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Chapter 2Chapter 2Fundamental Properties Fundamental Properties

of Antennasof Antennas

ECE 5318/6352Antenna Engineering

Dr. Stuart Long

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IEEE StandardsIEEE Standards

Definition of Terms for Antennas

IEEE Standard 145-1983

IEEE Transactions on Antennas and Propagation Vol. AP-31, No. 6, Part II, Nov. 1983

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Radiation PatternRadiation Pattern(or Antenna Pattern)(or Antenna Pattern)

“The spatial distribution of a quantity which characterizes the electromagnetic field

generated by an antenna.”

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Distribution can be aDistribution can be a

Mathematical function

Graphical representation

Collection of experimental data points

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Quantity plotted can be aQuantity plotted can be a

Power flux density W [W/m²]

Radiation intensity U [W/sr]

Field strength E [V/m]

Directivity D

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Graph can beGraph can be

Polar or rectangular

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Graph can beGraph can be

Amplitude field |E| or power |E|²

patterns

(in linear scale) (in dB)

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Graph can beGraph can be

2-dimensional or 3-D

most usually several 2-D “cuts”

in principleplanes

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Radiation pattern can beRadiation pattern can be

IsotropicEqual radiation in all directions (not physically realizable, but valuable for comparison purposes)

DirectionalRadiates (or receives) more effectively in some directions than in others

Omni-directionalnondirectional in azimuth, directional in elevation

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Principle patternsPrinciple patterns

E-plane Plane defined by E-field and direction of maximum radiation

H-plane Plane defined by H-field and direction of maximum radiation

(usually coincide with principle planes of the coordinate system)

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Coordinate SystemCoordinate System

Fig. 2.1 Coordinate system for antenna analysis.

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Radiation pattern lobesRadiation pattern lobes

Major lobe (main beam) in direction of maximum radiation (may be more than one)

Minor lobe -

any lobe but a major one

Side lobe -

lobe adjacent to major one

Back lobe –

minor lobe in direction exactly

opposite to major one

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Side lobe level or ratio (SLR)Side lobe level or ratio (SLR)

(side lobe magnitude / major lobe magnitude)

-

20 dB typical

< -50 dB very difficultPlot routine included on CD for rectangular and polar graphs

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Polar PatternPolar Pattern

Fig. 2.3(a) Radiation lobes and

beamwidths of an antenna pattern

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Linear PatternLinear Pattern

Fig. 2.3(b) Linear plot of power pattern and

its associated lobes and beamwidths

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Field RegionsField Regions

Reactive near fieldReactive near fieldenergy stored not radiated

λ= wavelengthD= largest dimension of the antenna

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62.0 DR

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Field RegionsField Regions

Radiating near field (Fresnel)Radiating near field (Fresnel)radiating fields predominatepattern still depend on Rradial component may still be appreciable

λ= wavelengthD= largest dimension of the antenna

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262.0 DRD

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Field RegionsField Regions

Far field (Far field (FraunhoferFraunhofer))

field distribution independent of Rfield components are essentially transverse

2

2 DR

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RadianRadian

Fig. 2.10(a) Geometrical arrangements for defining a radian

r2

radians in full circlearc length of circle

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SteradianSteradian

one steradian subtends an area of

4π

steradians in entire sphere

ddrdA sin2

Fig. 2.10(b) Geometrical arrangements for defining a steradian.

ddrdAd sin2

2rA

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Radiation power densityRadiation power density

HEW

Instantaneous Poynting vector

Time average Poynting vector

[ W/m ²

]

Total instantaneousPower

Average radiated Power

[ W/m ²

]

s

sWP d [ W ]

HEW

Re21

avg

s

avgrad dP s

W[ W ]

[2-8]

[2-9]

[2-4]

[2-3]

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Radiation intensityRadiation intensity“Power radiated per unit solid angle”

avgWrU 2

far zone fields without 1/r

factor

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),,(2

),(

rrU E

222

),,(),,(2

rErEr

[W/unit solid angle]

[2-12a]

2 2o o1 ( , ) ( , )2

E E

Note: This final equation does not have an r in it. The “zero”

superscript means that the 1/r term is removed.

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Directive GainDirective Gain

Ratio of radiation intensity in a given direction to the radiation intensity averaged over all directions

radog

PU

UUD 4

Directivity GainDirectivity Gain

((DDgg) --

directivity in a given direction

[2-16]

0 4radPU

(This is the radiation intensity if the antenna radiated its power equally in all directions.)

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1 , sin4 S

U U d d

Note:

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Directivity Directivity

rad

max

o

maxo

PU

UUD 4

Do (isotropic) = 1.0

og DD 0

DirectivityDirectivity

----

DDoo

value of directive gain in direction of maximum radiation intensity

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BeamwidthBeamwidth

Half power beamwidthHalf power beamwidthAngle between adjacent points where field strength is 0.707 times the maximum, or the power is 0.5 times the maximum (-3dB

below maximum)

First null beamwidthFirst null beamwidthAngle between nulls in pattern

Fig. 2.11(b) 2-D power patterns (in linear scale) of U()=cos²()cos³()

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Approximate directivity for Approximate directivity for omnidirectional patternsomnidirectional patterns

McDonaldMcDonald

2HPBW0027.0HPBW

101

oD

π

π

PozarPozar

(HPBW in degrees)

Results shown with exact values in Fig. 2.18

HPBW1818.01914.172 oD

nU sin

Better if no minor lobes [2-33b]

[2-32]

[2-33a]

For example

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Approximate directivity for directional patternsApproximate directivity for directional patterns

KrausKraus

1 2 1 2

4 41, 253o

r r d d

D

π/2

π

Tai & PereiraTai & Pereira

Antennas with only one narrow main lobe and very negligible minor lobes

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22

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815,7218.22

ddrr

oD

nU cos

[2-30b]

[2-31]

[2-27]

For example

(

) HPBW in two perpendicular planes in radians or in degrees)1 2,r r

1 2,d d

Note: According to Elliott, a better number to use in the Kraus formula is 32,400 (Eq. 2-271 in Balanis). In fact, the 41,253 is really wrong (it is derived assuming a rectangular beam footprint instead of the correct elliptical one).

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Approximate directivity for Approximate directivity for directional patternsdirectional patterns

Can calculate directivity directly (sect.2.5), can evaluate directivity numerically (sect. 2.6)

(when integral for

Prad

cannot be done analytically,analytical formulas cannot be used )

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GainGainLike directivity but also takes into account efficiency of antenna

(includes reflection, conductor, and dielectric losses)

oin

oin

ZZZZ

;1 2

eo

: overall eff.

er

: reflection eff.

ec

: conduction eff.

ed : dielectric eff.

Efficiency

source) isotropic(lossless,PU

PUeDeG

in

max

rad

maxooooabs

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dcro eeee dccd eee

[2-49c]

radcd

in

PeP

rado

inc

PeP

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GainGain

By IEEE definition “gain does not include losses arising from impedance mismatches (reflection losses) and polarization mismatches (losses)”

source) isotropic(lossless,PUDeG

in

maxocdo

4 [2-49a]

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BandwidthBandwidth

“frequency range over which some characteristic conforms to a standard”

Pattern bandwidth

Beamwidth, side lobe level, gain, polarization, beam direction

polarization bandwidth example: circular polarization with axial

ratio < 3 dB

Impedance bandwidth

usually based on reflection coefficient

under 2 to 1 VSWR typical

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BandwidthBandwidth

Broadband antennas usually use ratio (e.g. 10:1)

Narrow band antennasusually use percentage (e.g. 5%)

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PolarizationPolarization

Linear

Circular

Elliptical

Right or left handed

rotation in time

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PolarizationPolarization

Polarization loss factor

p

is angle between wave and antenna polarization

2 2ˆ ˆ cosw a pPLF [2-71]

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Input impedanceInput impedance“Ratio of voltage to current at terminals of antenna”

ZA

= RA

+ jXA

RA

= Rr

+ RL

Rr

= radiation resistanceRL

= loss resistance

ZA

= antenna impedance at terminals a-b

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Input impedanceInput impedance

Antenna radiation efficiencyAntenna radiation efficiency

2

2 2

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1 1( )2 2

g rr

cdr L

g r g L

I RPower Radiated by Antenna Pe

Power Delivered to Antenna P P I R I R

[2-90]

Lr

rcd

RRRe

Note: this works well for those antennas that are modeled as a series RLC circuit –

like wire antennas. For those that are modeled as parallel RLC circuit (like a microstrip antenna), we would use G values instead of R values.

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Friis Transmission EquationFriis Transmission Equation

Fig. 2.31 Geometrical orientation of transmitting and receiving antennas for Friis

transmission equation

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Friis Transmission EquationFriis Transmission Equation

et = efficiency of transmitting antenna

er = efficiency of receiving antennaDt = directive gain of transmitting antennaDr = directive gain of receiving antenna = wavelengthR = distance between antennas

assuming impedance andpolarization matches

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4),(),(

RDDee

PP rrrttt

rtt

r

[2-117]

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Radar Range EquationRadar Range Equation

Fig. 2.32 Geometrical arrangement of transmitter, target, and receiver for radar range equation

2

2144),(),(

RRDDee

PP rrrttt

t

rcdrcdt

[2-123]

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Radar Cross SectionRadar Cross Section

RCS

Usually given symbol

Far field characteristic

Units in [m²]

4 r

inc

UW

incident power density on body from transmit directionincW

scattered power intensity in receive directionrU

Physical interpretation: The radar cross section is the area of an equivalent ideal “black body”

absorber that absorbs all incident power that then radiates it equally in all directions.

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Radar Cross Section (Radar Cross Section (RCS)

Function of

Polarization of the wave

Angle of incidence

Angle of observation

Geometry of target

Electrical properties of target

Frequency

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Radar Cross Section (Radar Cross Section (RCS)