Chapter Two Fundamental Parameters of Antenna.pdf

7/21/2019 Chapter Two Fundamental Parameters of Antenna.pdf

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Chapter Two

Fundamental Parameters

of Antennas

By:By:By:By: AmareAmareAmareAmare KassawKassawKassawKassaw

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Lecture Outlines

Radiation Pattern

Radiation Power Density and Radiation Intensity

Beamwidth and Directivity

Gain and Radiation Efficiency

Input Impedance and Equivalent Areas

Antenna Measurements (Project Assignments )

Summary

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Antenna Radiation Pattern

It is a mathematical function or a graphical representation ofthe radiation properties of the antenna as a function of spacial

coordinates (See the convenient coordinates in the figure)

Mostly determine in the far field region and is represented asa function of the directional coordinates.

Even if the radiation properties include:

Power flux density,

Radiation intensity

Field strength

Directivity,

Phase or polarization.

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the most important radiation property is the two/ three dimensional

spatial distribution of radiated energy as a function of the

observers position along a path or surface of constant radius.

Amplitude Field Pattern: A graph of the received electric

(magnetic) field at a constant radius.

The field pattern( in linear scale): represents a plot of the

magnitude of the electric(magnetic) field as a function of the

angular space.

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Figure : Coordinate system for antenna analysis.6


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Example: Figures in next slide show a two-dimensional normalized

field pattern (plotted in linear scale), power pattern( plotted in linear

scale), and power pattern (plotted on a logarithmic (dB) scale ) of a

10-element linear antenna array of isotropic sources, with a spacingof d = 0.25 between the elements.

- -

maximum value when :

The field pattern is at 0.707 value of its maximum.

The power pattern (in linear scale) is at 0.5 value of its maximum

The power pattern (in dB) is at 3 dB value of its maximum

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All three patterns yield the same angular separation between the

two half-power points(38.64)on their respective patterns, this

angle is termed as HPBW.

The three-dimensional pattern is measured and recorded in a series

of two-dimensional patterns.

u or mos prac ca app ca ons, a ew p o s o e pa ern as a

function of for some particular values of , plus a few plots as a

function of for some particular values of , give most of the

useful information.

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Lobes of the Radiation Pattern

Radiation lobe: is a portion of the radiation pattern bounded by

regions ofrelatively weak radiation intensity.

Figure below demonstrates a symmetrical three dimensional polar

pattern with a number of radiation lobes.

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The linear two dimensional (one plane of the above figure) part is

shown below where the same pattern characteristics are indicated.

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Major/Main Lobe: is the radiation lobe containing the direction of

maximum radiation. In the above figure, the major lobe is pointing in

the = 0 direction.

Minor Lobe: is any lobe except a major lobe. In the above figure, all

the lobes except the major lob are classified as minor lobes.

Side Lobe: is a radiation lobe in any direction other than the intended

lobe. Usually a side lobe is adjacent to the main lobe and occupies thehemisphere in the direction of the main beam.

Back Lobe: is a radiation lobe whose axis makes an angle of

approximately 180 with respect to the beam of an antenna. Usually it

refers to a minor lobe that occupies the hemisphere in a direction

opposite to that of the major lobe.12


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Minor lobes: usually represent radiation in undesired directions,

and they should be minimized. Side lobes are normally the largest

of the minor lobes.

The level of minor lobes is usually expressed as a ratio of the

power density of the lobe in question to that of the major lobe.

s ra o s o en erme as e s e o e ra o s e o e eve .

Side lobe levels of 20 dB or smaller are usually not desirable in

most applications.

In most radar systems, low side lobe ratios are very important to

minimize false target indications through the side lobes. 13


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Directional Patterns of an Antenna

Isotropic, Directional, and Omni directional Patterns

Isotropic radiator: is a hypothetical lossless antenna having equal

radiation in all directions. It exists only in theory.

It radiates equally in all directions, horizontally and vertically.

It's radiation pattern would be a sphere surrounding the antenna.

It has a gain of 1 dB (unity).

Even if it is not physically realizable, it is used as a reference for

expressing the directive properties of real world antennas.

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Directional antenna : is one having the property of radiating or

receiving electromagnetic waves more effectively in some directions

than in others.

This term is usually applied to an antenna whose maximum

directivity is significantly greater than that of a half-wave dipole.

e mos common ypes are e ag - a an enna, e og-

periodic antenna, and the corner reflector antenna.

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Omnidirectional Antenna: is a real world antennas that radiate

equally well in all horizontal directions.

This antenna is generally dipole antennas orientated vertically.

These include actual dipole, ground plane and various end-fed 1/2

waves antennas.

Many gain measurements are made in reference to a dipole (dBd)rather than to an isotropic, although some manufacturers

reference is isotropic because of its better gain.

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Field Regions of the Antenna

The space surrounding an antenna is usually subdivided into three

regions:

reactive near-field

radiating near-field (Fresnel) and

far-field (Fraunhofer) regions

These regions are designated to identify the field structure in each

region.

Although no abrupt changes in the field configurations as the

boundaries are crossed, there are distinct differences among them.

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Figure: Field regions of an antenna.

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Reactive near-field region: is the portion of the near-field region

immediately surrounding the antenna wherein the reactive field

predominates.

The outer boundary of this region is at a distance from the

antenna surface, where is the wavelength and D is the largest dimension

of the antenna.

In this region, the relationship between the strengths of the E and H fields

is often too complex to predict.

Either field components (E or H) may dominate at one point, and the

opposite relationship dominate at a short distance away.

This makes finding the true power density in this region very difficult.

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Radiating near field (Fresnel) region: is the region of the field

between the reactive near field region and the far field region.

Here radiated fields are predominate and the angular field

distribution is dependent upon the distance from the antenna.

The over all boundary of this region is taken as

In this region, the field pattern is a function of the radial distance

and the radial field component may be appreciable.

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Far-field (Fraunhofer) region: is the region of the field of an

antenna where the angular field distribution is essentially

independent of the distance from the antenna.

The far-field region is commonly taken to exist at distances greater

than 2D2/ from the antenna.

n s reg on, e e componen s are essen a y ransverse an

the angular distribution is independent of the radial distance where

the measurements are made.

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22

As the observation distance is varied from the reactive near field to the far field,

the amplitude pattern of an antenna changes in shape because of variations of the

fields both in magnitude and phase.

In the reactive near field region, the pattern is more spread out and nearly

uniform with slight variations.

As the observation is moved to the radiating near-field region, the pattern begins

to smooth and form lobes.

In the far-field region, the pattern is well formed usually consisting of few minor

lobes and one or more major lobes.

Note that


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Radian and Steradian Measures

The measure of a plane angle is a radian.

One radian is the plane angle with its vertex at the centre of a

circle of radius r that is subtended by an arc whose length is r.

Since the circumference of a circle of radius r is C = 2r, there are

2 rad (2r/r) in a full circle.

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The measure of a solid angle is a steradian.

One steradian is the solid angle with its vertex at the centre of a

sphere of radius r that is subtended by a spherical surface area

equal to that of a square with each side of length r.

Since the area of a sphere of radius r is A = 4r 2, there are 4 sr

(4r2/r2) in a closed sphere.

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The infinitesimal area dA on the surface of a sphere of radius r is

given by

Therefore, the element of solid angle d of a sphere can be written

as

25

Example (See handout)


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Radiation Power Density and Radiation Intensity

Radiation Power Density (W) Electromagnetic waves are used to transport information from one

point to another through a wireless medium or a guiding structure.

Hence power and energy are associated with electromagnetic

fields.

The power associated with an electromagnetic wave is described

by the instantaneous Poynting vector ( Power density )

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Hence, the total power crossing a closed surface is given by

If the fields are time-harmonic as

The power density is given by

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Now the time average poynting vector ( real power density) is

Question: If the real part of (E H)/2 represents the average

(real) power density, what does the imaginary part of the same

quantity represent?

The imaginary part represents the reactive (stored) power

density associated with the electromagnetic fields.

More predominant in the reactive near field region

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Using this power density, the average(real) power radiated by the

antenna is

For isotropic radiator, the Poynting vector will not be a functionof the spherical coordinate angles and , and it will have only a

radial component.

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Hence, the total radiated power by isotropic radiator is

Thus the power density by isotropic radiator is

Which is uniformly distributed over the surface of the sphere.

Example (See Handout)

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Radiation Intensity (U)

It is the power radiated from an antenna per unit solid angle

(Power density in a particular solid angle).

It used to determine the rate of emitted energy from unit surfacearea through unit solid angle.

- ,

With respect to the far field parameter of the antenna

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Thus, the power pattern is also the measure of the radiation

intensity.

So, the total radiated power of an antenna is given by

For an isotropic radiator, U is independent of and , hence

32

Example( See Handout)


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Beamwidth and Directivity

Beamwidth (BW) It is as the angular separation between two identical points on

opposite side of the pattern maximum.

It is generally associated with the pattern of an antenna .

HPBW: the angle between the two directions in which the

radiation intensity is one-half value of the beam at the peak.

FNBW: is the angular separation between the first nulls of

the pattern.

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The beamwidth of an antenna is a very important figure of merit:

It is used as a trade-off between it and the side lobe level.

As the BW decreases, the side lobe increases and vice versa.

It is also used to describe the resolution capabilities of the antenna

to distinguish between two adjacent radiating sources or radar

targets.

The resolution capability of an antenna to distinguish between two

sources is equal to (FNBW)/2.

Hence two sources separated by an angular distance of

of an antenna with a uniform distribution can be resolved.

34

FNBW/2 HPBW

Example(See Handout)


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Directivity(D):

It is the ratio of the radiation intensity in a given direction from

the antenna to the radiation intensity averaged over all directions.

Where the average radiation intensity is

ence , e rec v y o a non so rop c source s equa o e

ratio of its radiation intensity in a given direction over that of an

isotropic source as (Unit less quantity)

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If the direction is not specified, it shows the direction of maximum

radiation intensity (directivity) as

For an isotropic source, U= Uo =Umax, hence D=1.

For antennas with orthogonal polarization components, the partial

directivity of an antenna is given by the part of the radiation

intensity corresponding to a given polarization divided by the total

radiation intensity averaged over all directions.

Here the total directivity is the sum of the partial directivities for

any two orthogonal polarizations.

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Example : for a spherical coordinate system, the total maximum

directivity, D0 for the orthogonal and components of an

antenna is given by

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The directivity is a figure of merit describing how well the radiator

directs energy in a certain direction.

It gives an indication of the directional properties of the antenna as

compared with those of an isotropic source.

Generally the directivity is bounded by

38


Th di i l di i i i f


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Three-dimensional radiation intensity patterns for

39

T d th di i l di ti it tt f /2 di l


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Two and three dimensional directivity patterns of a /2 dipole.

The graph shows the directivity of the dipole and the isotropic

antenna

40

G l E i f Di ti it


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General Expression of Directivity

Here, we include sources with radiation patterns that may be a

function of both spherical coordinate angles(and ).

Let the radiation intensity of an antenna has the form

The maximum value of U is given by

And the total radiated power is thus

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Now the general expression of the directivity and maximum

directivity is

(1)

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The beam solid angle is the solid angle through which all the power

of the antenna would flow if its radiation intensity is constant and

equal to the maximum value of U for all angles within

But this equation is very difficult to evaluate for real time design

procedures.

n er s con on, we use e approx ma e ana ys s o eva ua e

the radiation intensity of antennas.

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Approximate Analysis of Directivity


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Approximate Analysis of Directivity

( Kraus, Tai & Pereira Equations)A. Kraus Approximation

For design purposes the previous formula is difficult to evaluate.

Hence, for antennas with one narrow major lob and very negligible

minor lobes the beam solid an le is a roximatel e ual to the

product of the HPBW in to the perpendicular planes.

44Beam solid angles for non symmetrical and symmetrical radiation patterns.

F i ll i h HPBW i


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For a rotationally symmetricpattern, the HPBW in any two

perpendicular planes are the same.

Under this condition the beam solid angle is approximated

And then the directivity

Kraus Approximation

If the beamwidths are given in degrees

45Example(see Handout)

Radiation intensity pattern of the form U = cos in the upper


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Radiation intensity pattern of the form U cos in the upper

hemisphere (for previous example)

46

B Tai & Pereiras Approximation


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B. Tai & Pereira s Approximation

Here the maximum directivity is approximated by

and are the HPBW in radians of the E and H planes

respectively.

Rearranging the above equation , we get

47

Tai & Pereira

Approximation


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Analysis :


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Analysis :

From the table, it is evident that the error due to Tai & Pereirasformula is always negative.

Hence, it predicts lower values of maximum directivity than the

exact ones and monotonically decreases as n increases (the pattern

becomes more narrow).

However, the error due to Kraus formula is negative for small

values of n and positive for large values of n.

49

For small values of n the error due to Kraus formula is negative


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For small values of n, the error due to Kraus formula is negative

and positive for large values of n. The error is zero when n = 5.5

(HPBW of 56.35).

In addition , for symmetrically rotational patterns the absolute

error due to the two approximate formulas is identical when n =

. , . .

From these observations, we conclude that Kraus formula is more

accurate forsmall values of n (broader patterns) while Tai &

Pereiras is more accurate forlarge values of n (narrower

patterns).

50

Based on absolute error and symmetrically rotational patterns Kraus


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Based on absolute error and symmetrically rotational patterns, Kraus

formula leads to smaller error for n < 11.28 (HPBW greater than 39 .77)while Tai & Pereiras leads to smaller error for n > 11.28 ( HPBW

smaller than 39 .77).

51

Figure: Comparison of exact and approximate values of

directivity for directional power patterns.

Directivity of Omnidirectional Patterns


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y

Some antennas (such as dipoles, loops, broadside arrays) exhibitomnidirectional patterns as shown below.

In this case, the Omnidirectional pattern is given by ( n here is

both positive and negative) the equation

52

Figure: Omnidirectional patterns with and without minor lobes.

The directivity of antennas with patterns represented by previous


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The directivity of antennas with patterns represented by previous

equation can be expressed by :

Using the exact analysis

Approximate analysis as

McDonald approximation: based on the array factor of

road side array(we will see in chapter 4we will see in chapter 4we will see in chapter 4we will see in chapter 4)

Pozar approximation: based on curve fitting

More accurate for omnidirectional patterns with

very small( or no) minor lobes.53


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54

Figure: Comparison of exact and approximate values of

directivity for omnidirectional power patterns.

These curves can be used for design purposes as follows:


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These curves can be used for design purposes as follows:

Specify the desired directivity and determine the value of n and

half-power beamwidth of the omnidirectional antenna pattern or

Specify the desired value of n or half-power beamwidth anddetermine the directivity of the omnidirectional antenna pattern.

55

Example(see Handout)

Gain and Antenna Efficiency


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Antenna Efficiency

An antenna has different types of efficiencies.

The total antenna efficiency is used to take into account losses at

the input terminals and within the structure of the antenna.

e osses n an enna may e ue:

Reflections because of the mismatch between the transmission

line and the antenna

I 2R losses (conduction and dielectric)

56

Reference terminals and losses of an antenna


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57

The overall efficiency of the antenna is given by


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In general

Where antenna radiation efficiency, which is used to

relate the gain and directivity.

58

Antenna Gain


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It is the ratio of the radiation intensity in a given direction to theradiation intensity that would be obtained if the power accepted by

the antenna were radiated isotropically.

It is a measure that takes into account the efficiency of the antenna

as well as its directional ca abilities.

This gain does not include losses arising from impedance

mismatches (reflection losses) and polarization mismatches (losses)

59

The relative gain with respect to a reference antenna ( dipole,


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horn, or lossless isotropic) is given by the ratio of the power gain

in a given direction to the power gain of a reference antenna in its

referenced direction.

The power input must be the same for both antennas

The total radiated power (Prad) is related to the total input power

(Pin

) by

60

While does take into account the losses of the antenna


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element itself, it does not take into account the losses when the

antenna element is connected to a transmission line

These connection losses are usually referred to as reflections

(mismatch) losses, and they are taken into account by introducing a

coefficient by:

Thus, we can introduce an absolute gain that takes into account the

reflection/mismatch losses (due to the connection of the antenna

element to the transmission line) as

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The partial gain of an antenna for a given polarization in a given


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direction is that part of the radiation intensity corresponding to a

given polarization divided by the total radiation intensity that would

be obtained if the power accepted by the antenna were radiated

isotropically.

orthogonal polarizations.

For a spherical coordinate system, the total maximum gain G0 for the

orthogonal and components of an antenna can be

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For many practical antennas an approximate formula for the gain

for the approximate value of directivity is

63

Beam Efficiency

It is used to judge the quality of transmitting and receiving


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It is used to judge the quality of transmitting and receiving

antennas

Where 1 is the half-angle of the cone within which the percentage

of the total power is to be found.

If 1 is chosen as the angle where the first null or minimum occurs,

then the beam efficiency will indicate the amount of power in the

major lobe compared to the total power.64

A very high beam efficiency (between the nulls or minimums),


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usually in the high 90s, is necessary for antennas used in radiometry,

astronomy, radar, and other applications where received signals

through the minor lobes must be minimized.

65

Input impedance and Equivalent Areas

I t I d


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Input Impedance

The impedance presented by an antenna at its terminals

The ratio of the voltage to current at a pair of terminals or

The ratio of the appropriate components of the electric to

ma netic fields at a oint

For the equivalent circuit of antennas in transmitting mode(next

slide), the input impedance at terminal a-b is given by

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67

Where part of the impedance of the antenna is


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Now for a generator impedance ofZg= Rg+ jXg, the power

radiated and dissipated by the antenna is given by

68

The remaining power is dissipated as heat on the internal


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resistance Rg of the generator is given by

Maximum power is transferred to the antenna when we have

conjugate matching (Rr+ RL = Rgand XA = Xg), for this case

69

From the above equation we get


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Of the power that is generated by the generator:

Half is dissipated as heat in the internal resistance (Rg) of the

generator and the other half is delivered to the antenna.

Of the power that is delivered to the antenna, if the antenna is

lossless and matched to the transmission line(eo = 1):

Half of the total power supplied by the generator is radiated by

the antenna during conjugate matching

And the other half is dissipated as heat in the generator. 70

Equivalent Areas

An antenna in the recei ing mode is sed to capt re (collect)


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An antenna in the receiving mode is used to capture (collect)

electromagnetic waves and to extract power from them

For each antenna, an equivalent length and a number of equivalent

areas can be defined.

characteristics of an antenna when a wave is incident upon the

antenna.

71

Equivalent circuit of an antenna in receiving mode


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72

The equivalent areas describe the power capturing characteristics


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of the antenna when a wave impinges on it.

Effective area (aperture): is the ratio of the available power at

the terminals of a receiving antenna to the power flux density of a

plane wave incident on the antenna from that direction.

e rec on s no spec e , e rec on o max mum

radiation intensity is implied.

In equation form it is written as

73

The effective aperture is the area which when multiplied by the


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incident power density gives the power delivered to the load.Using the previous circuit, we get

Under conjugate matching (Rr+ RL = RT & XA = XT)

All of the power that is intercepted, collected, or captured by an

antenna is not delivered to the load.

In fact, under conjugate matching only halfof the captured poweris delivered to the load; the other halfis scattered and dissipated

as heat.

74

Therefore to account for the scattered and dissipated power we

need to define the scattering loss and capture equivalent areas


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need to define the scattering, loss and capture equivalent areas.

The scattering area: is the equivalent area when multiplied by the

incident power density is equal to the scattered or reradiated power

The loss area: is the e uivalent area which when multi lied b

the incident power density leads to the power dissipated as heat

through RL

The capture area: is the equivalent area which when multiplied

by the incident power density leads to the total power captured,

collected, or intercepted by the antenna.75

In general:

Capture Area = Effective Area + Scattering Area + Loss Area


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Finally based on the equivalent areas , the aperture efficiency is

given by

76

Example : See Handout

Maximum Effective Areas

Which is related to the maximum directivity of the antenna


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Let us consider figure below

77

Figure : Two antennas separated by a distanceR

Let the effective areas and directivities of each be At, Ar& Dt, Dr.


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If antenna one is atransmitter Antenna two is atransmitter

With similar analysis for linear ,

passive and isotropic medium

78

Now from the above equation


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79

Hence if the transmitter is an isotropic antenna and the receiver is an

infinitesimal dipole(l


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antenna is related to its maximum directivity (D0) by

When this is multiplied by the power density of the incident wave it

gives the maximum power that can be delivered to the load.

This is based on the assumption that there are no conduction-dielectric

losses (radiation efficiency ecd is unity), the antenna is matched to the

load (reflection efficiency, er is unity), and the polarization of the

impinging wave matches that of the antenna (polarization loss factor

PLF and polarization efficiency pe are unity).

80

If there are losses associated with an antenna, its maximum


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effective aperture must be modified to account for conduction-dielectric losses (radiation efficiency) as

If reflection and polarization losses are also included, then the

max mum e ec ve area s g ven y

81

Example : See Handout


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Summery

The fundamental parameters of antennas that are used for


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antenna design purposes are frequency, directivity, gain,

bandwidth, impedance, and polarization.

The radiation pattern: defines the variation of the power radiated

b an antenna as a function of the direction awa from the

antenna. This power variation as a function of the arrival angle is

observed in the antenna's far field.

The fields surrounding an antenna are divided into 3 principle

regions: Reactive near field, radiating near field and far field.

83

Directivity is a fundamental antenna parameter. It is a measure of


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how 'directional' an antenna's radiation pattern is. An antenna thatradiates equally in all directions would have effectively zero

directionality, and the directivity of this type of antenna would be

1 (or 0 dB).

antenna and the power radiated or dissipated within the antenna.

A high efficiency antenna has most of the power present at the

antenna's input radiated away. A low efficiency antenna has mostof the power absorbed as losses within the antenna, or reflected

away due to impedance mismatch.

84

The main beam of antenna is the region around the direction of


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maximum radiation (usually the region that is within 3 dB of thepeak of the main beam).

The sidelobes are smaller beams that are away from the main

beam. These sidelobes are usually radiation in undesired directions

.

The Half Power Beamwidth (HPBW) is the angular separation in

which the magnitude of the radiation pattern decrease by 50% (or -

3 dB) from the peak of the main beam

85

The antenna gain describes how much power is transmitted in the


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direction of peak radiation to that of an isotropic source.

Antenna gain is more commonly quoted in a real antenna's

specification sheet because it takes into account the actual losses

that occur.

n an enna w a ga n o means a e power rece ve ar

from the antenna will be 3 dB higher (twice as much) than what

would be received from a lossless isotropic antenna with the same

input power.

Antenna impedance relates the voltage to the current at the input

terminals of the antenna86

The effective aperture describes how much power is captured

f i l


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from a given plane wave.

Effective aperture or effective area can be measured on actual

antennas by comparison with a known antenna with a given

effective aperture

87

The polarization of an antenna is the polarization of the radiated fields

produced by an antenna, evaluated in the far field. Hence, antennas are


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often classified as "Linearly Polarized" or a "Right Hand Circularly

Polarized Antenna".

This simple concept is important for antenna to antenna communication.

First, a horizontally polarized antenna will not communicate with a

vertically polarized antenna. Due to the reciprocity theorem, antennas

transmit and receive in exactly the same manner. Hence, a vertically

polarized antenna transmits and receives vertically polarized fields.

Consequently, if a horizontally polarized antenna is trying to communicatewith a vertically polarized antenna, there will be no reception.

88

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Chapter Two Fundamental Parameters of Antenna.pdf

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