radiated by the antenna If I is the rms (root mean square)

antenna current and Rr is its radiation resistance then the power radiated is I2Rr

watts where Rr is a fictitious resistance which accounts for the radiated power

somewhat like a circuit resistance which dissipates heat The larger the radiation

resistance the larger the power radiated by the antenna In contrast for receiving

antenna its input impedance is important The input impedance is defined as the ratio

of voltage to current at its input and it must be generally matched to the connecting

line or cable The input impedance may or may not be equal to radiation resistance

though very often it does In most case Rr may be calculated or it can be determined

experimentally

Half-wavelength dipole

This type of antenna is a special case where each wire is exactly one-quarter of

the wavelength for a total of a half wavelength The radiation resistance is about 73

ohms if wire diameter is ignored making it easily matched to a coaxial transmission

line The directivity is a constant 164 or 215 dB Actual gain will be a little less due

to ohmic losses

Folded dipole

A folded dipole is a dipole where an additional wire (λ2) links the two ends of the

(λ2) half wave dipole The folded dipole works in the same way as a normal dipole

but the radiation resistance is about 300 ohms rather than the 75 ohms which is

expected for a normal dipole The increase in radiation resistance allows the antenna

to be driven from a 300 ohm balanced line

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RECIPROCITY

An antenna ability to transfer energy form the atmosphere to its receiver with the

same efficiency with which it transfers energy from the transmitter into the

atmosphere

Antenna characteristics are essentially the same regardless of whether an antenna

is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered

as having a shorter effective length Le over which the current is assumed to be uniform

and equal to its peak The relationship between Le and L is given by

Effective aperture

The power received by an antenna can be associated with collecting area Every

antenna may be considered to have such a collecting area which is called its effective

aperture A If Pd is a power density at the antenna and Pr is received power then

Polarization is the direction of the electric field and is the same as the physical

attitude of the antenna

A vertical antenna will transmit a vertically polarized wave

The receive and transmit antennas need to possess the same polarization

Antenna Gain

Relationship between antenna gain and effective area

G = antenna gain

Ae = effective area

f = carrier frequency

c = speed of light (raquo 3 acute 108 ms)

= carrier wavelength

Radiation Pattern

Radiation pattern is an indication of radiated field strength around the antenna

Power radiated from a 2 dipole occurs at right angles to the antenna with no

power emitting from the ends of the antenna Optimum signal strength occurs at

right angles or 180deg from opposite the antenna

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Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section

Beam width (or half-power beam width)

Measure of directivity of antenna

Reception pattern

Receiving antennarsquos equivalent to radiation pattern

Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment This temperature is not the physical temperature of the antenna Moreover

an antenna does not have an intrinsic antenna temperature associated with it rather the

temperature depends on its gain pattern and the thermal environment that it is placed in

To define the environment well introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates For

instance the night sky is roughly 4 Kelvin the value of the temperature pattern in the

direction of the Earths ground is the physical temperature of the Earths ground This

temperature distribution will be written as Hence an antennas temperature will

vary depending on whether it is directional and pointed into space or staring into the sun

For an antenna with a radiation pattern given by the noise temperature is

mathematically defined as

This states that the temperature surrounding the antenna is integrated over the entire

sphere and weighted by the antennas radiation pattern Hence an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna for a perfectly directional antenna (with a pencil beam) the antenna temperature

will only depend on the temperature in which the antenna is looking

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over

In the above K is Boltzmanns constant (138 10^-23 [JoulesKelvin = JK]) The

receiver also has a temperature associated with it ( ) and the total system temperature

(antenna plus receiver) has a combined temperature given by This

temperature can be used in the above equation to find the total noise power of the system

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics because the resulting systems very much depend on each other

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 9: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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RECIPROCITY

An antenna ability to transfer energy form the atmosphere to its receiver with the

same efficiency with which it transfers energy from the transmitter into the

atmosphere

Antenna characteristics are essentially the same regardless of whether an antenna

is sending or receiving electromagnetic energy

An antenna with a non-uniform distribution of current over its length L can be considered

as having a shorter effective length Le over which the current is assumed to be uniform

and equal to its peak The relationship between Le and L is given by

Effective aperture

The power received by an antenna can be associated with collecting area Every

antenna may be considered to have such a collecting area which is called its effective

aperture A If Pd is a power density at the antenna and Pr is received power then

Polarization is the direction of the electric field and is the same as the physical

attitude of the antenna

A vertical antenna will transmit a vertically polarized wave

The receive and transmit antennas need to possess the same polarization

Antenna Gain

Relationship between antenna gain and effective area

G = antenna gain

Ae = effective area

f = carrier frequency

c = speed of light (raquo 3 acute 108 ms)

= carrier wavelength

Radiation Pattern

Radiation pattern is an indication of radiated field strength around the antenna

Power radiated from a 2 dipole occurs at right angles to the antenna with no

power emitting from the ends of the antenna Optimum signal strength occurs at

right angles or 180deg from opposite the antenna

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Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section

Beam width (or half-power beam width)

Measure of directivity of antenna

Reception pattern

Receiving antennarsquos equivalent to radiation pattern

Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment This temperature is not the physical temperature of the antenna Moreover

an antenna does not have an intrinsic antenna temperature associated with it rather the

temperature depends on its gain pattern and the thermal environment that it is placed in

To define the environment well introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates For

instance the night sky is roughly 4 Kelvin the value of the temperature pattern in the

direction of the Earths ground is the physical temperature of the Earths ground This

temperature distribution will be written as Hence an antennas temperature will

vary depending on whether it is directional and pointed into space or staring into the sun

For an antenna with a radiation pattern given by the noise temperature is

mathematically defined as

This states that the temperature surrounding the antenna is integrated over the entire

sphere and weighted by the antennas radiation pattern Hence an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna for a perfectly directional antenna (with a pencil beam) the antenna temperature

will only depend on the temperature in which the antenna is looking

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over

In the above K is Boltzmanns constant (138 10^-23 [JoulesKelvin = JK]) The

receiver also has a temperature associated with it ( ) and the total system temperature

(antenna plus receiver) has a combined temperature given by This

temperature can be used in the above equation to find the total noise power of the system

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics because the resulting systems very much depend on each other

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

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Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

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The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 10: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Radiation pattern

Graphical representation of radiation properties of an antenna

Depicted as two-dimensional cross section

Beam width (or half-power beam width)

Measure of directivity of antenna

Reception pattern

Receiving antennarsquos equivalent to radiation pattern

Antenna Temperature

( ) is a parameter that describes how much noise an antenna produces in a given

environment This temperature is not the physical temperature of the antenna Moreover

an antenna does not have an intrinsic antenna temperature associated with it rather the

temperature depends on its gain pattern and the thermal environment that it is placed in

To define the environment well introduce a temperature distribution - this is the

temperature in every direction away from the antenna in spherical coordinates For

instance the night sky is roughly 4 Kelvin the value of the temperature pattern in the

direction of the Earths ground is the physical temperature of the Earths ground This

temperature distribution will be written as Hence an antennas temperature will

vary depending on whether it is directional and pointed into space or staring into the sun

For an antenna with a radiation pattern given by the noise temperature is

mathematically defined as

This states that the temperature surrounding the antenna is integrated over the entire

sphere and weighted by the antennas radiation pattern Hence an isotropic antenna

would have a noise temperature that is the average of all temperatures around the

antenna for a perfectly directional antenna (with a pencil beam) the antenna temperature

will only depend on the temperature in which the antenna is looking

The noise power received from an antenna at temperature can be expressed in terms of

the bandwidth (B) the antenna (and its receiver) are operating over

In the above K is Boltzmanns constant (138 10^-23 [JoulesKelvin = JK]) The

receiver also has a temperature associated with it ( ) and the total system temperature

(antenna plus receiver) has a combined temperature given by This

temperature can be used in the above equation to find the total noise power of the system

These concepts begin to illustrate how antenna engineers must understand receivers and

the associated electronics because the resulting systems very much depend on each other

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 11: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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A parameter often encountered in specification sheets for antennas that operate in certain

environments is the ratio of gain of the antenna divided by the antenna temperature (or

system temperature if a receiver is specified) This parameter is written as GT and has

units of dBKelvin [dBK]

UNIT _2 WIRE ANTENNAS AND ANTENNA ARRAYS

Half wave antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 12: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Quarter wave or unipole antenna

The quarter wave or unipole antenna is a single element antenna feed at one end

that behaves as a dipole antenna It is formed by a conductor in length It is fed in

the lower end which is near a conductive surface which works as a reflector (see

Effect of ground) The current in the reflected image has the same direction and

phase that the current in the real antenna The set quarter-wave plus image forms

a half-wave dipole that radiates only in the upper half of space

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

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The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 13: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Antenna array is a group of antennas or antenna elements arranged to provide the

desired directional characteristics Generally any combination of elements can form an

array However equal elements in a regular geometry are usually used

PATTERN MULTIPLICATION

The pattern multiplication principle states that the radiation patterns of an array of N

identical antennas is equal to the product of the element pattern Fe( ) (pattern of one of

the antennas) and the array pattern Fa( ) where Fa( ) is the pattern obtained upon

replacing all of the actual antennas with isotropic sources

LOOP ANTENNA The small loop antenna is a closed loop as shown in Figure 1 These antennas have low radiation resistance and high reactance so that their impedance is difficult to match to a transmitter As a result these antennas are most often used as receive antennas where impedance mismatch loss can be tolerated

The radius is a and is assumed to be much smaller than a wavelength (altlt ) The loop lies in the x-y plane

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

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Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 14: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 1 Small loop antenna

Since the loop is electrically small the current within the loop can be

approximated as being constant along the loop so that I=

The fields from a small circular loop are given by

The variation of the pattern with direction is given by so that the

radiation pattern of a small loop antenna has the same power pattern as that of a short dipole However the fields of a small dipole have the E- and H- fields switched relative to that of a short dipole the E-field is horizontally polarized

in the x-y plane

The small loop is often referred to as the dual of the dipole antenna because if a small dipole had magnetic current flowing (as opposed to electric current as in a regular dipole) the fields would resemble that of a small loop

While the short dipole has a capacitive impedance (imaginary part of impedance is negative) the impedance of a small loop is inductive (positive imaginary part) The radiation resistance (and ohmic loss resistance) can be increased by adding more turns to the loop If there are N turns of a small loop antenna each with a surface area S (we dont require the loop to be circular at this point) the radiation resistance for small loops can be approximated (in Ohms) by

For a small loop the reactive component of the impedance can be determined by finding the inductance of the loop which depends on its shape (then X=2pifL) For a circular loop with radius a and wire radius p the reactive component of the impedance is given by

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 15: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Small loops often have a low radiation resistance and a highly inductive component to their reactance Hence they are most often used as receive antennas Exaples of their use include in pagers and as field strength probes

used in wireless measurements

Loop antenna

A loop antenna has a continuous conducting path leading from

one conductor of a two-wire transmission line to the other conductor All planar loops are

directional antennas with a sharp null and have a radiation pattern similar to the dipole

antenna However the large and small loops have different orientations with respect to

their radiation pattern

Small loops

A loop is considered a small loop if it is less than 14 of a

wavelength in circumference Most directional receiving loops are about 110 of a

wavelength The small loop is also called the magnetic loop because it is more sensitivie

to the magnetic component of the electromagnetic wave As such it is less sensitive to

near field electric noise when properly shielded The received voltage of a small loop can

be greatly increased by bringing the loop into resonance with a tuning capacitor

Since the small loop is small with respect to a wavelength the

current around the antenna is nearly completely in phase Therefore waves approaching

in the plane of the loop will cancel and waves in the axis perpendicular to the plane of

the loop will be strongest This is the opposite mechanism as the large loop

Large loops

The (large) loop antenna is similar to a dipole except that the

ends of the dipole are connected to form a circle triangle () or square Typically a loop is

a multiple of a half or full wavelength in circumference A circular loop gets higher gain

(about 10) than the other forms of large loop antenna as gain of this antenna is directly

proportional to the area enclosed by the loop but circles can be hard to support in a

flexible wire making squares and triangles much more popular Large loop antennas are

more immune to localized noise partly due to lack of a need for a groundplane The large

loop has its strongest signal in the plane of the loop and nulls in the axis perpendicular to

the plane of the loop This is the opposite orientation to the small loop

AM loops

AM loops are loops tuned for the AM broadcasting band

Because of the extremely long wavelength an AM loop may have multiple turns of wire

and still be less than 110 of a wavelength Typically these loops are tuned with a

capacitor and may also be wound around a ferrite rod to increase aperture

Direction finding with loops

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 16: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Loops are somewhat directional along the axis of highest gain

but have a sharp null in the axis perpendicular to their highest gain Therefore when

using a loop for direction finding the plane of the antenna is rotated until the signal

disappears As planar loops have a 180 degree symmetry other methods must be used to

determine if the signal is in front or behind the loop

Frequently a dipole and a loop are used together to obtain a

combined cardioid radiation pattern with a sharp null on only one side

Uniform linear array

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 17: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

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Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

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The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 18: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

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The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 19: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 20: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 21: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Slot antennas are used typically at frequencies between 300 MHz and

24 GHz These antennas are popular because they can be cut out of whatever surface they are to be mounted on and have radiation patterns that are roughly omnidirectional (similar to a linear wire antenna as well see) The polarization

is linear The slot size shape and what is behind it (the cavity) offer design variables that can be used to tune performance

Consider an infinite conducting sheet with a rectangular slot cut out of dimensions a and b as shown in Figure 1 If we can excite some reasonable fields in the slot (often called the aperture) we have an antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 22: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 1 Rectangular Slot antenna with dimensions a and b

To gain an intuition about slot antennas first well learn Babinets principle (put into antenna terms by H G Booker in 1946) This principle relates the radiated fields and impedance of an aperture or slot antenna to that of the field of its dual antenna The dual of a slot antenna would be if the conductive material and air were interchanged - that is the slot antenna became a metal slab in space An example of dual antennas is shown in Figure 2

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 23: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 2 Dual antennas

Note that a voltage source is applied across the short end of the slot This induces an E-field distribution within the slot and currents that travel around the slot perimeter both contributed to radiation The dual antenna is similar to a dipole antenna The voltage source is applied at the center of the dipole so that the voltage source is rotated

Babinets principle relates these two antennas The first result states that the

impedance of the slot ( ) is related to the impedance of its dual antenna ( )

by the relation

In the above is the intrinsic impedance of free space The second major result of BabinetsBookers principle is that the fields of the dual antenna are

almost the same as the slot antenna (the fields components are interchanged and called duals) That is the fields of the slot antenna (given with a subscript S) are related to the fields of its complement (given with a subscript C) by

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

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Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

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The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 24: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Hence if we know the fields from one antenna we know the fields of the other antenna Hence since it is easy to visualize the fields from a dipole antenna the

fields and impedance from a slot antenna can become intuitive if Babinets principle is understood

Note that the polarization of the two antennas are reversed That is since the dipole antenna on the right in Figure 2 is vertically polarized the slot antenna on the left will be horizontally polarized

Duality Example

As an example consider a dipole similar to the one shown on the right in Figure 2 Suppose the length of the dipole is 144 centimeters and the width is 2

centimeters and that the impedance at 1 GHz is 65+j15 Ohms The fields from the dipole antenna are given by

What are the fields from a slot at 1 GHz with the same dimensions as the dipole

Using Babinets principle the impedance can be easily found

The impedance of the slot for this case is much larger and while the dipoles impedance is inductive (positive imaginary part) the slots impedance is

capacitive (negative imaginary part) The E-fields for the slot can be easily found

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 25: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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We see that the E-fields only contain a phi (azimuth) component the antenna is therefore horizontally polarized

Horn antennas are very popular at UHF (300 MHz-3 GHz) and higher frequencies (Ive heard of horns operating as high as 140 GHz) They often have a directional radiation pattern with a high gain which can range up to 25

dB in some cases with 10-20 dB being typical Horns have a wide impedance bandwidth implying that the input impedance is slowly varying over a wide frequency range (which also implies low values for S11 or VSWR) The bandwidth for practical horn antennas can be on the order of 201 (for instance operating from 1 GHz-20 GHz) with a 101 bandwidth not being uncommon

The gain often increases (and the beamwidth decreases) as the frequency of operation is increased Horns have very little loss so the directivity of a horn is roughly equal to its gain

Horn antennas are somewhat intuitive and not relatively simple to manufacture In addition acoustic horns also used in transmitting sound waves (for example

with a megaphone) Horn antennas are also often used to feed a dish antenna or as a standard gain antenna in measurements

Popular versions of the horn antenna include the E-plane horn shown in Figure 1 This horn is flared in the E-plane giving the name The horizontal dimension is constant at w

Figure 1 E-plane horn

Another example of a horn is the H-plane horn shown in Figure 2 This horn is flared in the H-plane with a constant height for the waveguide and horn of h

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 26: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 2 H-Plane horn

The most popular horn is flared in both planes as shown in Figure 3 This is a

pyramidal horn and has width B and height A at the end of the horn

Figure 3 Pyramidal horn

Horns are typically fed by a section of a waveguide as shown in Figure 4 The waveguide itself is often fed with a short dipole which is shown in red in Figure 4 A waveguide is simply a hollow metal cavity Waveguides are used to guide electromagnetic energy from one place to another The waveguide in Figure 4 is a rectangular waveguide of width b and height a with bgta The E-field distribution for the dominant mode is shown in the lower part of Figure 1

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 27: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 4 Waveguide used as a feed to horn antennas

Reflector Antenna To increase the directivity of an antenna a fairly intuitive solution is to use a reflector For example if we start with a wire antenna (lets say a half-wave dipole antenna) we could place a conductive sheet behind it to direct radiation in the forward direction To further increase the directivity a corner reflector

may be used as shown in Figure 1 The angle between the plates will be 90 degrees

Figure 1 Geometry of Corner Reflector

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 28: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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The radiation pattern of this antenna can be understood by using image theory and then calculating the result via array theory For ease of analysis well assume the reflecting plates are infinite in extent Figure 2 below shows the equivalent source distribution valid for the region in front of the plates

Figure 2 Equivalent sources in free space

The dotted circles indicate antennas that are in-phase with the actual antenna the xd out antennas are 180 degrees out of phase to the actual antenna

Assume that the original antenna has an omnidirectional pattern given by

Then the radiation pattern (R) of the equivalent set of radiators of Figure 2 can be written as

The above directly follows from Figure 2 and array theory (k is the wave number The resulting pattern will have the same polarization as the original vertically polarized antenna The directivity will be increased by 9-12 dB The above equation gives the radiated fields in the region in front of the plates Since we assumed the plates were infinite the fields behind the plates are zero

The directivity will be the highest when d is a half-wavelength Assuming the

radiating element of Figure 1 is a short dipole with a pattern given by

the fields for this case are shown in Figure 3

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 29: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 3 Polar and azimuth patterns of normalized radiation pattern

The radiation pattern impedance and gain of the antenna will be influenced by the distance d of Figure 1 The input impedance is increased by the reflector when the spacing is one half wavelength it can be reduced by moving the

antenna closer to the reflector The length L of the reflectors in Figure 1 are typically 2d However if tracing a ray travelling along the y-axis from the

antenna this will be reflected if the length is at least The height of the plates should be taller than the radiating element however since linear antennas do not radiate well along the z-axis this parameter is not critically important

The Parabolic Reflector

Antenna (Satellite Dish)

The most well-known reflector antenna is the parabolic reflector antenna commonly known as a satellite dish antenna Examples of this dish antenna are shown in the following Figures

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 30: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 1 The big dish of Stanford University

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 31: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 2 A random direcTV dish on a roof

Parabolic reflectors typically have a very high gain (30-40 dB is common) and low cross polarization They also have a reasonable bandwidth with the fractional bandwidth being at least 5 on commercially available models and can be very wideband in the case of huge dishes (like the Stanford big dish above which can operate from 150 MHz to 15 GHz)

The smaller dish antennas typically operate somewhere between 2 and 28 GHz The

large dishes can operate in the VHF region (30-300 MHz) but typically need to be extremely large at this operating band

The basic structure of a parabolic dish antenna is shown in Figure 3 It consists of a feed antenna pointed towards a parabolic reflector The feed antenna is often a horn antenna with a circular aperture

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 32: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 3 Components of a dish antenna

Unlike resonant antennas like the dipole antenna which are typically approximately a half-wavelength long at the frequency of operation the reflecting dish must be much larger than a wavelength in size The dish is at least several wavelengths in diameter but the diameter can be on the order of 100 wavelengths for very high gain dishes (gt50 dB gain) The distance between the feed antenna and the reflector is typically several

wavelenghts as well This is in contrast to the corner reflector where the antenna is roughly a half-wavelength from the reflector

In the next section well look at the parabolic dish geometry in detail and why a parabola is a desired shape

To start let the equation of a parabola with focal length F can be written in the (xz) plane as

This is plotted in Figure 1

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 33: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 1 Illustration of parabola with defining parameters

The parabola is completely described by two parameters the diameter D and the focal length F We also define two auxilliary parameters the vertical height of the reflector (H) and the max angle between the focal point and the edge of

the dish ( ) These parameters are related to each other by the following

equations

To analyze the reflector we will use approximations from geometric optics Since the reflector is large relative to a wavelength this assumption is reasonable though not precisely accurate We will analyze the structure via straight line rays from the focal point with each ray acting as a plane wave

Consider two transmitted rays from the focal point arriving from two distinct angles as shown in Figure 2 The reflector is assumed to be perfectly conducting so that the rays are completely reflected

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 34: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 2 Two rays leaving the focal point and reflected from the parabolic reflector

There are two observations that can be made from Figure 2 The first is that both rays end up travelling in the downward direction (which can be determined because the incident and reflected angles relative to the normal of the surface must be equal) The rays are said to be collimated The second important observation is that the path lengths ADE and ABC are equal This can be proved with a little bit of geometry which I wont reproduce here These facts can be proved for any set of angles chosen Hence it follows that

All rays emanating from the focal point (the source or feed antenna) will be

reflected towards the same direction

The distance each ray travels from the focal point to the reflector and then to

the focal plane is constant

As a result of these observations it follows the distribution of the field on the focal plane will be in phase and travelling in the same direction This gives rise

to the parabolic dish antennas highly directional radiation pattern This is why the shape of the dish is parabolic

Finally by revolving the parabola about the z-axis a paraboloid is obtained as shown below

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 35: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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For design the value of the diameter D should be increased to increase the gain of the antenna The focal length F is then the only free parameter typical values are commonly given as the ratio FD which usually range between 03

and 10 Factors affecting the choice of this ratio will be given in the following sections

In the next section well look at gain calculations for a parabolic reflector antenna

The fields across the aperture of the parabolic reflector is responsible for this antennas radiation The maximum possible gain of the antenna can be expressed in terms of the physical area of the aperture

The actual gain is in terms of the effective aperture which is related to the physical area by the efficiency term ( ) This efficiency term will often be on the order of 06-07 for a well designed dish antenna

Understanding this efficiency will also aid in understanding the trade-offs involved in the design of a parabolic reflector The efficiency can be written as the product of a series of terms

Well walk through each of these terms

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 36: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Radiation Efficiency

The radiation efficiency is the usual efficiency that deals with ohmic losses

as discussed on the efficiency page Since horn antennas are often used as feeds and these have very little loss and because the parabolic reflector is

typically metallic with a very high conductivity this efficiency is typically close to 1 and can be neglected

Aperture Taper Efficiency

The aperture radiation efficiency is a measure of how uniform the E-field is

across the antennas aperture In general an antenna will have the maximum gain if the E-field is uniform in amplitude and phase across the aperture (the far-field is roughly the Fourier Transform of the aperture fields) However the aperture fields will tend to diminish away from the main axis of the reflector

which leads to lower gain and this loss is captured within this parameter

This efficiency can be improved by increasing the FD ratio which also lowers the cross-polarization of the radiated fields However as with all things in engineering there is a tradeoff increasing the FD ratio reduces the spillover efficiency discussed next

Spillover Efficiency

The spillover efficiency is simple to understand This measures the amount

of radiation from the feed antenna that is reflected by the reflector Due to the finite size of the reflector some of the radiation from the feed antenna will

travel away from the main axis at an angle greater than thus not being

reflected This efficiency can be improved by moving the feed closer to the reflector or by increasing the size of the reflector

Other Efficiencies

There are many other efficiencies that Ive lumped into the parameter This

is a major of all other real-world effects that degrades the antennas gain and consists of effects such as

Surface Error - small deviations in the shape of the reflector degrades

performance especially for high frequencies that have a small wavelength and become scattered by small surface anomalies

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 37: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Cross Polarization - The loss of gain due to cross-polarized (non-desirable)

radiation

Aperture Blockage - The feed antenna (and the physical structure that holds

it up) blocks some of the radiation that would be transmitted by the reflector

Non-Ideal Feed Phase Center - The parabolic dish has desirable properties

relative to a single focal point Since the feed antenna will not be a point source there will be some loss due to a non-perfect phase center for a horn antenna

Calculating Efficiency

The efficiency is a function of where the feed antenna is placed (in terms of F and D) and the feed antennas radiation pattern Instead of introducing complex formulas for some of these terms well make use of some results by S Silver back in 1949 He calculated the aperture efficiency for a class of radiation patterns given as

TYpically the feed antenna (horn) will not have a pattern exactly like the above but can be approximated well using the function above for some value

of n Using the above pattern the aperture efficiency of a parabolic reflector

can be calculated This is displayed in Figure 1 for varying values of and the

FD ratio

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 38: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 1 Aperture Efficiency of a Parabolic Reflector as a function of FD or

the angle for varying feed antenna radiation patterns

Figure 1 gives a good idea on design of optimal parabolic reflectors First D is made as large as possible so that the physical aperture is maximized Then the FD ratio that maximizes the aperture efficiency can be found from the above

graph Note that the equation that relates the ratio of FD to the angle can be

found here

In the next section well look at the radiation pattern of a parabolic antenna

In this section the 3d radiation patterns are presented to give an idea of what they look like This example will be for a parabolic dish reflector with the diameter of the dish D equal to 11 wavelengths The FD ratio will be 05 A circular horn antenna will be used as the feed

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 39: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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The maximum gain from the physical aperture is the

actual gain is 293 dB = 851 so we can conclude that the overall efficiency is 77 The 3D patterns are shown in the following figures

As can be seen the pattern is highly directional The HPBW is approximately 5 degrees and the front-to-back ratio is approximately 33 dB

LENS ANTENNAmdashAnother antenna that can change spherical waves into flat plane waves is the lens antenna This antenna uses a microwave lens which is similar to an optical lens to straighten the

spherical wavefronts Since this type of antenna uses a lens to straighten the wavefronts its design is

based on the laws of refraction rather than reflection Two types of lenses have been developed

to provide a plane-wavefront narrow beam for tracking radars while avoiding the problems

associated with the feedhorn shadow These are the conducting (acceleration) type and

the dielectric (delay) type The lens of an antenna is substantially transparent to microwave energy that passes through it It will however cause the waves of energy to be either converged or

diverged as they exit the lens Consider the action of the two types of lenses The conducting type of lens

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 40: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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is illustrated in figure 1-10 view A This type of lens consists of flat metal strips placed parallel to the

electric field of the wave and spaced slightly in excess of one-half of a wavelength To the wave

these strips look like parallel waveguides The velocity of phase propagation of a wave is greater in a

waveguide than in air Thus since the lens is concave the outer portions of the transmitted

spherical waves are accelerated for a longer interval of time than the inner portion

Helical Antenna

Antennas List Antenna Theory Home

Helix antennas have a very distinctive shape as can be seen in the following picture

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 41: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Photo courtesy of Dr Lee Boyce

The most popular helical antenna (often called a helix) is a travelling wave antenna in the shape of a corkscrew that produces radiation along the axis of the helix These helixes are referred to as axial-mode helical antennas The benefits of this antenna is it has a wide bandwidth is easily constructed has a real input impedance and can produce circularly polarized fields The basic geometry is shown in Figure 1

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 42: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 1 Geometry of Helical Antenna

The parameters are defined below

D - Diameter of a turn on the helix

C - Circumference of a turn on the helix (C=piD)

S - Vertical separation between turns

- pitch angle which controls how far the antenna grows in the z-direction per

turn and is given by

N - Number of turns on the helix

H - Total height of helix H=NS

The antenna in Figure 1 is a left handed helix because if you curl your fingers on your left hand around the helix your thumb would point up (also the waves emitted from the antenna are Left Hand Circularly Polarized) If the helix was

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 43: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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wound the other way it would be a right handed helical antenna

The pattern will be maximum in the +z direction (along the helical axis in Figure 1) The design of helical antennas is primarily based on empirical results and the

fundamental equations will be presented here

Helices of at least 3 turns will have close to circular polarization in the +z direction when the circumference C is close to a wavelength

Once the circumference C is chosen the inequalites above roughly determine the operating bandwidth of the helix For instance if C=1968 inches (05 meters) then the highest frequency of operation will be given by the smallest wavelength

that fits into the above equation or =075C=0375 meters which corresponds to a frequency of 800 MHz The lowest frequency of operation will be given by

the largest wavelength that fits into the above equation or =1333C=0667 meters which corresponds to a frequency of 450 MHz Hence the fractional BW is 56 which is true of axial helices in general

The helix is a travelling wave antenna which means the current travels along the antenna and the phase varies continuously In addition the input impedance is primarly real and can be approximated in Ohms by

The helix functions well for pitch angles ( ) between 12 and 14 degrees

Typically the pitch angle is taken as 13 degrees

The normalized radiation pattern for the E-field components are given by

For circular polarization the orthogonal components of the E-field must be 90 degrees out of phase This occurs in directions near the axis (z-axis in Figure 1) of

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 44: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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the helix The axial ratio for helix antennas decreases as the number of loops N is added and can be approximated by

The gain of the helix can be approximated by

In the above c is the speed of light Note that for a given helix geometry (specified in terms of C S N) the gain increases with frequency For an N=10 turn helix that has a 05 meter circumference as above and an pitch angle of 13 degrees (giving S=013 meters) the gain is 83 (92 dB)

For the same example helix the pattern is shown in Figure 2

Figure 2 Normalized radiation pattern for helical antenna (dB)

The Half-Power Beamwidth for helical antennas can be approximated (in degrees) by

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 45: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Yagi-Uda Antenna

Antennas List Antenna Theory com

The Yagi-Uda antenna or Yagi is one of the most brilliant antenna designs It is

simple to construct and has a high gain typically greater than 10 dB These antennas typically operate in the HF to UHF bands (about 3 MHz to 3 GHz) although their bandwidth is typically small on the order of a few percent of the center frequency You are probably familiar with this antenna as they sit on top of roofs everywhere An example of a Yagi-Uda antenna is shown below

The Yagi antenna was invented in Japan with results first published in 1926 The work was originally done by Shintaro Uda but published in Japanese The work

was presented for the first time in English by Yagi (who was either Udas professor or colleague my sources are conflicting) who went to America and gave the first English talks on the antenna which led to its widespread use Hence even though the antenna is often called a Yagi antenna Uda probably invented it A picture of Professor Yagi with a Yagi-Uda antenna is shown below

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 46: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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In the next section well explain the principles of the Yagi-Uda antenna

The basic geometry of a Yagi-Uda antenna is shown in Figure 1

Figure 1 Geometry of Yagi-Uda antennaltFONTlt CENTERgt

The antenna consists of a single feed or driven element typically a dipole or a

folded dipole antenna This is the only member of the above structure that is actually excited (a source voltage or current applied) The rest of the elements

are parasitic - they reflect or help to transmit the energy in a particular direction The length of the feed element is given in Figure 1 as F The feed

antenna is almost always the second from the end as shown in Figure 1 This

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 47: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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feed antenna is often altered in size to make it resonant in the presence of the parasitic elements (typically 045-048 wavelengths long for a dipole antenna)

The element to the left of the feed element in Figure 1 is the reflector The length of this element is given as R and the distance between the feed and the reflector is SR The reflector element is typically slightly longer than the feed

element There is typically only one reflector adding more reflectors improves

performance very slightly This element is important in determining the front-to-back ratio of the antenna

Having the reflector slightly longer than resonant serves two purposes The first is that the larger the element is the better of a physical reflector it becomes Secondly if the reflector is longer than its resonant length the impedance of

the reflector will be inductive Hence the current on the reflector lags the voltage induced on the reflector The director elements (those to the right of the feed in Figure 1) will be shorter than resonant making them capacitive so that

the current leads the voltage This will cause a phase distribution to occur

across the elements simulating the phase progression of a plane wave across the array of elements This leads to the array being designated as a travelling wave antenna By choosing the lengths in this manner the Yagi-Uda antenna

becomes an end-fire array - the radiation is along the +y-axis as shown in Figure 1

The rest of the elements (those to the right of the feed antenna as shown in Figure 1) are known as director elements There can be any number of directors N which is typically anywhere from N=1 to N=20 directors Each element is of length Di and separated from the adjacent director by a length SDi As alluded

to in the previous paragraph the lengths of the directors are typically less than the resonant length which encourages wave propagation in the direction of the

directors

The above description is the basic idea of what is going on Yagi antenna design is done most often via measurements and sometimes computer

simulations For instance lets look at a two-element Yagi antenna (1 reflector 1 feed element 0 directors) The feed element is a half-wavelength dipole

shortened to be resonant (gain = 215 dB) The gain as a function of the separation is shown in Figure 2

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 48: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 2 Gain versus separation for 2-element Yagi antenna

The above graph shows that the gain is increases by about 25 dB if the separation SD is between 015 and 03 wavelengths Similarly the gain can be

plotted as a function of director spacings or as a function of the number of directors used Typically the first director will add approximately 3 dB of

overall gain (if designed well) the second will add about 2 dB the third about

15 dB Adding an additional director always increases the gain however the gain in directivity decreases as the number of elements gets larger For

instance if there are 8 directors and another director is added the increases in gain will be less than 05 dB

In the next section Ill go further into the design of Yagi-Uda antennas

The design of a Yagi-Uda antenna is actually quite simple Because Yagi antennas have been extensively analyzed and experimentally tested the process basically follows this outline

Look up a table of design parameters for Yagi antennas

Build it (or model it numerically) and tweak it till the performance is acceptable

As an example consider the table published in Yagi Antenna Design by P Viezbicke from the National Bureau of Standards 1968 given in Table I Note that the boom is

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 49: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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the long element that the directors reflectors and feed elements are physically attached to and dictates the lenght of the antenna

Table I Optimal Lengths for Yagi-Uda Elements for Distinct Boom Lengths

d=00085

SR=02

Boom Length of Yagi-Uda Array (in )

04 08 12 22 32 42

R 0482 0482 0482 0482 0482 0475

D1 0442 0428 0428 0432 0428 0424

D2 0424 0420 0415 0420 0424

D3 0428 0420 0407 0407 0420

D4 0428 0398 0398 0407

D5 0390 0394 0403

D6 0390 0390 0398

D7 0390 0386 0394

D8 0390 0386 0390

D9 0398 0386 0390

D10 0407 0386 0390

D11 0386 0390

D12 0386 0390

D13 0386 0390

D14 0386

D15 0386

Spacing

between

directors

(SD )

020 020 025 020 020 0308

Gain (dB) 925 1135 1235 1440 1555 1635

Theres no real rocket science going on in the above table I believe the authors of the above document did experimental measurements until they found an optimized set of spacings and published it The spacing between the directors is

uniform and given in the second-to-last row of the table The diameter of the

elements is given by d=00085 The above table gives a good starting point to estimate the required length of the antenna (the boom length) and a set of lengths

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 50: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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and spacings that achieves the specified gain In general all the spacings lengths diamters (including the boom diameter) are design variables and can be continuously optimized to alter performance There are thousands of tables that

further give results such as how the diamter of the boom affects the results and the optimal diamters of the elements

As an example of Yagi-antenna radiation patterns a 6-element Yagi antenna (with axis along the +x-axis) is simulated in FEKO (1 reflector 1 driven half-wavelength dipole 4 directors) The resulting antenna has a 121 dBi gain and the plots are given in Figures 1-3

Figure 1 E-plane gain of Yagi antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 51: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 2 H-Plane gain of Yagi antenna

Figure 3 3-D Radiation Pattern of Yagi antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 52: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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The above plots are just an example to give an idea of what the radiation pattern of the Yagi-Uda antenna resembles The gain can be increased (and the pattern made more directional) by adding more directors or optimizing spacing (or rarely

adding another refelctor) The front-to-back ratio is approximately 19 dB for this antenna and this can also be optimized if desired

A LONG-WIRE ANTENNA is an antenna that is a wavelength or more long at the operating frequency These antennas have directive patterns that are sharp in both the horizontal and vertical planes

BEVERAGE ANTENNAS consist of a single wire that is two or more wavelengths long

A V ANTENNA is a bi-directional antenna consisting of two horizontal long wires arranged to form a V

The RHOMBIC ANTENNA uses four conductors joined to form a rhombus shape This antenna has a

wide frequency range is easy to construct and maintain and is noncritical as far as operation and

adjustment are concerned

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 53: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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The TURNSTILE ANTENNA consists of two horizontal half-wire antennas mounted at right angles to

each other

LOG-PERIODIC ANTENNA

LOG-PERIODIC ANTENNA

In telecommunication a log-periodic antenna (LP

also known as a log-periodic array) is a broadband multielement

unidirectional narrow-beam antenna that has impedance and

radiation characteristics that are regularly repetitive as a

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 54: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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logarithmic function of the excitation frequency The individual

components are often dipoles as in a log-periodic dipole array

(LPDA)

Log periodic antennas are arrays that are designed to be

self-similar and thus are fractal antenna arrays It is normal to

drive alternating elements with a circa 180o (π radian) phase shift

from the last element This is normally done by wiring the

elements alternatingly to the two wires in a balanced transmission

lineThe length and spacing of the elements of a log- increase

logarithmically from one end to the otherThe result of this

structural condition is that if a plot is made of the input impedance

as a function of log of frequency then the variation will be periodic

ie the impedance will go through the cycles of variation in such a

way that each cycle is exactly like its preceding one and hence the

name

Log-Periodic Antenna 250 ndash 2400 MHz

Mutual impedanceamp self-impedance

The method helps us to compute voltages currents and

impedances in antenna systems The method understands the

voltage which is observed at the input port of every single

antenna element being induced by the radiation of all the

antenna elements (including the own element) The voltage

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 55: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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can be composed from contributions of single elements Each

contribution is proportional to the current of the respective

element Eg voltage U 1 at the input of the first antenna

element equals to the summation

where I 1 I 2 I 3 are currents at the input ports of single

elements Z 11 Z 12 Z 13 are impedances Z 11 is self-

impedance Z 1n are mutual impedances between the first

element and the other elements in the antenna system These

impedances depend on the mutual position and mutual

distance of antenna elements

Biconical antenna

A biconical antenna consists of an arrangement of two conical conductors which is

driven by potential charge or an alternating magnetic field (and the associated

alternating electric current) at the vertex The conductors have a common axis and vertex

The two cones face in opposite directions Biconical antennas are broadband dipole

antennas typically exhibiting a bandwidth of 3 octaves or more

Omnidirectional Biconical Antenna

Microstrip or patch antennas are becoming increasingly useful because they can be printed directly onto a circuit board They are becoming very widespread within the mobile phone market They are low cost have a low profile and are easily fabricated

Consider the microstrip antenna shown in Figure 1 fed by a microstrip transmission line The patch microstrip and ground plane are made of high conductivity metal The patch is of length L width W and sitting on top of a

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 56: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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substrate (some dielectric circuit board) of thickness h with permittivity

The thickness of the ground plane or of the microstrip is not critically important Typically the height h is much smaller than the wavelength of operation

(a) Top View

(b) Side View

Figure 1 Geometry of Microstrip (Patch) Antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 57: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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The frequency of operation of the patch antenna of Figure 1 is determined by the length L The center frequency will be approximately given by

The above equation says that the patch antenna should have a length equal to

one half of a wavelength within the dielectric (substrate) medium

The width W of the antenna controls the input impedance For a square patch fed in the manner above the input impedance will be on the order of 300 Ohms By increasing the width the impedance can be reduced However to decrease the input impedance to 50 Ohms often requires a very wide patch The width further controls the radiation pattern The normalized pattern is approximately given by

In the above k is the free-space wavenumber given by The magnitude of the fields given by

The fields are plotted in Figure 2 for W=L=05

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 58: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 2 Normalized Radiation Pattern for Microstrip (Patch) Antenna

The directivity of patch antennas is approximately 5-7 dB The fields are linearly polarized Next well consider more aspects involved in Patch (Microstrip) antennas

Spiral antenna

In microwave systems a spiral antenna is a type of RF antenna It is shaped as a two-

arm spiral or more arms may be used[1]

Spiral antennas operate over a wide frequency

range and have circular polarization Spiral antennas were first described in 1956

Applications

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

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A spiral antenna transmits EM waves having a circular polarization It will receive

linearly polarized EM waves in any orientation but will attenuate signals received with

the opposite circular polarization A spiral antenna will reject circularly polarized waves

of one type while receiving perfectly well waves having the other polarization

One application of spiral antennas is wideband communications Another application of

spiral antennas is monitoring of the frequency spectrum One antenna can receive over a

wide bandwidth for example a ratio 51 between the maximum and minimum frequency

Usually a pair of spiral antennas are used in this application having identical parameters

except the polarization which is opposite (one is right-hand the other left-hand oriented)

Spiral antennas are useful for microwave direction-finding[2]

Elements

The antenna includes two conductive spirals or arms extending from the center outwards

The antenna may be a flat disc with conductors resembling a pair of loosely-nested clock

springs or the spirals may extend in a three-dimensional shape like a screw thread The

direction of rotation of the spiral defines the direction of antenna polarization Additional

spirals may be included as well to form a multi-spiral structure Usually the spiral is

cavity-backed that is there is a cavity of air or non-conductive material or vacuum

surrounded by conductive walls the cavity changes the antenna pattern to a

unidirectional shape The output of the antenna

Measuring Radiation Pattern

and an Antennas Gain

Antennas (Home) Antenna Measurements

Home

Previous Measurements

Ranges

Now that we have our measurement equipment and an antenna range we can perform some measurements We will use the source antenna to illuminate the antenna under test with a plane wave from a specific direction The polarization and gain (for the fields radiated toward the test antenna) of the source antenna should be known

Due to reciprocity the radiation pattern from the test antenna is the same for both the receive and transmit modes Consequently we can measure the radiation pattern in the receive mode for the test antenna

The test antenna is rotated using the test antennas positioning system The

received power is recorded at each position In this manner the magnitude of the radiation pattern of the test antenna can be determined We will discuss phase measurements and polarization measurements later

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

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The coordinate system of choice for the radiation pattern is spherical coordinates

Measurement Example

An example should make the process reasonably clear Suppose the radiation pattern of a microstrip antenna is to be obtained As is usual lets let the direction the patch faces (normal to the surface of the patch) be towards the z-axis Suppose the source antenna illuminates the test antenna from +y-direction as

shown in Figure 1

Figure 1 A patch antenna oriented towards the z-axis with a Source illumination from the +y-direction

In Figure 1 the received power for this case represents the power from the angle

We record this power change the position and record again Recall that we only rotate the test antenna hence it is at the same distance from the source antenna The source power again comes from the same direction Suppose we want to measure the radiation pattern normal to the patchs surface (straight above the patch) Then the measurement would look as shown in Figure 2

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 61: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Figure 2 A patch antenna rotated to measure the radiation power at normal incidence

In Figure 2 the positioning system rotating the antenna such that it faces the source of illumination In this case the received power comes from direction

So by rotating the antenna we can obtain cuts of the radiation pattern - for instance the E-plane cut or the H-plane cut A great circle cut is

when =0 and is allowed to vary from 0 to 360 degrees Another common

radiation pattern cut (a cut is a 2d slice of a 3d radiation pattern) is when is

fixed and varies from 0 to 180 degrees By measuring the radiation pattern along certain slices or cuts the 3d radiation pattern can be determined

It must be stressed that the resulting radiation pattern is correct for a given polarization of the source antenna For instance if the source is horizontally polarized (see polarization of plane waves) and the test antenna is vertically polarized the resulting radiation pattern will be zero everywhere Hence the

radiation patterns are sometimes classified as H-pol (horizontal polarization) or V-pol (vertical polarization) See also cross-polarization

In addition the radiation pattern is a function of frequency As a result the measured radiation pattern is only valid at the frequency the source antenna is transmitting at To obtain broadband measurements the frequency transmitted must be varied to obtain this information

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 62: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

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Measuring Gain

Antennas (Home) Antenna Measurements Back Measurement of

Antenna Radiation Patterns

On the previous page on measuring radiation patterns we saw how the radiation pattern of an antenna can be measured This is actually the relative

radiation pattern in that we dont know what the peak value of the gain actually is (were just measuring the received power so in a sense can figure out how directive an antenna is and the shape of the radiation pattern) In this page we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave

We can measure the peak gain using the Friis Transmission Equation and a gain standard antenna A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear) The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 215 dB)

and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB) Consider the test setup shown in Figure 1 In this scenario a gain standard antenna is used in the place of the test antenna with the source antenna transmitting a fixed amount of power (PT) The gains of both of these antennas are accurately known

Figure 1 Record the received power from a gain standard antenna

From the Friis transmission equation we know that the power received (PR) is given by

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

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If we replace the gain standard antenna with our test antenna (as shown in Figure 2) then the only thing that changes in the above equation is GR - the gain of the receive antenna The separation between the source and test antennas is fixed and the frequency will be held constant as well

Figure 2 Record the received power with the test antenna (same source antenna)

Let the received power from the test antenna be PR2 If the gain of the test antenna is higher than the gain of the gain standard antenna then the received

power will increase Using our measurements we can easily calculate the gain of the test antenna Let Gg be the gain of the gain standard antenna PR be the power received with the gain antenna under test and PR2 be the power received with the test antenna Then the gain of the test antenna (GT) is (in linear units)

The above equation uses linear units (non-dB) If the gain is to be specified in decibels (power received still in Watts) then the equation becomes

And that is all that needs done to determine the gain for an antenna in a particular

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

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Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

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direction

Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern

without regard to what the gain is Typically this can be performed by approximated the integral as a finite sum which is pretty simple

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity

Hence once we have measured the radiation pattern and the gain the efficiency follows directly from these

In the next section well look at measuring the phase of an antennas radiation pattern

Anechoic chamber

An anechoic chamber

An anechoic chamber is a room designed to stop reflections of either sound or

electromagnetic waves They are also insulated from exterior sources of noise The

combination of both aspects means they simulate a quiet open-space of infinite

dimension which is useful when exterior influences would otherwise give false results

Anechoic chambers were originally used in the context of acoustics (sound waves) to

minimize the reflections of a room Their radiofrequency counterpart have also been in

use for a few decades for example to test antennas radars or electromagnetic

interference

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

wwwallsyllabuscom

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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wwwallsyllabuscom

Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

wwwallsyllabuscom

wwwallsyllabuscom

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

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The wavelength of audible sound in air falls in the same range as that of commonly used

radio waves and their propagation patterns bear many similarities This is why both types

look similar

Anechoic chambers range from small compartments to ones as large as aircraft hangars

The size of the chamber depends on the size of the objects to be tested and the frequency

range of the signals used although scale models can sometimes be used by testing at

shorter wavelengths

Acoustic anechoic chambers

Anechoic chambers are commonly used in acoustics to conduct experiments in nominally

free field conditions All sound energy will be traveling away from the source with

almost none reflected back Common anechoic chamber experiments include measuring

the transfer function of a loudspeaker or the directivity of noise radiation from industrial

machinery In general the interior of an anechoic chamber is very quiet with typical

noise levels in the 10ndash20 dBA range According to Guinness World Records 2005

Orfield Laboratorys NIST certified Eckel Industries-designed anechoic chamber is The

quietest place on earth measured at minus94 dBA [1][2]

The human ear can typically detect

sounds above 0 dB so a human in such a chamber would perceive the surroundings as

devoid of sound

The University of Salford has a number of Anechoic chambers of which unofficially one

is the quietest in the world with a measurement of minus124 dBA[3]

Semi-anechoic chambers

Full anechoic chambers aim to absorb energy in all directions Semi-anechoic chambers

have a solid floor that acts as a work surface for supporting heavy items such as cars

washing machines or industrial machinery rather than the mesh floor grille over

absorbent tiles found in full anechoic chambers This floor is damped and floating on

absorbent buffers to isolate it from outside vibration or electromagnetic signals A

recording studio may utilize a semi-anechoic chamber to produce high-quality music free

of outside noise and unwanted echoes

Radio-frequency anechoic chambers

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

wwwallsyllabuscom

wwwallsyllabuscom

surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

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Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

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Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

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wwwallsyllabuscom

Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

wwwallsyllabuscom

wwwallsyllabuscom

Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

wwwallsyllabuscom

wwwallsyllabuscom

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

wwwallsyllabuscom

wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

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An RF anechoic chamber

The internal appearance of the radio frequency (RF) anechoic chamber is sometimes

similar to that of an acoustic anechoic chamber however the interior surfaces of the RF

anechoic chamber are covered with radiation absorbent material (RAM) instead of

acoustically absorbent material [1] The RF anechoic chamber is typically used to house

the equipment for performing measurements of antenna radiation patterns

electromagnetic compatibility (EMC) and radar cross section measurements Testing can

be conducted on full-scale objects including aircraft or on scale models where the

wavelength of the measuring radiation is scaled in direct proportion to the target size

Coincidentally many RF anechoic chambers which use pyramidal RAM also exhibit

some of the properties of an acoustic anechoic chamber such as attenuation of sound and

shielding from outside noise

Radiation absorbent material

The RAM is designed and shaped to absorb incident RF radiation (also known as non-

ionising radiation) as effectively as possible from as many incident directions as

possible The more effective the RAM is the less will be the level of reflected RF

radiation Many measurements in electromagnetic compatibility (EMC) and antenna

radiation patterns require that spurious signals arising from the test setup including

reflections are negligible to avoid the risk of causing measurement errors and

ambiguities

One of the most effective types of RAM comprises arrays of pyramid shaped pieces each

of which is constructed from a suitably lossy material To work effectively all internal

surfaces of the anechoic chamber must be entirely covered with RAM Sections of RAM

may be temporarily removed to install equipment but they must be replaced before

performing any tests To be sufficiently lossy RAM can neither be a good electrical

conductor nor a good electrical insulator as neither type actually absorbs any power

Typically pyramidal RAM will comprise a rubberized foam material impregnated with

controlled mixtures of carbon and iron The length from base to tip of the pyramid

structure is chosen based on the lowest expected frequency and the amount of absorption

required For low frequency damping this distance is often 24 inches while high

frequency panels are as short as 3ndash4 inches Panels of RAM are installed with the tips

pointing inward to the chamber Pyramidal RAM attenuates signal by two effects

scattering and absorption Scattering can occur both coherently when reflected waves are

in-phase but directed away from the receiver or incoherently where waves are picked up

by the receiver but are out of phase and thus have lower signal strength This incoherent

scattering also occurs within the foam structure with the suspended carbon particles

promoting destructive interference Internal scattering can result in as much as 10dB of

attenuation Meanwhile the pyramid shapes are cut at angles that maximize the number

of bounces a wave makes within the structure With each bounce the wave loses energy

to the foam material and thus exits with lower signal strength [4]

An alternative type of RAM comprises flat plates of ferrite material in the form of flat

tiles fixed to all interior surfaces of the chamber This type has a smaller effective

frequency range than the pyramidal RAM and is designed to be fixed to good conductive

wwwallsyllabuscom

wwwallsyllabuscom

surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

wwwallsyllabuscom

wwwallsyllabuscom

Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

wwwallsyllabuscom

wwwallsyllabuscom

Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

wwwallsyllabuscom

wwwallsyllabuscom

Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

wwwallsyllabuscom

wwwallsyllabuscom

d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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wwwallsyllabuscom

Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

wwwallsyllabuscom

wwwallsyllabuscom

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

wwwallsyllabuscom

wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

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surfaces It is generally easier to fit and more durable than the pyramidal type RAM but is

less effective at higher frequencies Its performance might however be quite adequate if

tests are limited to lower frequencies (ferrite plates have a damping curve that makes

them most effective between 30ndash1000 MHz)[2]

There is also a hybrid type a ferrite in pyramidal shape Containing the advantages of

both technologies the frequency range can be maximized while the pyramid remains

small (10 cm)[3]

Effectiveness over frequency

Close-up of a pyramidal RAM

Waves of higher frequencies have shorter wavelengths and are higher in energy while

waves of lower frequencies have longer wavelengths and are lower in energy according

to the relationship λ = v f where lambda represents wavelength v is phase velocity of

wave and f is frequency To shield for a specific wavelength the cone must be of

appropriate size to absorb that wavelength The performance quality of an RF anechoic

chamber is determined by its lowest test frequency of operation at which measured

reflections from the internal surfaces will be the most significant compared to higher

frequencies Pyramidal RAM is at its most absorptive when the incident wave is at

normal incidence to the internal chamber surface when the pyramid height is

approximately equal to λ 4 where λ is the free space wavelength Accordingly

increasing the pyramid height of the RAM for the same (square) base size improves the

effectiveness of the chamber at low frequencies but results in increased cost and a

reduced unobstructed working volume that is available inside a chamber of defined size

Installation into a screened room

An RF anechoic chamber is usually built into a screened room designed using the

Faraday cage principle This is because most of the RF tests that require an anechoic

chamber to minimize reflections from the inner surfaces also require the properties of a

screened room to attenuate unwanted signals penetrating inwards and causing

interference to the equipment under test and prevent leakage from tests penetrating

outside

wwwallsyllabuscom

wwwallsyllabuscom

Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

wwwallsyllabuscom

wwwallsyllabuscom

Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

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wwwallsyllabuscom

Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

wwwallsyllabuscom

wwwallsyllabuscom

Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

wwwallsyllabuscom

wwwallsyllabuscom

d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

wwwallsyllabuscom

wwwallsyllabuscom

Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

wwwallsyllabuscom

wwwallsyllabuscom

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

wwwallsyllabuscom

wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 68: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

wwwallsyllabuscom

wwwallsyllabuscom

Chamber size and commissioning

The actual test setups usually require extra room than that required to simply house the

test equipment the hardware under test and associated cables For example the far field

criteria sets a minimum distance between the transmitting antenna and the receiving

antenna to be observed when measuring antenna radiation patterns Allowing for this and

the extra space that may be required for the pyramidal RAM means that a substantial

capital investment is required into even a modestly dimensioned chamber For most

companies such an investment in a large RF anechoic chamber is not justifiable unless it

is likely to be used continuously or perhaps rented out Sometimes for radar cross section

measurements it is possible to scale down the objects under test and reduce the chamber

size provided that the wavelength of the test frequency is scaled down in direct

proportion

RF anechoic chambers are normally designed to meet the electrical requirements of one

or more accredited standards For example the aircraft industry may test equipment for

aircraft according to company specifications or military specifications such as MIL-STD

461E Once built acceptance tests are performed during commissioning to verify that the

standard(s) are in fact met Provided they are a certificate will be issued to that effect

valid for a limited period

Operational use

Test and supporting equipment configurations to be used within anechoic chambers must

expose as few metallic (conductive) surfaces as possible as these risk causing unwanted

reflections Often this is achieved by using non-conductive plastic or wooden structures

for supporting the equipment under test Where metallic surfaces are unavoidable they

may be covered with pieces of RAM after setting up to minimize such reflection as far as

possible

A careful assessment of whether to place the test equipment (as opposed to the equipment

under test) on the interior or exterior of the chamber is required Normally this may be

located outside of the chamber provided it is not susceptible to interference from exterior

fields which otherwise would not be present inside the chamber This has the advantage

of reducing reflection surfaces inside but it requires extra cables and particularly good

filtering Unnecessary cables andor poor filtering can collect interference on the outside

and conduct them to the inside A good compromise may be to install human interface

equipment (such as PCs) electrically noisy and high power equipment on the outside and

sensitive equipment on the inside

One useful application of fiber optic cables is to provide the communications links to

carry signals within the chamber Fiber optic cables are non-conductive and of small

cross-section and therefore cause negligible reflections in most applications

It is normal to filter electrical power supplies for use within the anechoic chamber as

unfiltered supplies present a risk of unwanted signals being conducted into and out of the

chamber along the power cables

wwwallsyllabuscom

wwwallsyllabuscom

Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

wwwallsyllabuscom

wwwallsyllabuscom

Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

wwwallsyllabuscom

wwwallsyllabuscom

Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

wwwallsyllabuscom

wwwallsyllabuscom

d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

wwwallsyllabuscom

wwwallsyllabuscom

Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

wwwallsyllabuscom

wwwallsyllabuscom

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

wwwallsyllabuscom

wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 69: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

wwwallsyllabuscom

wwwallsyllabuscom

Health and safety risks associated with RF anechoic chamber

The following health and safety risks are associated with RF anechoic chambers

RF radiation hazard

Fire hazard

Trapped personnel

Personnel are not normally permitted inside the chamber during a measurement as this

not only can cause unwanted reflections from the human body but may also be a radiation

hazard to the personnel concerned if tests are being performed at high RF powers Such

risks are from RF or non-ionizing radiation and not from the higher energy ionizing

radiation

As RAM is highly absorptive of RF radiation incident radiation will generate heat within

the RAM If this cannot be dissipated adequately there is a risk that hot spots may

develop and the RAM temperature may rise to the point of combustion This can be a risk

if a transmitting antenna inadvertently gets too close to the RAM Even for quite modest

transmitting power levels high gain antennas can concentrate the power sufficiently to

cause high power flux near their apertures Although recently manufactured RAM is

normally treated with a fire retardant to reduce such risks they are difficult to completely

eliminate

Safety regulations normally require the installation of a gaseous fire suppression system

including smoke detectors Gaseous fire suppression avoids damage caused by the

extinguishing agent which would otherwise worsen damage caused by the fire itself A

common gaseous fire suppression agent is carbon dioxide Normally the fire detection

system is linked into the power supply to the chamber so that the fire detection system

can disconnect the power supply if smoke or a fire is detected

UNIT-5 WAVE PROPAGATION

Propagation Modes

Ground-wave propagation

Sky-wave propagation

Line-of-sight propagation

Ground-wave propagation

wwwallsyllabuscom

wwwallsyllabuscom

Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

wwwallsyllabuscom

wwwallsyllabuscom

Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

wwwallsyllabuscom

wwwallsyllabuscom

d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

wwwallsyllabuscom

wwwallsyllabuscom

Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

wwwallsyllabuscom

wwwallsyllabuscom

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

wwwallsyllabuscom

wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 70: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

wwwallsyllabuscom

wwwallsyllabuscom

Follows contour of the earth

Can Propagate considerable distances

Frequencies up to 2 MHz

Example

AM radio

Sky Wave Propagation

wwwallsyllabuscom

wwwallsyllabuscom

Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

wwwallsyllabuscom

wwwallsyllabuscom

d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

wwwallsyllabuscom

wwwallsyllabuscom

Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

wwwallsyllabuscom

wwwallsyllabuscom

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

wwwallsyllabuscom

wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 71: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

wwwallsyllabuscom

wwwallsyllabuscom

Signal reflected from ionized layer of atmosphere back down

to earth

Signal can travel a number of hops back and forth between

ionosphere and earthrsquos surface

Reflection effect caused by refraction

Examples

Amateur radio

CB radio

Line-of-Sight Propagation

Transmitting and receiving antennas must be within line of

sight

Satellite communication ndash signal above 30 MHz not

reflected by ionosphere

Ground communication ndash antennas within effective line

of site due to refraction

Refraction ndash bending of microwaves by the atmosphere

Velocity of electromagnetic wave is a function of the

density of the medium

When wave changes medium speed changes

Wave bends at the boundary between mediums

Optical line of sight

Effective or radio line of sight

wwwallsyllabuscom

wwwallsyllabuscom

d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

wwwallsyllabuscom

wwwallsyllabuscom

Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

wwwallsyllabuscom

wwwallsyllabuscom

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

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d = distance between antenna and horizon (km)

h = antenna height (m)

K = adjustment factor to account for refraction

rule of thumb K = 43

Maximum distance between two antennas for LOS

propagation

h1 = height of antenna one

h2 = height of antenna two

Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between any

two points on the surface of a sphere measured along a path on the surface of the sphere

(as opposed to going through the spheres interior) Because spherical geometry is rather

different from ordinary Euclidean geometry the equations for distance take on a different

form The distance between two points in Euclidean space is the length of a straight line

from one point to the other On the sphere however there are no straight lines In non-

Euclidean geometry straight lines are replaced with geodesics Geodesics on the sphere

are the great circles (circles on the sphere whose centers are coincident with the center of

the sphere)

Between any two different points on a sphere which are not directly opposite each other

there is a unique great circle The two points separate the great circle into two arcs The

length of the shorter arc is the great-circle distance between the points A great circle

endowed with such a distance is the Riemannian circle

Between two points which are directly opposite each other called antipodal points there

are infinitely many great circles but all great circle arcs between antipodal points have

the same length ie half the circumference of the circle or πr where r is the radius of

the sphere

Because the Earth is approximately spherical (see Earth radius) the equations for great-

circle distance are important for finding the shortest distance between points on the

surface of the Earth (as the crow flies) and so have important applications in navigation

Formulae

21573 hh

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Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

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From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

wwwallsyllabuscom

wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

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wwwallsyllabuscom

wwwallsyllabuscom

Let be the geographical latitude and longitude of two points (a base standpoint and the

destination forepoint) respectively and their differences and the (spherical) angular

differencedistance or central angle which can be constituted from the spherical law of

cosines

A useful way to remember this formula is cos(central angle)= cos(longitude difference

CTM ) where CTM could be taken to mean Only the cos terms in longitude angle

difference cosine expansion to be multiplied with cos(latitude difference)

The central angle is alternately expressed in terms of latitude and longitude differences

dlatdlong using only cosines as arccos( cos(dlat) - cos(lat1)cos(lat2)(1 - cos(dlong)

)

The distance d ie the arc length for a sphere of radius r and given in radians is then

This arccosine formula above can have large rounding errors for the common case where

the distance is small however so it is not normally used for manual calculations Instead

an equation known historically as the haversine formula was preferred which is much

more numerically stable for small distances[1]

Historically the use of this formula was simplified by the availability of tables for the

haversine function hav(θ) = sin2 (θ2)

Although this formula is accurate for most distances it too suffers from rounding errors

for the special (and somewhat unusual) case of antipodal points (on opposite ends of the

sphere) A more complicated formula that is accurate for all distances is the following

special case (a sphere which is an ellipsoid with equal major and minor axes) of the

Vincenty formula (which more generally is a method to compute distances on

ellipsoids)[2]

When programming a computer one should use the atan2() function rather than the

ordinary arctangent function (atan()) in order to simplify handling of the case where the

denominator is zero and to compute unambiguously in all quadrants

When using a spreadsheet program such as Excel the arccosine formula is suitable since

it is simpler and rounding errors disappears with high precision used

If r is the great-circle radius of the sphere then the great-circle distance is

Vector version

Another representation of similar formulas but using using n-vector instead of

latitudelongitude to describe the positions is[3]

where and are the n-vectors representing the two positions s and f Similarly to the

equations above based on latitude and longitude the expression based on arctan is the

only one that is well-conditioned for all angles If the two positions are originally given

as latitudes and longitudes a conversion to n-vectors must first be performed

wwwallsyllabuscom

wwwallsyllabuscom

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

wwwallsyllabuscom

wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 74: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

wwwallsyllabuscom

wwwallsyllabuscom

From chord length

A line through three-dimensional space between points of interest on a spherical Earth is

the chord of the great circle between the points The central angle between the two points

can be determined from the chord length The great circle distance is proportional to the

central angle

The great circle chord length may be calculated as follows for the corresponding unit

sphere by means of Cartesian subtraction[4]

Spherical cosine for sides derivation

By using Cartesian products rather than differences the origin of the spherical cosine for

sides becomes apparent

] Radius for spherical Earth

The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial

radius a of 6378137 km distance b from the center of the spheroid to each pole is

6356752 km When calculating the length of a short north-south line at the equator the

sphere that best approximates that part of the spheroid has a radius of b2 a or

6335439 km while the spheroid at the poles is best approximated by a sphere of radius

a2 b or 6399594 km a 1 difference So as long as were assuming a spherical Earth

any single formula for distance on the Earth is only guaranteed correct within 05

(though we can do better if our formula is only intended to apply to a limited area) The

average radius for a spherical approximation of the figure of the Earth is approximately

637101 km (395876 statute miles 344007 nautical miles)

LOS Wireless Transmission Impairments

Attenuation and attenuation distortion

Free space loss

Noise

Atmospheric absorption

Multipath

Refraction

Thermal noise

Atmospheric absorption ndash water vapor and oxygen contribute

to attenuation

Multipath ndash obstacles reflect signals so that multiple copies

with varying delays are received

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

wwwallsyllabuscom

wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

Page 75: EC2353 -Antenna and wave propagation Introductionanna.allsyllabus.com/ECE/sem_6/Antenna and Wave Propagation/ec2… · EC2353 -Antenna and wave propagation Introduction An antenna

wwwallsyllabuscom

wwwallsyllabuscom

Refraction ndash bending of radio waves as they propagate

through the atmosphere

Multipath Propagation

Reflection - occurs when signal encounters a surface that is

large relative to the wavelength of the signal

Diffraction - occurs at the edge of an impenetrable body that

is large compared to wavelength of radio wave

Scattering ndash occurs when incoming signal hits an object

whose size in the order of the wavelength of the signal or less

The Effects of Multipath Propagation

Multiple copies of a signal may arrive at different phases

If phases add destructively the signal level relative to

noise declines making detection more difficult

Intersymbol interference (ISI)

One or more delayed copies of a pulse may arrive at the

same time as the primary pulse for a subsequent bit

Types of Fading

Fast fading

Slow fading

Flat fading

Selective fading

wwwallsyllabuscom

wwwallsyllabuscom

Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques

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Rayleigh fading

Rician fading

Error Compensation Mechanisms

Forward error correction

Adaptive equalization

Diversity techniques


Recommended