AWP Unit I Antenna Basics

8/18/2019 AWP Unit I Antenna Basics

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INTRODUCTION & BASICS

Unit I


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Antenna• An antenna is a region of transition

between a transmission line and space.• Antennas

radiate/couple/concentrate/directelectromagnetic (EM) energy in thedesired direction.

• A radio antenna may be de ned as thestructure associated with the region oftransition between a guided wave & a freespace wave or vice versa.


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Basic equation of radiation

whereİ ! time"varying current A/sL! length of current element mQ! charge # ! acceleration of charge m/s$. s

%adiation is produced by time"changingcurrent & accelerated charges.

vQ L I = (A m / s)

v


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Basic Antenna ParametersRadiation patternsThey are 3-dimensional (3-D) quantities involvingvariation of field or power as a function of sphericalcoordinates θ & .

It determines the distri ution of radiated energy inspace.To represent radiation pattern on plain paper (in !-D)" across-section through middle of 3-D pattern is ta#en. It

are called principal plane pattern.$ower pattern P (θ, φ ) is proportional to square of thefield strength pattern E (θ, φ ).


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'attern parameters• Main beam or main obe ! t is the lobe containing the

ma imum radiation.• Minor obes ! *hey are all the lobes e cept the ma+or

lobes. *hey are formed of side & bac, lobes.i. Side obe ! t is the lobe that is in the hemisphere in

the direction of the main lobe.ii. Bac! obe ! t is the lobe in the opposite (bac,)

hemisphere of the main lobe.•. Nu s! 'laces between lobes where the eld goes to -ero.•. "a f Po#er Beam#idt$ ("PB% ) or ' dB

beam#idt$ ! t is the angular beamwidth at the half"power level or at the level where eld drops to . 0.

•. Beam#idt$ bet#een (rst nu s ()NB% or B%)N )! tis the angular beamwidth between the rst nulls on boththe sides of the main lobe.


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Norma i*ed or re ati+e (e d ,attern ! t is obtained bydividing a eld component by its ma imum value.

ma%)"()"(

)"( φ θ φ θ

φ θ θ θ

θ E E

E n = (dimensionless)

Norma i*ed ,o#er ,attern ! t is ratio of 'oynting vector(power per unit area) S (θ " ) to its ma imum value.

ma%)"()"(

)"(φ θ

φ θ φ θ

S S

P nn = (dimensionless)

!!

')"()"()"( Z E E S φ θ φ θ φ θ φ θ +=where (1/s$. m))"(log* * φ θ n P dB =n d2

ma imum values of normali-ed eld or power patterns are


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%adiation 'atterns


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Beam Area (or Beam So id An- e ) . A


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*he beam area or beam solid angle (3 A) of anantenna is given by the integral of the normali-ed

power pattern over a sphere (4 π sr).

φ θ θ φ θ π θ

θ

π φ

φ d d P n A sin)"(

!

∫ ∫ =

=

=

==Ω

also Ω=Ω ∫ ∫ d P n A π φ θ + )"( (sr)where φ θ θ d d d sin=Ω (sr)

Also HP HP A φ θ ≅Ω (sr)5'21s in two principal planes neglecting minor lo," HP HP φ θ


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21 or φ HP ! A-imuth beamwidth

21 6 or θ HP ! Elevation beamwidth


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Radiation Intensit/ (U )

t is the power radiated from an antenna perunit solid angle.

π φ θ

+)"( P

U = (1/sr or 1/s$.deg)

is related to normali-ed power pattern as

ma%ma% )"(

)"(

)"(

)"()"(

φ θ

φ θ

φ θ

φ θ φ θ

S

S

U

U P n ==

is independent of the distance from the antenna.

(dimensionless)


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Beam 01cienc/ (ε M ) *he total beam area Ω A ( or beam solid angle) consistsof the main beam area ΩM plus the minor"lobe area

Ωm.m M A Ω+Ω=Ω

*he ratio of the main beam area ( ΩM) to the total beamarea ( Ω A) is called the (main) beam e1cienc/ ε M.

A

M M Ω

Ω=ε (dimensionless)

*he ratio of the minor"lobe area ( Ωm ) to the total

beam area ( Ω A) is called the stra/ factor ε m .

A

mm Ω

Ω=ε (dimensionless)

7rom above relations *=+ m M ε ε


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Directi+it/ 2 D 3 *he directivity of an antenna is the ratio of

the ma imum power density P(6 )ma) to itsaverage value over a sphere as observed inthe far eld of an antenna.

av P P

D )"()"( ma%

φ θ φ θ

=t is a dimensionless ratio 8 9.

*he average power density over a sphere is given by

φ θ φ θ π

φ θ π θ

θ

π φ

φ

d d P P av sin)"(+*

)"(!

∫ ∫ =

=

=

==


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or

:o the directivity

)()(+

)"(+

+

sr sr

d P D

An Ω=Ω= ∫∫ π φ θ π π

Ω= ∫∫ d P P avπ

φ θ π

φ θ +

)"(+*

)"(

∫∫ ∫∫ Ω=

Ω=

π π φ θ φ θ π φ θ π

φ θ

+ma%

+

ma%

)"(')"()+'*(

*

)"()+'*(

)"(

d P P d P

P D

or


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*he smaller the beam area 3 A the larger thedirectivity D.

*he ideali-ed isotro,ic antenna radiates e$uallyin all the directions so its beam area . A 4 5 π sr .

ts directivity is

*+++

==Ω= π π π

A D

n decibels DdB D *log*)( =

e numerical value of D always lies between 6 and

(; d2)

is is the lowest possible directivity ( D ; 9) .

actual antennas have directivities greater than 9 (


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Alsoas

°°==Ω= HP HP HP HP A D

φ θ φ θ π π )(deg! 3"+*++

!

Appro imately°°=

HP HP

Dφ θ

)(deg&&&"+& !

HP HP A φ θ ≅Ω

hence


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=ain can be of following types!

9. 'ower =ain ( G p)@. irective =ain ( Gd)

9. Po#er 8ain ( G p )! t is the ratio ofradiation intensity in a given direction to theaverage total input power.

T T p P

U P U

G)"(+

+

)"( φ θ π

π

φ θ ==

*otal input power PT ; Pr + PlPr ! %adiated power

Pl ! Bhmic losses in antenna


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@. Directi+e 8ain (G d )! t is the ratio ofradiation intensity in a particular direction tothe average radiated power.

Gd does not depend upon the power input tothe antenna & its ohmic losses .

*he ma9imum +a ue of directi+e -ain ist$e directi+it/ D of the antenna.Also

r r d P

U P

U G

)"(+

+

)"( φ θ π

π

φ θ ==

d p GG η =

! E>ciency factor which lies between to 9


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Directi+it/ and Reso ution *he reso ution of an antenna may be de ned ase$ual to half the beamwidth between rst nulls.

!esolution/ntenna

FNBW =

lf the beamwidth between rst nulls is appro imatual to the half power beamwidth (5'21). :o

HPBW FNBW

≅!

ence product of 7C21/@ in the two principal planetenna pattern is the beam area. *hus

φ θ

=Ω!!

FNBW FNBW A


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Radiation Resistance 2 R r 3

t is the ctitious resistance which when substitutedin series with an antenna will consume the samepower as is actually radiated by the antenna.

7rom circuit point of view the antennasappear to the transmission lines as aresistance Rr called the radiation resistance.

t is a Dvirtual resistance that does not e ist physicallybut is a $uantity coupling the antenna to distantregions of space via a Dvirtual transmission line.


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Antenna A,erturen an antenna it concerns with the area utili-ed

for reception or radiation of EM waves.Recei+in- case ! #onsider a rectangular hornas receivingantenna placed in the eld of a uniform planewave.

Fet power density of plane wave be S

watts/m@

. @


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*otal power P absorbed from the wave by thehorn over its entire physical aperture is

Z A E

Z EA E HA E SA P p p p p

!

.. ====

as H E S ×= and H E

Z = or Z E

H =

(1atts)

:o tota ,o#er the horn e tracts from passingwave is ,ro,ortiona to t$e a,erture or area ofits mout$ ( A p).2ut the eld response of the horn is not uniform across the aperture A p as eld E atthe sidewalls must be -ero.:o the eGective aperture Ae of horn is less

than the physical aperture A p.


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*he ratio of eGective aperture Ae to the physicalaperture A p is called aperture e>ciency εap .

pap A

A=ε (dimensionless)

εap can have values from ; to 7 .

0


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iatin- case ! #onsider an antenna with Ae radiatints power in a conical pattern of beam area Ω A.

a A Z E

P !

= (1atts)

Assuming a uniform eld Ea over theaperture powerradiated is


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/ssuming a uniform field E r in the far field at a distancer " power radiated is also given y

0quating oth powers" we get

Ar r Z E

P Ω= !&

!

(1atts)

Ar a r Z E A Z E Ω=!

!!

2sing the relation E r E a A ! r" " we get aperture- eam

area relation

Ar a r E A E Ω= !!!or

A A Ω=!λ (m ! )

as" A

D

Ω= π + so" we get from last equation" !

+

λ

π A D =


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Recei+in- antenna ! EGective height can be

de ned in terms of induced voltage V andincident eld E.Holtage V induced in a receiving antenna is theproduct of its eGective height he (meters) & theincident eld E (H/m) of the same polari-ation.

0


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Transmittin- antenna ! n this case eGectiveheight e$uals the physical height # p (or length % )multiplied by the (normali-ed) average current I av.

d& & I I

# p#

∫ = )(*

or pav #

I I #

&

= (m)

EGective height is used for transmittingtower type antennas & small antennas.


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Re ation bet#een 0


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on solving

&

!!!

+ Z A E

R

E #

r

=

&! Z A R

# r

= r R Z #

A+

&!

=(m) and (m@

)

:o eGective height & eGective aperture arerelated via radiation resistance & intrinsicimpedance of free space.


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T$e Radio Communication =in!2)riis Transmission formu a3

*his formula gives the power received over aradio communication lin,.

Assuming transmitting antenna as isotropic the power per unit area available at receiving antenna is

!

+ r

P S ' r

π

=

f * t h i G th it


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f * antenna has gain G the power per unit areaavailable at receiving antenna will be increased inproportion as given by

!+ r

G P

S ' '

r π = *he power collected by lossless matchedreceiving antenna of eGective aperture Aer is

!+ r AG P AS P r ' ' r r r π

==

As!

+λ π '

' A

G = using in above relation gives

!! λ r A A

P P ' r

'

r = (dimensionless)

or!! λ r

A A P P ' r

' r = (1atts)


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Antenna e1cienc/ 2 η 3t is the ratio of the total power radiated by the

antenna to the total power fed to the antenna.

*otal input power P T P r ( P % Pr ! *otal radiated powerPl ! 'ower losses in antenna

T

r

P P =η (dimensionless)

Antenna e>ciency can have values from ; to 6 or from ; 0 to 6;; 0.


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Rr ! %adiation resistance 3 RT ! Antenna total resistance ( RT Rr 4 R% ) 3

R% ! Antenna loss resistance 3

'owers can be e pressed in terms of rms currents. :o

T

r

T rms

r rms

R

R

R I

R I == !!

η

% r

r

T

r

R R R

R R

+==η (dimensionless)or

5ence summari-ing for e>ciency

% r

r

T

r

T

r

d

p

R R

R

R

R

P

P

G

G

D

G

+=====η (dimensionless)


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Antenna band#idt$t is the range of fre$uency over which an antenna

maintains its certain re$uired characteristics li,egain radiation resistance polari-ation front tobac, ratio :1% impedance etc.

*! ω ω ω −=∆2andwidth

)ront to bac! ratio 2 FBR 3t is the ratio of power radiated in the front (desired)

direction through the main lobe to the power radiated

in the bac, (opposite) direction through the bac, lobes.

directionoppositeinradiated$owerdirectiondesiredinradiated$ower

56 =


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Sin- e to Noise Ratio 2SNR3

t is a measure of detection capability of a systemfor a signal.Fet a networ, be given an input electrical signalpossessing certain characteristics.

f this signal emerges out of the networ, (atoutput port) with some changes in thesecharacteristics (li,e variation in magnitude &phase) it is presumed that these variations can bedue to addition or subtraction of an unwantedsignal (called Dnoise ) introduced by the networ,itself.

*he ratio of the signal D ! fed to the networ, andthe noise D N is termed as s in- e to noise ratio2SNR3 .


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f the input signal is already mi ed with somenoise (i.e. ; ! " J N") the output obtained is furthermodi ed by the networ, (i.e. output ; ! # J N#).

:o a new parameter called Noise )i-ure F canbe de ned as

N S

SNR =

)

)

*

*

N S

N S

F =


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Antenna Tem,erature 2 T A 3

*he noise temperature T A of a lossless antenna

is e$ual to the s,y temperature T s and not thephysical temperature of antenna.7or a radio"telescope antenna the noise powerper unit bandwidth is given by

AkT p = (1/5-)T A is also the temperature of the antenna s radiation

resistance determined by the s,y temperature atwhich the antenna beam is directed.

Multiplying above e$uation by bandwidth B+

we obtain total power available as


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%eceived noise power per unit bandwidth isalso e pressed in terms of >u9 densit/ S as

BkT P A= (1)

A

AkT

A p

S == (1 m "@5- "9)

ork

SAT

A = (K)

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AWP Unit I Antenna Basics