Antenna & Array Fundamentals Technical Training Courses Sampler

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What you will learn from this course

• Basic antenna concepts and definitions

• The appropriate antenna for yourapplication

application

• Factors that affect antenna array designsand antenna systems

• Measurement techniques commonly usedin anechoic chambers

Example of a “Real World” Radar Antenna Array

The MU (Middle and Upper atmosphere) radar constructed by the Radio Atmospheric Science Center of Kyoto University at Shigaraki,Shiga prefecture, Japan

• Investigates atmospheric and plasma dynamics in the wide region from the troposphere to the ionosphere.• The radar is a powerful monostatic pulse Doppler radar operating at 46.5MHz• It uses active phased array antenna, which consists of 475 crossed Yagi antennas and identical number of solid-state transmit/receive modules.• The antenna beam direction can be switched to any direction within the steering range of 30deg from zenith from pulse to pulse.• The antenna aperture is 8,330m^2 (103m in diameter), and the peak and average output power is 1MW and 50kW, respectively.• The antenna beam has a conical shape with the round-trip (two-way) half-power beamwidth of 2.6deg.

Examples of Antennas

CSIRO Parkes radio telescope is the largest and oldestof the eight antennas comprising the 'AustralianTelescope National Facility'. The Compact Array of six22-metre dishes near Narrabri and another nearCoonabarabran link up with the 64 meter Parkes tosynthesize a telescope some 300 kilometers across.

The VLA is an array of telescopes that can be linkedtogether to synthesize the resolving power of a telescopeupto 36 km (22 miles) across, or grouped together tosynthesize one only a km (0.6 mile) across: the varyingresolutions are the equivalent of an astronomical zoomlens. This array is located near Socorro, NM

Radio TelescopeArecibo, Puerto Rico

305m in Diameter

Missile DefenseWorking inside a 10-story Pave Phased Array Warning System, or

Pave PAWS, the men and women of the 7th Space WarningSquadron continuously scan the horizon for missiles, satellites and

other man-made objects in space.

Eglin FPS-85 radar located near Ft. WaltonBeach, FL. This phased array radar is a dedicated

sensor to the U.S. satellite catalog.

European Remote Sensing satellite (ERS)Provides information about the

Earth’s land, oceans and polar caps

InmarsatUsed for Global Communications

Types of Antennas

• Electrically small antennas

• Resonant antennas

• Broadband antennas

• Aperture antennas

Electrically Small Antennas

The extent of the antenna structure is much less than the wavelength• Very low directivity• Low input resistance• High input reactance• Low radiation efficiency

Short Dipole

Small Loop

Resonant Antennas

The antenna operates well at a single or selected narrow frequency band• Low to moderate gain• Real input impedance• Narrow bandwidth

Half-wave Dipole

Microstrip Patch

Broadband AntennasThe pattern, gain, and impedance remain acceptable and are nearly constantover a wide frequency range. They are characterized by an active region witha circumference of one wavelength or an extent of a half-wavelength whichrelocates on the antenna as the frequency changes

• Low to moderate gain• Constant gain• Real input impedance

• Real input impedance• Wide Bandwidth

SpiralLog-periodic dipole array

Aperture AntennasHave a physical aperture through which the waves flow.

• High Gain• Gain increases with frequency• Moderate bandwidth

Aperture Aperture

Basic Concepts

• Directivity

• Gain

• Antenna Patterns

• Beamwidth

• Polarization

• Bandwidth

• Radiation Resistance/Input impedance

• Reciprocity

• Effective Aperture

What is the directivity of antenna?

Ratio of radiation intensity in a given directionto the radiation intensity that would be

obtained if the total power radiated by theantenna were to be radiated isotropically

What is the gain of antenna?

Ratio of radiation intensity in a given direction tothe radiation intensity that would be obtained ifthe total power accepted by the antenna were to

be radiated isotropically

Simple Illustration (light bulb)Radiating with equal intensity in all

directions (isotropic radiation) Power meter reading radiatedpower (isotropic)

P (isotropic)

Radiation is focused in a particulardirection due to the reflector

Power meter reading of radiatedpower (in a given direction)

P (direction)

Note that polarization must be considered with RF antennas

Directivity and Gain• The directivity can be thought of as the ratio of the maximum radiation

intensity emanating from an antenna to the total power leaving the antennaradiated isotropically per solid angle of a sphere.

• The radiation intensity of an isotropic source is: (Prad ) / (solid angle of asphere).

• The gain of an antenna can be thought of as the ratio of the maximumradiation intensity emanating from an antenna to the total power introduced

/ 4isotropic radiatedU P

• The gain of an antenna can be thought of as the ratio of the maximumradiation intensity emanating from an antenna to the total power introducedinto the antenna: (Pin ) / (solid angle of a sphere).

• Losses prevent the power input into the antenna from equaling the radiatedpower.

rad inP P

• The gain of an antenna is always less than thedirectivity of a antenna.

Formulas for Directivity and Gain

,, max

)(10)(10)(10dBiG

:formloginexpressedusuallyisGain

maxmax

LogDLogDLog

oradin

A Directed Beam is Described by itsAntenna Pattern

Main lobe

Side lobes

Back lobes

More Details about RadiationPatterns

Beamwidth (between 3 dB points)

Patterns

Omni-directional pattern

Equal power in one plane.

Hemispherical pattern

Equal power everywhere

in upper half-plane.

Isotropic pattern

Equal power everywhere.

Polarization

• Electric fields must be aligned for maximumpower transfer between two antennas.

• The alignment is described by a polarization lossfactor (PLF).

factor (PLF).

• Analytically, the polarization loss factor is theelectric field of the incoming wave dotted withthe electric field that would be transmitted bythe receiving antenna.

An Introduction to Polarization

• When speaking of “polarization,” we are describingthe behavior of electric field of the antenna.

• The field may remain oriented in one direction as theelectric field propagates (linear polarization)

• The field may spin as the electric field propagates(circular or elliptical polarization)

(circular or elliptical polarization)

• Polarization will be considered in detail later in thiscourse, but you already have enough material tounderstand how our math can describe such electricfields!

Here is an interesting antenna that has two input ports. We willdesignate these as port 1 and port 2

Port 1

Port 2

Port 1

Port 2

Addsome

geometry!

Port 1

Exciting port 1 causes an electric field to exist between the two horizontal finsand the field at the “aperture” of the antenna is oriented in the x-direction

ˆ x oE a E

Port 2

Exciting port 2 causes an electric field to exist between the two vertical finsand the field at the “aperture” of the antenna is oriented in the y-direction

ˆ y oE a E

We already know that we can represent time-varying fields as phasors.

If we excited both ports at once (with equal strength) , we expect the

phasor representation of the electric field at the aperture to be of the

The time-dependent behavoir at the aperture becomes:

x o y oE a E a E

The time-dependent behavoir at the aperture becomes:

ˆ ˆ ˆ ˆ( ) Re[ ( ) ] ( ) ( )

It is illustrative to plot this

j tx o y o x o y ot a E a E e a E a E Cos t

electric field using certain "snapshots" of time.

Holding " " as a constant, there is an instant when the product equals

zero. Similarly, there are different instances when equals /2 and

/2 and so forth. Letting 1 / , we can make a table and

parametrically plot the time-dependent electric field at the aperture.

oE V m

ˆ ˆ( ) ( )

ˆ ˆ0 ( )

ˆ ˆ( )

3 / 2 0

t a a Cos t

The y-axis is pointed downward so that the z-axis would be into the page.

We observe the behavior of the electric field at 0 (at the aperture.)

The electric field is linearly polarized oriented at a

45 Degree angle with the

y-axis (the tilt angle " .") It is also at a 45 Degree angle with the x-axis,

but we define the tilt angle with respect to the y-axis.

Now we make one "small" change to our phasor representation of

ˆthe electric field at the aperture placing a " " in front of the term:

This t

x o y o

E a E j a E

erm has a significant impact on the time-dependent behavoir of

the elctric field:

ˆ ˆ( ) Re[ ( ) ]

ˆ ˆRe[ ( ) ( ( ) ( )) ]

ˆ ˆ( ) ( )

Again, we hol

j tx o y o

x o y o

t a E j a E e

a E j a E Cos t j Sin t

a E Cos t a E Sin t

d " " as a constant and parametrically plot the time-

dependent electric field at the aperture. Again, let 1 / .oE V m

ˆ ˆ( ) ( )

ˆ3 / 2

t a Cos t a Sin t

3 / 2t

The electric field is spinning in a counter-clockwise direction!33

Is it right-hand or left-hand polarization?

1) Place your thumb towards the direction of propagation. This would be

into the page.

2) If your fingers align with the "spin" you have answered the question!

Try it with each hand and you will find that this example is left-hand

circularly polarized (LHCP.) / 2t

3 / 2t 34

So, is left-hand polarization counterclockwise and right-hand clockwise?

Answer: Not enough information!

You must state whether the field is "leaving" or "arriving."

A thumb pointed away from you indicates a leaving wave.

A thumb pointed toward you indicates an arriving wave.

le f t-h a n d is

c lo c k w ise

a rr iv in g

rig h t-h a n d is

c lo c k w ise

le a v in g

le f t-h a n d is

c o u n te rc lo c k w ise

le a v in g

rig h t-h a n d is

c o u n te rc lo c k w ise

a rr iv in g 35

Port 1Port 2

This antenna is capable of exciting orthogonal electric fields (i.e., in the x- and y-directions.)If the fields are excited in phase, the field leaving the antenna will be linearly polarized

leaving the antenna at a 45 Degree angle – if the signal strength is the same at both feeds.

o oFor example: Port 1 = V ( ) and Port 2 = V ( )Cos t Cos t 36

Port 1Port 2

Again, the antenna is capable of exciting orthogonal electric fields (i.e., in the x- and y-directions.) If the fields are excited in phase quadrature, the field leaving the antenna will

be circularly polarized – if the signal strength is the same at both feeds.

o oFor example: Port 1 = V ( ) and Port 2 = V ( )Cos t Sin t 37

We could achieve circular polarization with and RF source, a power splitter, and a 90 Degreephase shifter.

Power Splitter

RF Source

Polarization (elliptical)

yx EE ,

Assume any value

Not necessarily equal

OARatioAxial AR

Tilt angle

+ for RH polarization- for LH polarization

CP Measurements

Axial Ratio

Polarization Loss Factor2

Inc Trans

E EPLF

Inc Transw a

Inc trans

The electric fields are in phasor form andmay be complex quantities

PolarizationPolarization is a critical issue when considering antennas

Antenna “A” transmits avertically polarized signal

Proper alignment – Maximum power transferred from antenna A to antenna B.

Antenna “B” is oriented

to receive a vertically

polarized signal

Improper alignment – Minimum power transferred from antenna A to antenna B.

Antenna “A” transmits acircularly polarized signal

Circular to linear – 1 / 2 the power transferred from antenna A to antenna B.

Antenna “B” is oriented to receivelinear polarization in any direction

Antenna “A” transmits avertically polarized signal

Antenna “B” is oriented

to receive a horizontally

polarized signal

Bandwidth

• There are 3 equivalent ways do describe thebandwidth of an antenna

– Return loss (-10 dB convention)

– VSWR (2:1 convention)

– Polar Plot (Smith chart) 0.316228

Definition of the Reflection Coefficient

Characteristic impedance of the transmission line

Transmitted Voltage

Reflected Voltage

Reflection Coefficient – a complex ratio of thereflected voltage divided by the transmitted voltagemeasured at a defined reference place (e.g., the inputport of the antenna.

Reflected Power

2 * 2 2

r i r i r ij j

2Percentage of power reflected from the antenna

21 Percentage of power entering the antenna

Note that the power entering the antenna is not equal to the power radiatedby the antenna. Some power is consumed in conductor and other losses

Bandwidth – A Logarithmic Plot

A return loss of -10 dB is conventionally defines as the bandwidth of the antenna

H LBandwidth f f

2 4 6 8 10Frequency

Bandwidth – VSWR Plot

The impedance mismatch between theAntenna’s input impedance and thecharacteristic impedance of thetransmission line causes a standingwave to exist along the length of thetransmission line.

0.2 0.4 0.6 0.8 1

Distance back from the reference plane

H LBandwidth f f

0.2 0.4 0.6 0.8 1

Frequency

2 4 6 8 10Frequency

Distance back from the reference plane

Bandwidth – Polar Plot

H LBandwidth f f 1

LfDiscrete Data pointsmeasured on aNetwork Analyzer

0.316228

Bandwidth – Polar Plot/Smith Chart

IFrom transmission line theory

LfWhen the real andimaginary parts of the loadimpedance aredetermined as a function

0.316228

determined as a functionof the real and imaginaryparts of the reflectioncoefficient, the resultingcircles and arcs define theSmith Chart.

Realized (or actual) Gain

oorealized DGG )1()1(22

oorealized DGG )1()1(

Bandwidth – Equivalent Quantities

Return Loss

-10 dB

1.9245

0.316228 0.9

-20 dB

-30 dB

1.2222

1.0653

0.100000

0.031622

Antenna Impedance(Transmit)

The input impedance is theimpedance presented by an

antenna at its terminals

agenerator

radiated waves

AAA jXRZ

A R LR R R

radiation resistance

Input Impedance of Antennas (Transmit)

( ) ( )

A g R L g A g

Z Z R R R j X X

2 2 ( ) ( )

g rr g R

R L g A g

V RP I R

R R R X X

2 2 ( ) ( )

g LL g L

V RP I R

R R R X X

Power delivered to theantenna for radiation

Power dissipated asheat on the antenna

From circuit theory

2 22 2 ( ) ( )L g L

R L g A g

P I RR R R X X

2 2 ( ) ( )

R L g A g

V RP I R

R R R X X

*gA ZZ

R L gR R R

heat on the antenna

Power dissipated as heaton the internal resistanceof the generator

Conjugate matched conditions deliverthe the maximum power to the antenna.

Input Impedance of Antennas (transmit)2

28 ( )

28 ( ) 8

Radiated power assuming conjugate matching

Dissipated power in the antenna assuming conjugate matching

Dissipated power in the generator’s internal impedance

28 ( ) 8g

PR R R

g R LP P P

VP V I

The total power is:

Power supplied by thegenerator :

Therefore, under conjugate match conditions, half the power that issupplied by the generator is dissipated as heat in its internal resistanceand the other half is delivered to the antenna.

Antenna Impedance(receive)

Again, the input impedance isthe impedance presented byan antenna at its terminals

Input Impedance of Antennas (receive)

R Power delivered to the antenna’s terminating impedance

Assuming conjugate matched conditions delivering the maximum power to the antenna.

28 ( )T L

28 ( )T R

Power across the radiation resistance of the antenna

Power dissipated as heat due to the losses in the antenna

Reciprocity for Antennas

2 ( , )V

1( , )V

Important Point!!! The transmit and receive patterns of an antenna arethe same for a reciprocal antenna.

Transmitting pattern of antenna “1” Receiving pattern of antenna “2”

( , )( , )

12 21( , ) ( , )Z Z

Aperture Size

• Antenna engineers frequently discuss antennas interms of Aperture Size.

• A common term is the “effective aperture” size.

• Another term is the “physical aperture” size.

• Aperture size is related to the beamwidth and

• Aperture size is related to the beamwidth andaccordingly the directivity and gain.

Effective Aperture Size

• The effective aperture size is a relationship between theincident electromagnetic field and the power delivered to theterminating impedance on the antenna’s input port.

(w)impedancengterminatitheacrossdevelopedpowerThe

incident

Teffective

)(w/mantennatheofapertureat the

fieldneticelectromagincidenttheofstrengthThe

(w)impedancengterminatitheacrossdevelopedpowerThe

incident

LZincidentWTP

Effective Aperture Size

• The effective aperture size is related to the directivity of the antenna

• Anything that diminishes the power across the terminating impedancedecreases the effective aperture size

• If no power develops across the terminating impedance, the effectiveaperture size is zero - even if there is an incident electromagnetic field.

LZincidentWTP

)(mˆˆD4

Physical Aperture Size andAperture Efficiency

idthLength x WArea 2rArea

AreaPhysical

ApertureEffectiveMaximiumap

Friis Transmission Formula

r erP W A

Time average power density transmitted by satellite

effective aperture ofreceiving antenna

total transmitted power

SatelliteAntenna

dishantenna

tt GP ,

4r erG A

Friis transmission formula

gain of transmitting antenna

4er rA G

2(4 )r t t rP P G G

Communication Link

),( tttG ),( rrrG

2 2 22 ˆ ˆ(1 ) (1 ) ( ) ( , ) ( , )4

rt r t t t r r r w a

Communication Links in dBm

2(4 )r t t rP P G G

GdBG log10)(

Power Milliwatts( ) 10

1 MilliwattrP dBm Log

Friis transmission formula

Divide each side by 1 mw and take the log

( ) ( ) ( ) ( )

20 log ( ) 20 log ( ) 32.44

r t t rP dBm P dBm G dB G dB

R km f MHz

Note:f

C = Speed of light

F = frequency

Divide each side by 1 mw and take the log

The Friis Transmission Formula

Our work with the Friis transmissionformula presumed a rather pristine

environment where one did not haveto worry about the attenuation through

the atmosphere. Of course, theseeffects cannot be ignored. Shown tothe left is a plot of attenuation effects

due to oxygen and water vapor.

Accordingly, any link budget would needto be adjusted to take these (and other)propagation effects into account. At this

point we begin to leave the study ofantenna theory and enter the realm of

propagation theory.

R. E. Collin, Antennas and Radiowave Propagation, New York, McGraw Hill, 1985, pp 409.

Much more!!!