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Directivity andgain in

antenna

Rohit NairElectronics and communication engineering

Lovely Professional University

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What is an antenna?

An antenna is a passive structure thatserves as transition between atransmission line and air used totransmit and receive electromagneticwaves.

Source

Tx

ReceiverCircuit

Rx

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Outline

Antenna parameters Solid angle, WA and Radiation intensity, U Radiation pattern, Pn, sidelobes, HPBW Far field zone, rff

Directivity, D or Gain, G Antenna radiation impedance, Rrad Effective Area, Ae

All of these parameters are expressed in terms of a

transmission antenna, but are identicallyapplicable to a receiving antenna.

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Solid Angle

s1 = r dq s2 = rsin qds =qr dA = s1 s2

dA = r2

sin qd dq= r2d

q= angle of plane d = steredianArea of sphere:

= 4pr2 total Angle : = 2p [radianes] total angle: =4p [rad2]

=4p [sr]1 steradian (sr) = (1 radian)2

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Radiation Intensity

Is the power densityper solid angle:

vector.Poyntingasknown

alsodensitypowertheis

][W/mRe 2

r2

rH*}{E

where

rU

r

P

P [W/sr]

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Total radiated power by antenna

Can be calculated as;

[W]

[W]

W

dSP

or

dUP

rrad

rad

P

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Radiation Pattern

Radiation pattern isthe 3D plot of thegain, but usually the2D horizontal andvertical cross sections

of the radiationpattern areconsidered.

Refers to the variationof the relativeamplitude of theradiation as a function

ofdirection.

),(

),(

),(

),(),(

maxmax q

q

q

qq

U

UFn

P

P

Field pattern:

Where U is the radiationintensity to be defined later.

),(

),(),(

max q

qq

E

EEn

Power pattern:

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Total solid angle of an antenna

z

y

x

A

Patrn

|P |

n

[sr]),(4

A WW dFnp

qWA

Is as if you changed theradiation patternbeam of an antenna

into a pencil beamshape and find outwhats the equivalentsolid angle occupied bythis pattern.

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Isotropic antenna

Its an hypothetic antenna,i.e., it does not exist in reallife, yet its used as ameasuring bar for real

antenna characteristics.

Its a point source thatoccupies a negligible space.Has no directionalpreference.

Its pattern is simply a sphereso it has WA= Wisotropic= 4p

[steradians].

pqqp

q

p

p

4sin)1(

)1(

0

2

0

4

isotropic

WW

dd

d

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Sidelobes

Antennas sometimes show side lobes inthe radiation pattern.

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

Side lobes have bad impact to the

antenna quality whenever the system isbeing used to determine the direction of asignal, for example in RADAR systems.

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Sidelobes of dipole arrays

sidelobe

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Gain or Directivity

An isotropic antenna and a practical antennafed with the same power. Their patterns

would compare as in the figure on the right.

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Directivity and Gain

All practical antennas radiate more than theisotropic antenna in some directions and less inothers.

Gain is inherently directional; the gain of anantenna is usually measured in the directionwhich it radiates best.

aveave /UUDD maxmaxmax /),( PPq

If lossless antenna, G=D

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Gain or Directivity

Gain is measured by comparing anantenna to a model antenna,typically the isotropic antenna which

radiates equally in all directions.

radAVE P

r

dAA

D

),(4

1/),(

2 qpq

q

P

P

),P(

PP

//44

AisotropicAmax WWW p

p

rad

o

P

UD

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Antenna gain

Sources of Antenna System Loss

1. losses due to impedance mismatches

2. losses due to the transmission line

3. conductive and dielectric losses in the antenna

4. losses due to polarization mismatches

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Directivity

For an antenna with a single main lobepointing in the z-direction , WA can beapproximated to the product of the HPBW

yzxz

yzxzA

D

then

pp

4/4 A W

W

The Directivity:

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Beamwidth, HPBW

Is the distance in radians o degreesbetween the direction of theradiation pattern where the radiated

power is half of the maximum. Can be found by solving Fn(q,)=.5

DHPBM

dB-.

dB-.

o

70

shape;beam"pencil"for

37070log20

350log10

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APPLICATIONS

Application to several researchprojects: CASA, NASA-FAR,

NASA-TCESS Show results from undergrads

working in NASA and NSF

projects Relation to Grad students