Introduction to Introduction to Antenna Antenna TheoryTheory

What is an antenna?What is an antenna?

An antenna is a An antenna is a passive structurepassive structure that that serves as transition between a serves as transition between a transmission linetransmission line and and airair used to used to transmit and/or receive electromagnetic transmit and/or receive electromagnetic waves. waves.

Source

Tx

Receiver Circuit

Rx

Antenna Antenna

Ulaby, 1999

Types of antennasTypes of antennas

Can be divided into Can be divided into two groupstwo groups

• WireWire antennas: antennas: dipoles, loops, Yagi-Uda…dipoles, loops, Yagi-Uda…

• ApertureAperture antennas: antennas: parabolic, horns, microstrip antennas…parabolic, horns, microstrip antennas…

http://www.kyes.com/antenna/antennatypes/antennatypes.html

http://en.wikipedia.org/wiki/Antenna_(electronics)#Overview

Wire antennasWire antennas

YagiLog periodic

Yagi

Wire antennasWire antennas

Log periodicLog periodic

Yagi-Uda with reflectorYagi-Uda with reflector

Aperture antennas Aperture antennas

Spherical (main reflector) with Gregorian feed

Dipole with parabolic and corner reflector

Reflector and Pyramidal horn Reflector and Pyramidal horn antennasantennas

Related parametersRelated parameters Solid angle, Solid angle, and Radiation intensity, and Radiation intensity, UU Radiation pattern, Radiation pattern, PPnn, sidelobes, HPBW, sidelobes, HPBW Far field zone, Far field zone, rrffff Directivity, Directivity, DD or Gain, or Gain, GG Antenna radiation impedance, Antenna radiation impedance, RRradrad Effective Area, Effective Area, AAee

All of these parameters are expressed in terms of a All of these parameters are expressed in terms of a transmissiontransmission antenna, but are identically antenna, but are identically applicable to a applicable to a receivingreceiving antenna. We’ll also antenna. We’ll also study: study:

Friis Transmission EquationFriis Transmission Equation Radar EquationRadar Equation

Spherical coordinatesSpherical coordinates

z (zenith)

x

y

= azimuth

= elevation =90=0

=0

=90=90

Solid AngleSolid Angle

s1 = r ds2 = r sin døs =r = arc dA = s1 s2

dA = r2 sin dø d = r2 dΩ

= Plan angle dΩ = Element of solid angle•The arc of a complete cirlce: • Area of a complete sphere:

= 2r = 4r2

•Total angle: = 2 [radianes] •Total solid angle: =4 [rad2]=4 [sr]

1 steradian (sr) = (1 radian)2

Radiation IntensityRadiation Intensity

Is the Is the power densitypower density per solid angleper solid angle::

vector.Poynting asknown

alsodensity power theis

][W/m ˆRe 2

r2

rH*E½

where

rU

r

P

P [W/sr]

Total radiated power by antennaTotal radiated power by antenna

Can be calculated as;Can be calculated as;

[W]

[W]

dSP

or

dUP

rrad

rad

P

Radiation PatternRadiation Pattern Radiation pattern is the Radiation pattern is the

3D plot of the gain, but 3D plot of the gain, but usually the two usually the two dimensional horizontal dimensional horizontal and and verticalvertical cross cross sections of the radiation sections of the radiation pattern are considered.pattern are considered.

Refers to the variation Refers to the variation of the relative of the relative amplitude of the amplitude of the radiation as a function radiation as a function of direction. of direction.

),(

),(

),(

),(),(

maxmax

U

UFn

PP

Field pattern:

Where U is the radiation intensity to be defined later.

),(

),(),(

max

E

EEn

Power pattern:

Total Total Solid AngleSolid Angle of an antenna of an antenna

z

y

x

žA

Patrón |P |n

[sr] ),(4

A dFn

A

Is as if you changed the radiation pattern beam of an antenna into a pencil beam shape and find out what’s the equivalent solid angle occupied by this pattern.

Isotropic antennaIsotropic antenna It’s an It’s an hypothetic antennahypothetic antenna, ,

i.e., it does not exist in real i.e., it does not exist in real life, yet it’s used as a life, yet it’s used as a measuring bar for real measuring bar for real antenna characteristics. antenna characteristics.

It’s a point source that It’s a point source that occupies a negligible space. occupies a negligible space. Has no directional preference. Has no directional preference.

Its pattern is simply a Its pattern is simply a spheresphere so it has so it has AA= = isotropicisotropic= = 44steradianssteradians..

4sin)1(

)1(

0

2

0

4

isotropic

dd

d

Radiation PatternRadiation Pattern

Whenever we Whenever we speak of speak of radiation radiation patterns, we patterns, we normally mean normally mean we are at a we are at a distance far distance far enough from enough from the antenna the antenna known as the known as the far fieldfar field..

_ 1

HPBWø

-.25

-.7

|En|

- 0 dB

-3dB

-10dB

| | | |HPBW

Patrón de campo o de potencia (Escala logarítmica)

Patrón de Campo (Escala lineal)

COORDENADAS RECTANGULARES

Patrón normalizado

Note that when plotted in decibels, the power and field patterns look exactly the same.

Pattern – polar plotPattern – polar plot

Lóbulo principal

.5

1

HPBW

Lóbulos menores

NNBW

("Mainlobe")

|Pn|

PATRON TIPICO (Coordenadas polares esféricas, 2 dimensiones)

Dipole antenna patternDipole antenna pattern

Note the radiation pattern is donut shaped.

SidelobesSidelobes

Antennas sometimes show Antennas sometimes show side lobesside lobes in in the radiation pattern. the radiation pattern.

Side lobes are peaks in gain other than the Side lobes are peaks in gain other than the main lobe (the "beam").main lobe (the "beam").

Side lobes have bad impact to the Side lobes have bad impact to the antenna quality whenever the system is antenna quality whenever the system is being used to determine the being used to determine the direction of a of a signal, for example in signal, for example in RADAR systems. systems.

Sidelobes of dipole arraysSidelobes of dipole arrays

sidelobe

Antenna Pattern with sidelobesAntenna Pattern with sidelobes

Many applications require sidelobe levels (SLL) to be below -20dB.

Gain or DirectivityGain or Directivity

An isotropic antenna and a practical antenna fed with the same power. Their patters would compare as in the figure on the right.

Directivity and GainDirectivity and Gain

All practical antennas radiate more than the All practical antennas radiate more than the isotropic antenna in some directions and less in isotropic antenna in some directions and less in others.others.

Gain is inherently directional; the gain of an Gain is inherently directional; the gain of an antenna is antenna is usually measured in the usually measured in the direction which it radiates bestdirection which it radiates best. .

aveave /UUDD maxmaxmax /),( PP

If lossless antenna, G=D

Gain or DirectivityGain or Directivity

Gain is measured by comparing an Gain is measured by comparing an antenna to a model antenna, antenna to a model antenna, typically the typically the isotropic antenna which which radiates equally in all directions. radiates equally in all directions.

pn dF

rD

4

,

4),(

4

2

/ Aisotropic oD

Directivity Directivity For an antenna with a single main lobe For an antenna with a single main lobe

pointing in the z-direction , pointing in the z-direction , AA can be can be approximated to the product of the HPBWapproximated to the product of the HPBW

eyzxz

yzxzA

AD

then

2A

4 4 /4

The Directivity:

Far fieldFar field

The distance at which the fields The distance at which the fields transmitted by an antenna (spherical) transmitted by an antenna (spherical) can be approximated to plane waves. can be approximated to plane waves.

It’s defined asIt’s defined as

/2 2Drff D = is the largest physical dimension of the antenna = wavelength of operationrff = distance from the antenna to the observation point

Beamwidth, HPBWBeamwidth, HPBW

Is the “distance” in radians o degrees Is the “distance” in radians o degrees between the direction of the between the direction of the radiation pattern where the radiated radiation pattern where the radiated power is half of the maximum.power is half of the maximum.

DHPBM

dB - .

dB - .

o 70

shape; beam" pencil"for

37070log20

350log10

Antenna ImpedanceAntenna Impedance An antenna is “seen" by the generator as a load with An antenna is “seen" by the generator as a load with

impedance impedance ZZA A ,, connected to the line. connected to the line.

The real part is the radiation resistance plus the The real part is the radiation resistance plus the ohmic resistanceohmic resistance..• Minimizing impedance differencesMinimizing impedance differences at each interface will at each interface will

reduce SWRreduce SWR and and maximize power transfermaximize power transfer through each part through each part of the antenna system.of the antenna system.

• Complex impedance, Complex impedance, ZZA A ,, of an antenna is related to the of an antenna is related to the electrical length of the antenna at the wavelength in use. electrical length of the antenna at the wavelength in use.

The impedance of an antenna can be matched to the feed line The impedance of an antenna can be matched to the feed line and radio by adjusting the impedance of the feed line, using the and radio by adjusting the impedance of the feed line, using the feed line as an impedance feed line as an impedance transformer. .

More commonly, the impedance is adjusted at the load (see More commonly, the impedance is adjusted at the load (see below) with an antenna tuner, a balun, a matching transformer, below) with an antenna tuner, a balun, a matching transformer, matching networks composed of inductors and capacitors, or matching networks composed of inductors and capacitors, or matching sections such as the gamma match.matching sections such as the gamma match.

ALradA jXRRZ ZA

Antenna efficiency, Antenna efficiency, EfficiencyEfficiency is the ratio is the ratio

of power put into the of power put into the antenna terminals to antenna terminals to the power actually the power actually radiated radiated

Radiation in an Radiation in an antenna is caused by antenna is caused by radiation resistance radiation resistance which can only be which can only be measured as part of measured as part of total resistance total resistance including loss including loss resistance. resistance.

in rad P P

D G

Radiation ResistanceRadiation Resistance

The antenna is connected to a T.L., and The antenna is connected to a T.L., and it “sees” it as an impedance.it “sees” it as an impedance.

The power radiated is The power radiated is

The loss power isThe loss power is

loss rad

rad

loss rad

rad

R

R

PP

P

R

rad2o rad RI

2

1 P

L2o loss RI

2

1 P

Radar equationRadar equation What is a radar?What is a radar?

Received power by a radar from a single target Received power by a radar from a single target isis

Where Where is the backscattering coefficient of is the backscattering coefficient of the target [mthe target [m22]]

2

43

22

4 e

R

GPP oot

r

Antenna polarizationAntenna polarization

The The polarizationpolarization of an antenna is the of an antenna is the polarization of the signals it emits. polarization of the signals it emits. • The ionosphere changes the polarization of The ionosphere changes the polarization of

signals unpredictably, so for signals which will signals unpredictably, so for signals which will be reflected by the ionosphere, polarization is be reflected by the ionosphere, polarization is not crucial. not crucial.

• However, for line-of-sight communications, it However, for line-of-sight communications, it can make a tremendous difference in signal can make a tremendous difference in signal quality to have the transmitter and receiver quality to have the transmitter and receiver using the same polarization. using the same polarization.

• Polarizations commonly considered are Polarizations commonly considered are verticalvertical, , horizontalhorizontal, and , and circularcircular..

Antenna BandwidthAntenna Bandwidth The The bandwidthbandwidth of an antenna is the range of of an antenna is the range of

frequencies over which it is effective, usually frequencies over which it is effective, usually centered around the operating or resonant centered around the operating or resonant frequency. frequency.

• The bandwidth of an antenna may be increased by The bandwidth of an antenna may be increased by several techniques, including using thicker wires, several techniques, including using thicker wires, replacing wires with replacing wires with cagescages to simulate a thicker wire, to simulate a thicker wire, tapering antenna components (like in a feed horn), and tapering antenna components (like in a feed horn), and combining multiple antennas into a single assembly and combining multiple antennas into a single assembly and allowing the natural impedance to select the correct allowing the natural impedance to select the correct antenna.antenna.

Effective AreaEffective Area

How a Rx antenna extracts energy How a Rx antenna extracts energy from incident wave and delivers it to from incident wave and delivers it to a load?a load?

Above is valid for any antenna under Above is valid for any antenna under matched-load conditionsmatched-load conditions

4

P 2

inc

rec DAe

P

Example Example

Determine the direction of maximum Determine the direction of maximum radiation , pattern solid angle, radiation , pattern solid angle, directivity and HPBW in the directivity and HPBW in the y-zy-z plane plane for an antenna with normalized for an antenna with normalized radiation intensity given by radiation intensity given by

elsewhere 0

20 and 2

0for cos),(

2

F

oAnswers 90,6,3

2),0,0(:

Friis Transmission Eq.Friis Transmission Eq.

In any communication link, there is In any communication link, there is a transmitting antenna and a a transmitting antenna and a receiver with a receiver antenna.receiver with a receiver antenna.

2t

R4

P

isotrP

22t t

2t t

R

PA

R4

PG

isotrtt G PP

22t rt

R

PAA

trrec A PP

2t rt

R4

PGG 2

recP

TX

RX

Antenna ArraysAntenna Arrays Uses many antennas synchronized Uses many antennas synchronized

with each other to increasewith each other to increase Pattern multiplication, AFPattern multiplication, AF

FactorArray Pattern Antenna

Individual)(

rE

2sin

2sin

N

N

AFN

1

-1 1x

|T (x)|4

-R

x0°

Uniform illumination Tschebyscheff Illumination

Planar ArraysPlanar Arrays