Antenna Engineering for Ete(LPU)

7/23/2019 Antenna Engineering for Ete(LPU)

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Text Books:1. Antenna Theory, Balanis C.A, John Wiley & sons 2nd

edition Reprint 2008

2. Electromanetic and radiatin systems, Jordan E.C,

!"#., 2nd edition, 2008

$. Antennas, John % ra's & R J (arhe)*a $rd Edition,

2002.

+. Antenna and Wae !ropaation, .%. !rasad, -atya

!ra*ashan, $rd edition 200



CONTENTS Antennas

/'ndamental !arameters o) Antennas

Arrays

Apert're Antennas and Re)lector antenna

Radio Wae propaation



CONTENTS Antennas


Arrays

Apert're, "orn and Re)lector antennas




ATEA-

#ntrod'ction

Types o) Antenna

Radiation (echanism

!hysical concept o) Radiation in sinle ire, to ire

and dipole

C'rrent %istri'tion on a Thin Wire Antenna



#TR3%4CT#3

Antenna or Aerial 5

6 is a transd'cer that transmits or receies

electromanetic aes

6 conerts the oltae and c'rrent into the

electromanetic radiation and ice6ersa

6 is a transitional str'ct're eteen )ree6space and a

'idin str'ct're

6 The American "eritae %ictionary5 A metallic

apparat's )or sendin and receiin electromanetic

aes. 6 Wester7s %ictionary5 A 's'ally metallic deice as a

rod or ire9 )or radiatin or receiin radio aes



#TR3%4CT#3

What is an Antenna:

An antenna is a deice )or radiatin and receiin radioaes. The antenna is the transitional str'ct're eteen)ree6space and a 'idin deice.



#TR3%4CT#3 A transmission6line Theenin e;'ialent o) the antenna

system



#TR3%4CT#3 A transmission6line Theenin e;'ialent o) the antenna

system



.

#TR3%4CT#3

.



.

#TR3%4CT#3



Antennas

#ntrod'ction

Types o) Antenna

Radiation (echanism

!hysical concept o) Radiation in sinle ire, to ire




T<!E- 3/ ATEA-

Wire antennas

Apert're antennas

(icrostrip antennas

Array antennas

Re)lector antennas=ens antennas



Wire antennas seen irt'ally eeryhere6 on a'tomoile,

'ildin, ships, aircra)t, and so on.-hapes o) ire antennas5

straiht ire dipole9, loop circ'lar9, and heli>,

=oop antenna may ta*e the shape o) a rectanle ,

ellipse or any other shape con)i'ration



15

Aperture-antenna

ote5 The apert're concept is applicale also to ired antennas.

/or instance, the ma> e))ectie apert're o) linear λ?2

aelenth dipole antenna is λ2?8

EM wave

Power

absorbed: P [watt]Effective

aperture: A[m2]

@ Apert're antennas deried

)rom ae'ide technoloy

circ'lar, rectan'lar9

@ Can trans)er hih poer

manetrons, *lystrons9

4tiliation o) hiher)re;'encies

Applications: aircraft, and spacecraft



Microstrip antenna consist o) metallic patch on a ro'nded s'strate

E>amples5 rectan'lar and circ'lar shape Applications5 aircra)t, spacecra)t, satellite, missiles,

cars etc

RECTANGLE

CIRCLE



atc!

Antennas

Radiation is )rom to slots on le)t and riht edes o) patch here slot is

reion eteen patch and ro'nd plane

=enth λd D λο?εr 1?2 Thic*ness typically 0.01 λο

The i adantae is con)ormal, i.e. )lat, shape and lo eiht

%isadantaes5 =o ain, arro andidth oercome y )ancy shapes and

other heroic e))orts9, Becomes hard to )eed hen comple>, e.. )or ide

and operation



atc! Antenna attern



Arra" antennasa collection o) simple antennas

6 ies desire d radiation characteristics

6 The arranement o) the array may e s'ch that the radiation )rom

the elements adds 'p to ie a radiation ma>im'm in a partic'lar

direction or directions, minim'm in others, or otherise as desired

6 Examples: yai6'da array, apert're array, microstrip patch array,

slotted ae'ide array



Arra" o# patc!

Antennas



Re$ector

antennas

6 'sed in order to transmit and receie sinals that had to trael

millions o) miles

6 A ery common re)lector antenna F paraolic re)lector



ara%o&ic

Re$ectors

A paraolic re)lector operates

m'ch the same ay a re)lectintelescope does

Re)lections o) rays )rom the)eed point all contri'te inphase to a plane ae leainthe antenna alon the antennaore siht a>is9

Typically 'sed at 4"/ andhiher )re;'encies



Lens antennas@ lenses are primarily 'sed to collimate incident dierent enery to

preent it )rom spreadin in 'ndesired directions

@ Trans)orm ario's )orms o) dierent enery into plane aes

@ 4sed in most o) applications as are the paraolic re)lectors,

especially at hiher )re;'encies. Their dimensions and eiht

ec0me e>ceedinly lare at loer )re;'encies.



'(

=enses play a similar role to that o) re)lectors in re)lector antennas5

they collimate dierent enery3)ten pre)erred to re)lectors at )re;'encies G 100 H".



Antennas

#ntrod'ction

Types o) Antenna

Radiation (echanism

!hysical concept o) Radiation in sinle ire, to ire and dipole




PHYSICAL CONCEPT OFRADIATION

or RADIATIONMECHANISM

How is Radiation Accomplished?

Principle of radiationWhen electric chares 'ndero acceleration or deceleration,

electromanetic radiation ill e prod'ced. "ence it is the

motion o) chares i.e., c'rrents9 that is the so'rce o) radiation

basic equation of radiation

IL !"

#here

#time aryin c'rrent

Ichare

=lenth o) c'rrent element

time chane o) elocity

Radiation $echanism in a% &in'le wire, b% (wo wire and c% )ipole



Radiation $echanism

&in'le wire:

Cond'ctin ires are characteried y the motion o) electric chares and the

creation o) c'rrent o. Ass'me that an electric ol'me chare density, ;, co'loms?m$9, is

distri'ted 'ni)ormly in a circ'lar ire o) cross6sectional area A and ol'me K

;, 6 ol'me chare density

A6 cross6sectional area

K6Kol'me



Radiation $echanism&in'le wire:

#nstead o) e>aminin all three c'rrent densities, e ill primarily

concentrate on the ery thin ire.

The concl'sions apply to all three. #) the c'rrent is time aryin.



Radiation $echanism



Radiation $echanism

(hin wire



Radiation $echanism&in'le wire:



Radiation $echanism(wo*#ires:

@ Applyin a oltae across the to6cond'ctor transmission line

creates an electric Leld eteen the cond'ctors. @ The moement o) the chares creates a c'rrent that in t'rn

creates a manetic Leld intensity.

@ The creation o) time6aryin electric and manetic Lelds eteen

the cond'ctors )orms electromanetic aes hich trael alon

the transmission line.




@ The electromanetic aes enter the antenna and hae

associated ith them electric chares and correspondin c'rrents.

@ #) e remoe part o) the antenna str'ct're, )ree6space aes can

e )ormed y connectin the open ends o) the electric lines




@ #) the initial electric dist'rance y the so'rce is o) a short d'ration, the created

electromanetic aes trael inside the transmission line, then into the antenna,

and Lnally are radiated as )ree6space aes, een i) the electric so'rce hasceased to e>ist.

@ #) the electric dist'rance is o) a contin'o's nat're, electromanetic aes

e>ist contin'o'sly and )ollo in their trael ehind the others.

@ "oeer, hen the aes are radiated, they )orm closed loops and there are no

chares to s'stain their e>istence.

@ Electric chares are re;'ired to e>cite the Lelds 't are not needed to s'stain

them and may e>ist in their asence.



Radiation $echanism)ipole Antenna:

A radio antenna that can e made o) a simple ire, ith a centre6)ed

drien element

Consist o) to metal cond'ctors o) rod or ire, oriented parallel and

collinear ith each other in line ith each other9, ith a small space

eteen them.

Consider the e>ample o) a small dipole antenna here the

time o) trael is neliile



Radiation $echanism /ormation and detachment o) electric )ield line )or short %ipole Antenna

)ipo&e



)ipo&e

C t )i t i% ti t!i i



Current )istri%ution on a t!in *ireantenna=et 's consider the eometry o) a lossless to6ire

transmission line

The moement o) the chares creates a traelin ae

c'rrent, o) manit'de #0 ?2, alon each o) the ires.

When the c'rrent arries at the end o) each o) the ires,

it 'nderoes a complete re)lection e;'al manit'de and

180 phase reersal9

The re)lected traelin ae, hen comined ith the

incident traelin ae, )orms in a each ire a p're

standin ae pattern o) sin'soidal )orm.




Current )istri%ution on a t!in *ireantenna




Current )istri%ution on a t!in *ireantenna

/or the to6ire alanced symmetrical9 transmission line, thec'rrent in a hal)6cycle o) one ire is o) the same manit'de 't 180

o't6o)6phase )rom that in the correspondin hal)6cycle o) the

otherire

Current )istri%ution on a t!in *ire



Current )istri%ution on a t!in *ireantenna #) s is also ery small, the to )ields are canceled

The net res'lt is an almost ideal, non6radiatin transmission line.

When the line is )lared, eca'se the to ires o) the )lared section

are not necessarily close to each other, the )ields do not cancel each

other

There)ore ideally there is a net radiation y the transmission linesystem




Current )istri%ution on a t!in *ireantennaWhen the line is )lared into a dipole, i) s not m'ch less than M, the

phase o) the c'rrent standin ae pattern in each arm is the same

thro'h o't its lenth. #n addition, spatially it is oriented in the same

direction as that o) the other arm

Th's the )ield s radiated y the to arms o) the dipole ertical parts

o) a )lared transmission line9 ill primarily rein)orce each other

toard most directions o) oseration




Current )istri%ution on a t!in *ireantennaThe c'rrent distri'tions e hae seen represent the ma>im'm

c'rrent e>citation )or anytime. The c'rrent aries as a )'nction o)

time as ell.



CONTENTS Antennas

+undamental Parameters of Antennas

Arrays






+undamental Parameters of Antennas #ntrod'ction

Radiation !attern

Radiation !oer %ensity

Radiation intensity

%irectiity, Hain, Antenna e))iciency, Beamidth

Bandidth

=inear, circ'lar, and elliptical polariation

!olariation loss )actor and e))iciency Antenna #np't #mpedance

Elementary idea ao't sel) and m't'al impedance

Radiation e))iciency

E))ectie apert're, Antenna Temperat're

(E&(*

, &-llabus upto here





Radiation !attern


Radiation intensity


Bandidth

!olariation, =inear, circ'lar, and elliptical polariation





(E&(*


#ntrod'ction



#ntrod'ction

To descrie per)ormance o) an antenna

%e)inition o) ario's parameters





Radiation !attern


Radiation intensity


Bandidth






(E&(*


Radiation pattern



Radiation pattern

(athematical )'nction or Hraphical representation o) radiation properties

o) an antenna as a )'nction o) space coordinates. Radiation properties

incl'de poer )l'> density, radiation intensity, )ield strenth, directiity,phase or polariation.

Radiation pattern 's'ally indicate either electric )ield intensity or poer

intensity. (anetic )ield intensity has the same radiation pattern as the

electric )ield intensity

A directional antenna radiates and receies pre)erentially in some

direction

%epicted as to or three6dimensional spatial distri'tion o) radiated

enery as a )'nction o) the oserer7s position alon a path or s'r)ace o)constant radi's

=oes are classi)ied as5 maNor, minor, side loes, ac* loes

Radiation pattern



Radiation pattern

Coordinate system )or antenna analysis

Radiation pattern



Radiation pattern

/or an antenna

(he +ield pattern.in linear scale%:

typically represents a plot o) the manit'de o) the electric or manetic )ield as a )'nction o) the an'lar space.

(he Power pattern.in linear scale%:

typically represents a plot o) the s;'are o) the manit'de o) the electric or manetic )ield as a )'nction o) the

an'lar space

(he Power pattern.in d/%:

represents the manit'de o) the electric or manetic )ield, in deciels, as a )'nction o) the an'lar space.

Radiation pattern



Radiation pattern

Radiation pattern



Radiation pattern

ario's parts o) a radiation pattern are re)erred to as a loes

Total electric )ield

is ien as

Three dimensional polar pattern

Radiation pattern



Radiation pattern

ario's parts o) a radiation pattern are re)erred to as a loes

To dimensional polar pattern

Radiation pattern lobes



p

Kario's parts o) a radiation pattern are re)erred to as lobes

$a0or lobe .main lobe%:

The radiation loe containin the direction o) ma>im'm radiation

(aNor loe is pointin at OD0 direction in )i're #n spilt6eam antennas, there may e>ist more than one maNor

loes

$inor Lobe

is any loe e>cept a maNor loe

all the loes e>ception o) the maNor loe

&ide lobe5 a radiation loe in any direction other than intended loe

4s'ally it is adNacent to main loe

/ac1 lobe:

a radiation loe hose a>is ma*es an anle o) appro>imately

1800 ith respect to the eam o) antenna

's'ally it re)ers to a minor loe that occ'pies the hemisphere in

a direction opposite to that o) maNor loe





Radiation !attern


Radiation intensity


Bandidth






(E&(*






!oyntin Kector or !oer density9

The instantaneo's poyntin ector descrie the poer

associated ith electromanetic ae

!oyntin ector de)ined as

W D E x +

W6 instantaneo's poyntin ector W?m29

E6 instantaneo's electric )ield intensity K?m9

+- instantaneo's manetic )ield intensity A?m9




Radiation !oer %ensityThe total poer crossin a closed s'r)ace can e otained y

interatin the normal component o) poyntin ector oer the entire

s'r)ace.

pD instantaneo's total poer W9

Pn D 'nit ector normal to the s'r)ace da D in)initesimal are a o) the closed s'r)ace m2 9

e de)ine the comple> )ields E and " hich are related to their

instantaneo's co'nter parts E and + y




Radiation !oer %ensity identity

W D E x + , The )irst term o) is not a )'nction o) time, and the time ariations o) the

second are tice the ien )re;'ency.

Aerae !oer %ensity5

The aerae poer density is otained y interatin the

instantaneo's !oyntin ector oer one period and diidiny the period.

WaD the real part o) represents the aerae real9 poer density the imainary

part ('st represent the reactie stored9 poer density associated ith the

electromanetic )ields




Radiation !oer %ensity The aerae poer radiated y an antenna radiated poer9

can e ritten as

Radian and -teradian



A radian is de)ined ith the 'sin /i're a9

#t is the anle s'tended y an arc alon the

perimeter o) the circle ith lenth e;'al tothe radi's.

A steradian may e de)ined 'sin /i're 9

"ere, one steradian sr9 is s'tended y an

area r 2 at the s'r)ace o) a sphere o) radi's r.

The in)initesimal area dA on the s'r)ace o)

radi's r is de)ined as

dA Dr 2 sinO dO dϕm29

A di))erential solid anle, dΩ, in sr, is ien

y

dQ D dA?r 2 D sinO dO dϕsr9

Q D sinO dO dϕ

4nit o) plane Anle is a radian

4nit o) -olid Anle is a steradian

#sotropic antenna



#sotropic antenna Isotropic antenna or isotropic radiator or

isotropic source or omnidirectional radiator

or simple unipole

is a hypothetical not physically realiale9

lossless antenna hain e;'al radiation in all

directions

'sed as a 'se)'l re)erence antenna to

descrie real antennas.

#ts radiation pattern is represented y a

sphere o) radi's r9 hose center coincides

ith the location o) the isotropic radiator.

All the enerypoer9 m'st pass oer the

s'r)ace area o) sphereD+r 2

#sotropic antenna



#sotropic antenna!oyntin ector or poer density9 at any point on the sphere

poer radiated per 'nit area in any direction

The manit'de o) the poyntin ector is e;'al to the radial componentonlyeca'se pO D pSD09

Dr

The total radiated poer

!Trad D .ds

D r .ds

D r ds

D r +r 2

or r D !Trad ?+r 2 att?m2

here

Wr radiated poer o) aerae poer density

!Trad total poer radiated

#sotropic antenna



#sotropic antennaThe total poer radiated y it is ien y5

The poer density is ien y5

hich is 'ni)ormly distri'ted oer the s'r)ace o) a sphere o) radi's r.

#sotropic antenna



#sotropic antenna

)irectiona&



)irectiona&antennais an antenna, hich radiates or receies9 m'ch more

poer in or )rom9 some directions than in or )rom9 others

2ote:

4s'ally, this term is applied to antennas hose

directiity is m'ch hiher than that o) a hal)6ae dipole

rincipa&



/or linearly polaried antenna per)ormance is o)ten descried

in terms o) its principal E6and "6!lane patterns

E* Plane : the plane containin the electric )ield ector and the

ma>im'm radiationH* Plane : the plane containin the manetic )ield ector and the

ma>im'm radiation x-/ e&e0ation p&ane contain principa& E-p&ane

x-" a/iut!a& p&ane contain principa& +-p&ane

rincipa&atterns

Principal E and H plane pattern for a pyramidal horn antenna

2ie&3



The space s'rro'ndin an antenna is 's'ally s'diided into three

reions5

2ie&3Re4ions

2ie&3



The space s'rro'ndin an antenna is 's'ally s'diided into threereions5

Reacti"e near*field re'ion:That portion o) the near6)ield reion

immediately s'rro'ndin the antenna herein the reactie )ieldpredominates.

Radiatin' near*field .+resnel% re'ion:That reion o) the )ield o) anantenna eteen the reactie near6)ield reion and the )ar6)ieldreion herein radiation )ields predominate and herein the an'lar

)ield distri'tion is dependent 'pon the distance )rom the antenna+ar*field .+raunhofer% re'ion:That reion o) the )ield o) an antenna

here the an'lar )ield distri'tion is essentially independent o) thedistance )rom the antenna.

Re4ions

2ie&3



The space s'rro'ndin an antenna is 's'ally s'diided into threereions5

Re4ions




#ntrod'ction

Radiation !attern


Radiation intensity


Bandidth






(E&(*


Radiation #ntensity



Radiation intensity in a ien direction is de)ined as the poer radiated

)rom an antenna per 'nit solid anle.

4 D !rad? d U Where

!radradiated poer

UD d U solid anel

The radiation intensity is a )ar6)ield parameter, and it can e otained y

simply m'ltiplyin the radiation density y the s;'are o) the distance.

4 D r 2Wrad

Wrad F radiation density W?m29

r F distance m9

4 6 radiation intensity W? 'nit solid anle9

y

Radiation #ntensity



The radiation intensity is also related to the )ar6one electric )ield o)an antenna, y

The total poer is otained y interatin the radiation intensity,oer the entire solid anle o) +. Th's

y

Radiation #ntensity



Radiation patterns may e )'nctions o) oth spherical coordinateanles O and S

=et the radiation intensity o) an antenna e o) the )orm

The ma>im'm al'e o) radiation intensity

The total radiated poer is )o'nd 'sin

y




#ntrod'ction

Radiation !attern


Radiation intensity


Bandidth






(E&(*


)irecti"it-%irectiity %95



%irectiity %95 the ratio o) the radiation intensity in a ien direction )rom the antenna to the

radiation intensity aeraed oer all directions

the directiity o) a nonisotropic so'rce is e;'al to the ratio o) its radiation intensity in

a ien direction oer that o) isotropic so'rce

The aerae radiation intensity 409 is e;'al to the total poer radiated y the

antenna diided y +π.

#) the direction is not speci)ied, it implies the direction o) ma>im'm radiation intensityma>im'm directiity9 e>pressed as

4 D radiation intensity W?'nit solid anle9

4ma> D ma>im'm radiation intensity W?'nit solid anle9

40D radiation intensity o) isotropic so'rce W?'nit solid anle9

!rad D total radiated poer W9

% D directiitydimensionless9

%0D ma>im'mdirectiitydimensionless9

)irecti"it-The eneral e>pression )or the directiity and ma>im'm



The eneral e>pression )or the directiity and ma>im'm

directiity %09 'sin

%irectiity



y

( ) ( )

( )

,,

,

n

n avg

P

P D

θ φ θ φ

θ φ =

The directive gain,, o) an antenna is the ratio o) the

normalied poer in a partic'lar direction to theaerae normalied poer, or

( ) ( )

( )max

max max

,

,,

n

n avg

P D D

P

θ φ

θ φ θ φ = =

The directivity, Dmax , is the ma>im'm directie ain,

max

4

p

D π =

Ω

%irectie ain

( ) ( ),

,4

n p

n avg

P d P

d

θ φ θ φ

π

Ω Ω= =

Ω

∫ ∫ ∫ ∫

Where the normalied poer7s aerae al'e ta*enoer the entire spherical solid anle is

( )max

1,n P θ φ =4sin

)irecti"it-Partial )irecti"it- of antenna:



Partial )irecti"it- of antenna:

!artial directiity o) an antenna )or a ien polariation in a ien direction as

that part o) the radiation intensity correspondin to a ien polariation

diided y the total radiation intensity aeraed oer all directions.

With this de)inition )or the partial directiity, then in a ien direction

the total directiity is the s'm o) the partial directiities )or any to

orthoonal polariations

/or a spherical coordinate system, the total ma>im'm directiity %0 )or theorthoonal O and S components o) an antenna can e ritten as

While the partial directiities %O and %S are e>pressed as

)irecti"it-)irectional Patterns:



)irectional Patterns:

#n /i're2.1+a9. /or a rotationally symmetric pattern, the hal)6poer eam idths in any

to perpendic'lar planes are the same, as ill'strated in /i're2.1+9.With this appro>imation, ma>im'm directiity can e appro>imated y

)irecti"it-)irectional Patterns:



)irectional Patterns:

With this appro>imation, ma>im'm directiity can e appro>imated y




#ntrod'ction

Radiation !attern


Radiation intensity


Bandidth


!olariation loss )actor and e))iciency

Antenna #np't #mpedance




(E&(*


Antenna Hain



The ratio o) the intensity, in a ien direction, to the radiation

intensity that o'ld e otained i) the poer accepted y the

antenna ere radiated isotropically

The radiation intensity correspondin to the isotropically

radiated poer is e;'al to the poer accepted inp't9 y the

antenna diided y +

#n e;'ation )orm this can e e>pressed as

Antenna Hain



the ratio o) the !oer ain in a ien direction to the poer

ain o) a re)erence antenna in its re)erenced direction

The poer inp't m'st e the same )or oth antennas

(ostly Re)erence antenna is a lossless isotropic so'rce. Th's

When the direction is not stated, the poer ain is 's'ally ta*en in the

direction o) ma>im'm radiation.

We can rite that the total radiated poer related to the total inp't

poer

Antenna Hain



Antenna Hain



!artial ain o) an antenna

/or a ien polariation in a ien direction

Total ain

Antenna Hain



Antenna Hain

Relationship eteen antenna ain and e))ectie area

G D antenna ain

Ae D e))ectie area f D carrier )re;'ency

c D speed o) liht $>108 m?s9

λ D carrier aelenth

2

2

2

44

c

A f AG ee π

λ

π ==

+undamental Parameters of Antennas # t d ti



#ntrod'ction

Radiation !attern


Radiation intensity


Bandidth







(E&(*


Antenna



Ecienc"#n eneral, the oer all

E))iciency can e ritten as

Ra3iation Resistance 6 Antenna



Ecienc"Radiation resistance Rrad9 is a )ictitio's resistance,

s'ch that the aerae poer )lo o't o) the antenna is!a, D 1?29 #2 Rrad

4sin the e;'ations )or o'r short "ertian9 dipole e )ind that

Rrad D 80 π2 l?λ92 ohms

Antenna E))iciency

εo D Rrad?RradV Rloss9

here Rloss ohmic losses as heat

@ Hain D εo> %irectiity

H D εo %

+undamental Parameters of Antennas # t d ti



#ntrod'ction

Radiation !attern


Radiation intensity


Bandidth







(E&(*


Bea*i3t



! Half*power beamwidth "!BW9 O"9

is the anle eteen to ectors )rom the pattern7s oriin to the

points o) the maNor loe here the radiation intensity is hal) itsma>im'm

3)ten 'sed to descrie the antenna resol'tion properties

#mportant in radar technoloy, radioastronomy, etc.

!oer pattern o) 4O9D

+irst*null beamwidth /BW9 O9

is the anle eteen to ectors, oriinatin at the pattern7s oriin

and tanent to the main eam at its ase.

3)ten /BW 2"!BW

Beam e))iciency



To N'de the ;'ality o) transmittin and receiin antennas

#) O1 is chosen as the anle here the )irst n'll or minim'm

occ'rs, then the eam e))iciency ill indicate the amo'nt o)

poer in the maNor loe compared to the total poer.




#ntrod'ction

Radiation !attern


Radiation intensity


Bandidth







(E&(*


Bandwid



th/andwidth: the rane o) )re;'encies ithin hich the per)ormance o)

the antenna, ith respect to some characteristic, con)orms to a

speci)ied standard

/or roadand antennas, the andidth is 's'ally e>pressed as theratio o) the 'pper6to6loer )re;'encies o) acceptale operation

/.E. 1051 andidth indicates that the 'pper )re;'ency is 10 times

reater than the loer

/or narroand antennas, the andidth is e>pressed as a

percentae o) the )re;'ency di))erence 'pper min's loer9 oer the

center )re;'ency o) the andidth

/.E. a XY andidth indicates that the )re;'ency di))erence o)

acceptale operation is XY o) the center )re;'ency o) the

andidth

ain, side loe leel,eamidth,

polariation, andeam direction

Pattern

bandwidth

inputipe3ancean3 ra3iationecienc"

Ipe3ance%an3*i3t!




#ntrod'ction

Radiation !attern


Radiation intensity


Bandidth






(E&(*


Polarizati



onPolari3ation of an antenna:

the polariation o) the ae transmitted radiated9 y the antenna

When the direction is not stated, the polariation is ta*en to e

the polariation in the direction o) ma>im'm ain

!olariation o) the radiated enery aries ith the direction )rom

the center o) the antenna, so that di))erent parts o) the pattern

may hae di))erent polariations

!olariation may e classi)ied as linear, circ'lar, or elliptical

Polarizati



onPolari3ation of a radiated wa"eis de)ined as that property o) an electro manetic ae

descriin the time aryin direction and relatie manit'de o)the electric6)ield ectorZ speci)ically, the )i're traced as a

)'nction o) time y the e>tremity o) the ector at a )i>ed location

in space, and the sense in hich it is traced, as osered alon

the direction o) propaation.

!olariation then is the c're traced y the end point o) the

arro ector9 representin the instantaneo's electric )ield. The

)ield m'st e osered alon the direction o) propaation. A

typical trace as a )'nction o) time is shon in /i're

Polarization of EM Wa!"



Cloc*ise rotation o) the E ectorD riht6hand polariation

co'ntercloc*ise rotation o) the E ector D le)t6hand

polariation

Polarization of EM Wa!"



"oriontal polariation

Kertical polariation

Circ'lar polariation

RC!9

Circ'lar polariation

=C!9

Wa!"



AR: The ratio o) the maNor a>is to the minor a>is is re)erred to as the a>ial ratio AR9

,and it is e;'al to






#ntrod'ction

Radiation !attern


Radiation intensity


Bandidth






(E&(*


o ar za on oWa!"



The instantaneo's )ield o) a plane ae, traelin in the

neatie z direction:

#nstantaneo's components are related to their comple>co'nterparts y

here E xo and E yo are, respectively, the maximum magnitudesof the x and y components.

Lin!ar Polarization#



A time6harmonic ae is linearly polaried at a ien point in

space i) the electric6)ield or manetic6)ield9 ector at that point

is alays oriented alon the same straiht line at eery instanto) time.

This is accomplished i) the )ield ector electric or manetic9

possesses5

3nly one component, or

To orthoonal linear components that are in time phase or 180[

or m'ltiples o) 180[9 o't6o)6phase.

the time6phase di))erence eteen the to components m'ste

n!ar $ %o ar z! % an!wa!"



)ta!

)"cose)"cose

#

#1

2

#

2

#

##

x

y

y x

y y x x

E

E

E E E E

kz t E kz t E E

−=

+==

−+−=

θ

@ Any to orthoonal plane aes

Can e comined into a linearly

!olaried ae.

@Conersely, any aritrary linearly

polaried ae can e resoled

into to independent 3rthoonal

plane aes that are in phase.

\261X]




t od'ct o

Radiation !attern


Radiation intensity


Bandidth

!olariation, =inear , circ'lar , and elliptical polariation





(E&(*, &-llabus upto here

Cir&'lar Polarization#



A time6harmonic ae is circ'larly polaried at a ien point inspace i) the Electric or manetic9 )ield ector at that point traces

a circle as a )'nction o) time

The necessary and s'))icient conditions to accomplish this are i)the )ield ector electric or manetic9 possesses all o) the)olloin5

a. The )ield m'st hae to orthoonal linear components,and

. The to components m'st hae the same manit'de, and

c. The to components m'st hae a time6phase di))erence o)odd m'ltiples o) ^0[.

Cir&'lar4i l P l i ti



Cir&'larPolarization#

4ircular Polari3ation:

manit'des o) the to

components are same

the time6phase di))erence eteen

components is odd m'ltiples o)

_?2

Cir&'lar Polariz!d wa!#



po$ari%edcircu$ar$&$eft:' po$ari%ed,circu$ar$&ri(t:

2 * :o! po$ari%ati+ircu$ar ###

+

±=== π

δ E E E y x\261`]

3ptical /ier comm'nications, $rd ed.,H.eiser,(cHra"ill, 2000




Radiation !attern


Radiation intensity


Bandidth







Elli%ti&al Polarization#A ti h i i lli ti ll l i d i) th ti



A time6harmonic ae is elliptically polaried i) the tip

o) the )ield ector electric or manetic9 traces an

elliptical loc's in space.

At ario's instants o) time the )ield ector chanes

contin'o'sly ith time at s'ch a manner as to

descrie an elliptical loc's.

#t is riht6hand cloc*ise9 elliptically polaried i) the

)ield ector rotates cloc*ise, and it is le)t6hand

co'ntercloc*ise9 elliptically polaried i) the )ieldector o) the ellipse rotates co'ntercloc*ise

Elli%ti&al Polarization#manit'des o) the to components are 3T same the



manit'des o) the to components are 3T same the

time6phase di))erence eteen components is odd

m'ltiples o) _?2

3r hen the time phase di))erence eteen the to

components is not e;'al to m'ltiples o) _?2

irrespectie o) their manit'des9

Elli%ti&al Polarization#The necessary and s'))icient conditions



The necessary and s'))icient conditions

The )ield m'st hae to orthoonal linear components, and

The to components can e o) the same or di))erent

manit'de

19 #) the to components are not o) the same manit'de, thetime6phase di))erence eteen the to components m'st not

e 0 or m'ltiples o) 180 eca'se it ill then e linear 9.

29#) the to components are o) the same manit'de, the time6

phase di))erence eteen the to components m'st not e

odd m'ltiples o) ^0 eca'se it ill then e circ'lar 9.

Ellipticall- Polari3ed plane wa"es



2

#

2

#

##

2

##

2

#

2

#

#

cos2)2ta!

si!cos2

)"cose)"cose

Eee

y x

y x

y

y

x

x

y

y

x

x

y x x

y y x x

E E

E E

E

E

E

E

E

E

E

E

kz t kz t E

E E

−=

=

−

+

+−+−=

+=

δ α

δ δ

δ

\261]

Polarization(-pical Applications



(-pical Applications

Kertical polariation is most commonly 'sed hen it is

desired to radiate a radio sinal in all directions oer ashort to medi'm rane.

"oriontal polariation is 'sed oer loner distances to

red'ce inter)erence y ertically polaried e;'ipmentradiatin other radio noise, hich is o)ten predominantly

ertically polaried.

Circ'lar polariation is most o)ten 'sed in satellitecomm'nications.




Radiation !attern


Radiation intensity %irectiity, Hain, Antenna e))iciency, Beamidth

Bandidth







o ar za on o"" a& orE)&i!n&$



4s'ally, polariation o) the receiin antenna polariation o)

the incomin incident9 aepolariation mismatch.

The amo'nt o) poer e>tracted y the antenna )rom the

incomin sinal ill not e ma>im'm eca'se o) the

polariation loss

Ass'min that the electric )ield o) the incomin ae can e

ritten as

unit 0ector o#t!e *a0e

E)&i!n&$



!olariation o) the electric )ield o) the receiin

antenna

!olariation loss )actor !=/9

an4&e %et*een t!et*o unit 0ectors

E)&i!n&$

Polari3ation efficienc-



Polari3ation efficienc-

= Polarization mismatch = loss factor :

the ratio o) the poer receied y an antenna )rom a ien

plane ae o) aritrary polariation to the poer that o'ld e

receied y the same antenna )rom a plane ae o) the same

poer )l'> density and direction o) propaation, hose state o)

polariation has een adN'sted )or a ma>im'm receied poer

E)&i!n&$ *Cont+,

!=/ )or transmittin and receiin apert're antennas



!=/ )or transmittin and receiin apert're antennas

E)&i!n&$



!=/ )or transmittin and receiin linear ire antennas




Radiation !attern



Bandidth








-od!,I i d



Input impedance5the impedance presented y an antenna at its terminals or

the ratio o) the oltae to c'rrent at a pair o) terminals or the ratio o) the appropriate components o) the electric to

manetic )ields at a point

We are primarily interested in the inp't impedance at the inp't terminalso) the antenna

In%'t I-%!dan&!

R ti ) th lt t t t th t i l ith l d



Ratio o) the oltae to c'rrent at these terminals, ith no load

attached, de)ines the impedance o) the antenna as

In%'t I-%!dan&!

A th t th t i tt h d t t ith



Ass'me that the antenna is attached to a enerator ith

internal impedance

We can )indthe amo'nt o) poer deliered to ! r for radiation "y

the amo'nt o) poer dissipated in ! # as heat "y

In%'t I-%!dan&!C t d l d ithi th l i



C'rrent deeloped ithin the loop is

In%'t I-%!dan&!( it d ) t d l d ithi th l i



(anit'de o) c'rrent deeloped ithin the loop is

The poer deliered to the antenna )or radiation is ien y

and that dissipated as heat y

In%'t I-%!dan&!The remainin poer !9 is dissipated as heat on the



internal resistance R and it is ien y

The ma>im'm poer deliered to the antenna occ'rs hen

e hae conN'ate matchin

/or this case

In%'t I-%!dan&! /rom e;'ations 26819F268$9, #t is clear that



The poer s'pplied y the enerator d'rin conN'ate

matchin is

Mod!



The incident ae impines 'pon the antenna, and it

ind'ces a oltae $ %

All the )orm'lation is same as the transmittin mode N'st

replace s'script ith T9

Mod!4nder conN'ate matchin



!oers deliered to Rr ,R= ,and RT are ien, respectiely,

y

While the ind'ced collected or capt'red9 is

4nder conN'ate matchin o) the total poer collected or capt'red !c9 hal) is

deliered to the load RT and the other hal) is scattered or reradiated thro'h Rr

and dissipated as heat thro'h R=


Radiation !attern



Radiation !attern



Bandidth









Radiation !attern



Radiation !attern



Bandidth








Ant!nna Radiation E)&i!n&$

R th t t ))i i th t t * i t t th



Rememer that antenna e))iciency that ta*es into acco'nt the

re)lection, cond'ction, and dielectric losses

The cond'ction and dielectric losses o) an antenna are ery

di))ic'lt to comp'te

Een ith meas'rements, they are di))ic'lt to separate and theyare 's'ally l'mped toether to )orm the ecd efficiency.

The resistance ! # is used to represent the conduction&dielectric

losses

Ant!nna Radiation E)&i!n&$



power deli"ered to the radiation resistance

the power deli"ered to Rr and RL

4onduction*dielectric efficienc-

here

Rr Radiation Resistance

R= =oss Resistance


Radiation !attern



Radiation !attern



Bandidth








Equi"alent areasWith each antenna, e can associate an 'mer o) e;'ialent areas.



These are 'sed to descrie the poer capt'rin characteristics o) the

antenna hen a ae impines on it

Effecti"e area .aperture% Ae

&catterin' area .aperture% As

loss area .aperture% AL

4apture area .aperture% Ac

Effecti"e area .Aperture% Ae

the ratio o) the aailale poer at the terminals o) a receiin antenna

to the poer )l'> density o) a plane ae incident on the antenna )rom

that direction, the ae ein polariation matched to the antenna. #)

the direction is not speci)ied, the direction o) ma>im'm radiation

intensity is implied.

Equi"alent areas

Effecti"e area Ae



Effecti"e area Ae

The e))ectie apert're is the area hich hen m'ltiplied y

the incident poer density ies the poer deliered to the

load

Equi"alent areas

Effecti"e area Ae



ect e a ea e

4nder conN'ate matchin

The ma>im'm e))ectie area Aem

Equi"alent areas

(he scatterin' area As



' s

is de)ined as the e;'ialent area hen m'ltiplied y the

incident poer density is e;'al to the scattered orreradiated poer.


As

Equi"alent areas

(he loss area AL



L

is de)ined as the e;'ialent area, hich hen m'ltiplied y

the incident poer density leads to the poer dissipated asheat thro'h R=


Equi"alent areas

4apture area Ac



4apture area Ac

is de)ined as the e;'ialent area, hich hen m'ltiplied y

the incident poer density leads to the total poercapt'red, collected, or intercepted y the antenna


#n eneral, the total capt're area is e;'al to the s'm o) theother three

4apture Area Effecti"e Area5&catterin' Area5Loss Area

Ac Ae 5 A&5 AL

Equi"alent areas

Aperture Efficienc-: /ap



Aperture Efficienc-: /ap

is de)ined as the ratio o) the ma>im'm e))ectie area Aem

and o) the antenna to its physical area Ap

the ma>im'm e))ectie apert're o) any antenna is related to its

ma>im'm directiity %0 y


Radiation !attern



Radiation !attern



Bandidth








Antenna Temperat're

The rihtness temperat're emitted y the di))erent so'rces is



The rihtness temperat're emitted y the di))erent so'rces is

intercepted y antennas, and it appears at their terminals as an

antenna temperat'reThe temperat're appearin at the terminals o) an antenna is that

ien y

Antenna Temperat're

Antenna temperature e))ectie noise temperat're o) the antenna radiation



Antenna temperature e))ectie noise temperat're o) the antenna radiation

resistanceZ 9 (A

Ass'min no losses or other contri'tions eteen the antenna and thereceier, the noise poer trans)erred to the receier is ien y

Antenna Temperat're

Antenna 2oise Power .P %



Antenna 2oise Power .Pr %

Antenna Temperat'reAntenna temperature at the recei"er terminals



Antenna Temperat're(he effecti"e antenna (emperature .(a% at the recei"er

t i l i i b



terminals is 'i"en b-

Antenna Temperat're(he antenna noise power



(he s-stem noise power#) the receier itsel) has a certain noise temperat're Tr d'e to

thermal noise in the Receier components9, the system noise

poer at the receier terminals is ien y

Antenna Temperat're



Antenna Temperat're



CONTENTS Antennas




Arra-s



Arra-s Introduction



(wo*Element Arra-

2*Element Linear Arra-: 6niform Amplitude and &pacin'

777777777777777777$(E88888888888888888888888

/roadside Arra-

9rdinar- End*+ire Arra- Hansen*#ood-ard End*+ire Arra-

2*Element Linear Arra- : 6niform &pacin', 2on 6niform

Amplitude

Anal-sis of /inomial and )olph*(scheb-scheff Arra- &cannin' Arra-, &uperdirecti"e arra-

Arra-s Introduction



(wo*Element Arra-

2*Element Linear Arra-: 6niform Amplitude and &pacin' /roadside Arra-

9rdinar- End*+ire Arra-

Hansen*#ood-ard End*+ire Arra-

2*Element Linear Arra- : 6niform &pacin', 2on 6niformAmplitude

Anal-sis of /inomial and )olph*(scheb-scheff Arra-

&cannin' Arra-, &uperdirecti"e arra-

Arra-s

I2(R9)64(I92



I2(R9)64(I92

Enlarin the dimensions o) sinle elements o)ten leads to

more directie characteristics ery hih ains9 to meet the

demands o) lon distance comm'nication

An other ay to enlare the dimensions o) the antenna,

itho't necessarily increasin the sie o) the indiid'alelements, is to )orm an assemly o) radiatin elements in

an electrical and eometrical con)i'ration. This ne

antenna, )ormed y m'lti elements, is re)erred to as an

array

Arra-sI2(R9)64(I92

The total )ield o) the array is determined y the ector addition o)



the )ields radiated y the indiid'al elements

To proide ery directie patterns, it is necessary that the )ields

)rom the elements o) the array inter)ere constr'ctiely add9 in

the desired directions and inter)ere destr'ctiely cancel each

other9 in the remainin space

There are at least )ie controls that can e 'sed to shape theoerall pattern o) the antenna

1. The eometrical con)i'ration o) the oerall array linear,

circ'lar, rectan'lar, spherical, etc.9

2. The relatie displacement eteen the elements

$. The e>citation amplit'de o) the indiid'al elements

+. The e>citation phase o) the indiid'al elements

X. The relatie pattern o) the indiid'al elements

Arra-sApplications

An array that is idely 'sed



as a ase6station antenna )or

moile comm'nication.

#t is a trian'lar array consistin

o) tele dipoles, ith )o'r

dipoles on each side o) the

trianle.

Each )o'r element array, on

each side o) the trianle, is

asically 'sed to coer anan'lar sector o) 120 )ormin

hat is 's'ally re)erred to as a

sectoral array

Arra-s Introduction



(wo*Element Arra-







Arra-s(#9*ELE$E2( ARRA;:

To in)initesimal horiontal dipoles positioned alon the 6



a>is, as shon in )i're .1a9

/i're .1 Heometry o) a to element array positioned alon

the 6a>is.


The total )ield radiated y the to elements, ass'min no



co'plin eteen the elements, is e;'al to the s'm o) the

to and in the y6 plane it is ien y

b!hase di))erence eteen the elements adNacentelement

*D2π?λ

The manit'de e>citation o) the radiators is identical #09

!hase di))erenceD2π?λ)x Path difference


Ass'min )ar6)ield oserations and



re)errin to /i're .19

E;'ation 61red'ces to




The total )ield o) the array is e;'al to the )ield o) a sinleelement positioned at the oriin m'ltiplied y a )actor

hich is idely re)erred to as the array )actor.

Th's )or the to6element array o) constant amplit'de, theArra- +actor is ien y

hich in normalied )orm can e ritten as




The array )actor is a )'nction o) the eometry o) the arrayand the e>citation phase.

By aryin the separation d and ?or the phase b eteen

the elements, the characteristics o) the array )actor and o)the total )ield o) the array can e controlled.


Pattern $ultiplication:



The )ar6one )ield o) a 'ni)orm to element array o)

identical elements is e;'al to the prod'ct o) the )ield o) asinle element, at a selected re)erence point 's'ally the

oriin9, and the array )actor o) that array. That is,

Arra-s Introduction



(wo*Element Arra-







Arra-s2*ELE$E2( LI2EAR ARRA;: 6niform Amplitude and

&pacin'

= t li th th d t i l d l t R ) i t



=et 's eneralie the method to incl'de elements. Re)errin to

the eometry o) /i're .Xa9,

=et 's ass'me that all the elements hae identical amplit'des

't each s'cceedin element has a b proressie phase lead

c'rrent e>citation relatie to the precedin one.

An array o) identical elements all o) identical manit'de

and each ith a proressie phase is re)erred to as a

'ni)orm array


&pacin'




&pacin'

(he Arra- factor .A+%



(he Arra- factor .A+%

By applyin pattern m'ltiplication r'le on arrays o) identicalelement . The array )actor is ien y

Total phase di))erence D !hase di))erence d'e to path di))erence V bDkdcosθ+ b

!hase di))erenceD2π?λ)x Path difference=kdcosθ!hase di))erence eteen the elements adNacent element


&pacin'



('ltiplyin oth sides y e N

s'tractin E; . )rom E; .8

Which can also e ritten as

.


&pacin'



A/

#) the re)erence point is the physical center o) the array, the array

)actor o) 6109 red'ces to

i) is small


&pacin'

ma>im'm al'e o) array )actor is e;'al to



ma>im'm al'e o) array )actor is e;'al to

2ormali3ed Arra- +actor

Arra-s2*ELE$E2( LI2EAR ARRA;: 6niform Amplitude and &pacin'

2ulls of the Arra-:

To )ind the n'lls o) the array



.A+%n<=> >n

To )ind the n'lls o) the array,

E; 610c9 or 610d9 is set e;'al

to ero

D 2nπ?

(kdcosθn+b9 D 2nπ?

cosθnD λ?2πd96b 2nπ?9

/or n D ,2,$,..., 610c9 attains itsma>im'm al'es eca'se it red'ces to a

sin09?0 )orm.

The al'es o) n determine the order o) the

n'lls )irst, second, ff, etc.9

Arra-s2*ELE$E2( LI2EAR ARRA;: 6niform Amplitude and &pacin'

$aximum

The ma im m al es o) normali ed arra )actor occ r hen



The ma>im'm al'es o) normalied array )actor occ'r hen

sin?29 D0=> >m

+irst $aximum or Principal $aximum

The )irst ma>im'm o) the array )actor occ'rs hen m D 0

?2 D 0 or D 0

Arra-s Introduction

(wo Element Arra-



(wo*Element Arra-







Arra-s3n the asis o) the main loe array

/roadside Arra-

9rdinar- End*fire Arra-



9rdinar- End*fire Arra-

/roadside Arra-:The ma>im'm radiation o) an array directed normal to the a>is

o) the array roadsideZ OD^009

The )irst ma>im'm o) the array )actor occ'rs hen

D 0 or *dcosθ+ 7 D 0

*dcos900+7 D 0 or 7 D 0

&ince it is desired to ha"e the first maximum directed toward θ=900

Th's to hae the ma>im'm o) the array )actor o) a 'ni)orm linear array

directed roadside to the a>is o) the array, it is necessary that all theelements hae the same phase e>citation in addition to the same

amplit'de e>citation9. The separation eteen the elements can e o)

any al'e.

Arra-s/roadside Arra-:

To ens're that there are no principal ma>ima in other

directions, hich are re)erred to as 'ratin' lobes, the



, ' ' ,

separation eteen the elements sho'ld not e e;'al to

m'ltiples o) a aelenth dnλ, n=1,2,3,….) and β=0.

f d=nλ, n=1,2,3,…. !nd β =0, then

Th's )or a 'ni)orm array ith b D 0 and d D n λ, in addition to hain the

ma>ima o) the array )actor directed roadside θ D ^0 9 to the a>is o) the

array, there are additional ma>ima directed alon the a>is θ D 0 ,180 9 o)the array end6)ire radiation9.


ratin' Lobes: m'ltiple ma>ima, in addition to the main ma>im'm

To aoid any ratin loe the larest spacin eteen the elements



To aoid any ratin loe, the larest spacin eteen the elements

-ho'ld e less than one aelenthdma>g λ9

Arra-s Introduction

(wo Element Arra-



(wo*Element Arra-







Arra-s9rdinar- End @ +ire:

The ma>im'm radiation o) an array directed to alon the a>is o)

the array end6)ire9. As a matter o) )act, it may e necessary



y 9 , y y

that it radiates toard only one direction either O0D00 or 18009

To direct the )irst ma>im'm toard O0D00

To direct the )irst ma>im'm toard O0D1800 , then

f d=nλ, n=1,2,3…than in addition to ha"in# endfireradiation, there a$so exist %axi%a in the &roadside direction.

To aoid any ratin loe, the larest spacin eteen the elements

-ho'ld e less than one aelenthdma>g λ9

Arra-s9rdinar- End * +ire



Arra-s Introduction

(wo*Element Arra-



(wo*Element Arra-







Arra-sHansen*#ood-ard End*+ire Arra-:

To enhance the directiity o) an end6)ire array itho't

destroyin any o) the other characteristics.



y y

"ansen and Woodyard proposed that the re;'ired phase shi)t

eteen closely spaced elements o) a ery lon array sho'ld

e


To realie the increase in directiity as a res'lt o) the "ansen6

Woodyard conditions, it is necessary that, in addition to the



y y

conditions o) 62$a9 and 62$9. ass'mes al'es o)

/or ma>im'm radiation alon O0D00

/or ma>im'm radiation alon O0D1800


/or an array o) elements, the condition o) D π is satis)ied

y 'sin e;n 62$a9 )or O D0 and e;n 62$9 )or OD180 and



choosin )or each a spacin o) d

#) the n'mer o) elements is lare,62X9 can e appro>imated y

Th's )or a lare 'ni)orm array, the "ansen6Woodyard condition can only yield an

#mproed directiity proided the spacin eteen the elements is appro>imately

λ?+.

Arra-s)irecti"it-:



where L is the o"erall len'th of the arra-


)irecti"it-:



here = is the oerall lenth o) the array

Arra-s



Arra-s Introduction

(wo*Element Arra-



(wo Element Arra-







Arra-s2*Element Linear Arra- : 6niform &pacin', 2on 6niform

Amplitude

Introduction



#n this section, roadside arrays ith 'ni)orm spacin 't non

'ni)orm amplit'de distri'tion ill e considered.

(ost o) the disc'ssion ill e directed toard inomial and

%olph6 Tscheysche)) roadside arrays

a 'ni)orm amplit'de array yields the smallest hal)6poer

eamidth. #t is )olloed, in order, y the %olph6Tscheysche))

and inomial arrays.

#n contrast, inomial arrays 's'ally possess the smallest sideloes )olloed, in order, y the %olph6Tscheysche)) and

'ni)orm arrays.


Amplitude

Introduction



As a matter o) )act, inomial arrays ith element spacin e;'al

or less than λ?2 hae no side loes.

#t has een shon analytically that )or a ien side loe leel

the %olph6Tscheysche)) array prod'ces the smallest

eamidth eteen the )irst n'lls.

Conersely, )or a ien eamidth eteen the )irst n'lls, the

%olph6Tscheysche)) desin leads to the smallest possile side

loe leel.


Amplitude

Introduction



4ni)orm arrays 's'ally possess the larest directiity.

"oeer, s'perdirectie or s'per ain as most people re)er to

them9 antennas possess directiities hiher than those o) a

'ni)orm array.

Altho'h a certain amo'nt o) s'perdirectiity is practically

possile, s'perdirectie arrays 's'ally re;'ire ery lare

c'rrents ith opposite phases eteen adNacent elements.

Arra-s

.% +or e"en

number of

2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude



number of

elements .$%

.% +or oddnumber of

elements

.$5%

Arra-s

.% +or e"en number of elements .$%




An array o) an een n'mer o) isotropicelements 2( here ( is an inteer9 is

positioned symmetrically alon the 6a>is, as

shon in /i're .1^a9.

The separation eteen the elements is d,and ( elements are placed on each side o)

the oriin.

Ass'min that the amplit'de e>citation is

symmetrical ao't the oriin

/i're .1^ on 'ni)orm amplit'de arrays o) een n'mer o) elements.

Arra-s.% +or e"en number of elements .$%

Arra- +actor : The array )actor )or a non 'ni)orm




amplit'de road side array can e ritten as

Which in normalied )orm red'ces to

/i're .1^ on 'ni)orm amplit'de arrays o) een n'mer o) elements.

Where an7s are the e>citation coe))icients o) the array elements.

Arra-s

.% +or odd number of elements .$5%

An array o) odd n'mer o) isotropic elements 2(V1




An array o) odd n'mer o) isotropic elements 2(V1

here ( is an inteer9 as shon in /i're .1^a9.Arra- +actor

Which in normalied )orm red'ces to

/i're .1^ on 'ni)orm amplit'de arrays o) odd n'mer o) elements.

(he amplitude excitation of the center element is a

Arra-s2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude



The e>citation coe))icients may e determine thro'h

/inomial expansion /inomial Arra-

(scheb-scheff plo-nomial )olph*(scheb-scheff Arra-

Arra-s Introduction

(wo*Element Arra-



-







Arra-s/inomial Arra-:

The array )actor )or the inomial array is represented y 61a9F61c9




The array )actor )or the inomial array is represented y 1a9 1c9

here the an7s are the e>citation coe))icients hich ill no e deried

.A% Excitation 4oefficients :

the )'nction 1V>9m61 e ritten in a series, 'sin the inomial

e>pansion, as

Arra-s.A% Excitation 4oefficients :

The positie coe))icients o) the series e>pansion )or di))erent al'es o) m are

/inomial Arra-:



( n'mer o) elements o) the array,

The coe))icients o) the e>pansion amplit'des o) the elements.

-ince the coe))icients are determined )rom a inomial series e>pansion, the array is *non as a

inomial array.

!ascal7s trianle

Arra-s.A% Excitation 4oefficients :

Re)errin to 61a9, 619, and 6$9, the amplit'de coe))icients

/inomial Arra-:



)or the )olloin arrays are5

(he coefficients for other arra-s can be determined in a similar manner

Arra-s./% )esi'n Procedure :

/inomial Arra-:



(hese expressions can be used effecti"el- to desi'n binomial

arra-s with a desired half*power beamwidth or directi"it-

Arra-s



Arra-s)olph*(scheb-scheff Arra-:

.A% Arra- +actor:




. % -

Re)errin to 61a9 and 619, the array )actor o) an array o) een orodd n'mer o) elements ith symmetric amplit'de e>citation is nothin

more than a s'mmation o) ( or ( V1 cosine terms.

The larest harmonic o) the cosine terms is one less than the total

n'mer o) elements o) the array. Each cosine term, hose ar'ment isan inteer times a )'ndamental )re;'ency, can e reritten as a series

o) cosine )'nctions ith the )'ndamental )re;'ency as the ar'ment.

That is,


.A% Arra- +actor:




. % -


.A% Arra- +actor:




. % -


.A% Arra- +actor:




. % -

The rec'rsion )orm'la )or Tscheysche)) polynomials is

#t can e 'sed to )ind one Tscheysche)) polynomial i) the polynomials

o) the preio's to orders are *non. Each polynomial can also e

comp'ted 'sin


.A% Arra- +actor:




-

properties o) the Tscheysche)) polynomials are


./% Arra- )esi'n:&tatement:




%esin a roadside %olph6Tscheysche)) array o) 2( or 2( V1elements ith spacin d eteen the elements. The side loes are R

dB elo the ma>im'm o) the maNor loe. /ind the e>citation

coe))icients and )orm the array )actor

Procedure


./%Arra- )esi'n:




Arra-s Introduction

(wo*Element Arra-



2*Element Linear Arra-: 6niform Amplitude and &pacin'

/roadside Arra-






Arra-s&6PER )IRE4(IBI(;

Antennas hose directiities are m'ch larer than the directiity o) a re)erence

antenna o) the same sie are *non as s'per directie antennas.



#n an array, s'per directiity is accomplished y insertin more elements ith in a

)i>ed lenthdecreasin the spacin9.

%oin this leads eent'ally to ery lare manit'des and rapid chanes o) phase in

the e>citation coe))icients o) the elements o) the array.

This necessitates a ery precise adN'stment o) their al'es. Associated ith this areincreases in reactie poer relatie to the radiated poer9 and the I o) the array.

Arra-s&uper directi"e arra-

Th's a s'per directie array is one hose directiity is larer than that o) a

re)erence array 's'ally a 'ni)orm array o) the same lenth9



re)erence array 's'ally a 'ni)orm array o) the same lenth9.

Efficienc- and )irecti"it-:

Beca'se o) the ery lare c'rrents in the elements o) s'perdirectie arrays, the

ohmic losses increases and the antenna e))iciency decreases ery sharply.

Altho'h practically the ohmic losses can e red'ced y the 'se o) s'per

cond'ctie materials, there is no easy sol'tion )or the precise adN'stment o) theamplit'des and phases o) the array elements.

"ih radiation e))iciency s'perdirectie arrays can e desined 'tiliin array

)'nctions that are insensitie to chanes in element al'es.

Arra-s)esi'ns #ith 4onstraints:

To ma*e the desins more practical, applications that arrant some s'per

directiity sho'ld in corporate constraints.



3ne constraint is ased on the sensitiity )actor 9 , and it as 'tilied )or

the desin o) s'per directie arrays .

The sensitiity )actor desinated as 9 is an important parameter hich is

related to the electrical and mechanical tolerances o) an antenna, and it can

e 'sed to descrie its per)ormance especially its practical implementation9.

/or an 6element array, it can e ritten as

an the c'rrent e>citation o) the nth element,

r n the distance )rom the nth element to the

)ar6)ield oseration point


To derie desin constraints, the realied c'rrent e>citation coe))icients cn7s

are related to the desired ones an7s y

Where a represents the error in the nth e>citation coe))icient The mean



Where nan represents the error in the nth e>citation coe))icient. The mean

s;'are al'e o) n is denoted y

To ta*e into acco'nt the error associated ith the positionin o) the

elements, e introd'ce

Where σ is the root6mean6s;'are al'e o) the element position error.


Cominin 68$9 and 68$c9 red'ces to



Where is a meas're o) the comined electrical and mechanical errors

#) the realied pattern is to e ery close to the desired one, then

E;'ation68$e9 can e reritten, y introd'cin a sa)ety )actor -, as

- is chosen lare eno'h so that68$e9 is satis)ied.

CONTENTS Antennas




Arrays

Aperture, "orn and Re)lector antennas


Aperture Antennas Apert're antennas are most common at microae )re;'encies.

There are many di))erent eometrical con)i'rations o) an apert're

antenna ith some o) the most pop'lar shon in elo /i're



antenna ith some o) the most pop'lar shon in elo /i're

They may ta*e the )orm o) a ae'ide or a horn hose apert're

may e s;'are, rectan'lar, circ'lar, elliptical, or any other

con)i'ration.

Aperture Antennas Apert're antennas are ery practical )or space applications, eca'se

they can e )l'sh mo'nted on the s'r)ace o) the space cra)t or

aircra)t.



aircra)t.

Their openin can e coered ith a dielectric material to protect

them )rom enironmental conditions. This type o) mo'ntin does not

dist'r the aero dynamic pro)ile o) the cra)t, hich in hih speed

applications is critical.

Aperture AntennasH6;E2&C PRI24IPLE

states that each !oint on a primary ae )ront can e considered to

e a ne so'rce o) a secondary -pherical ae and that a



e a ne so'rce o) a secondary -pherical ae and that a

secondary ae )ront can e constr'cted as the enelope o) these

secondary spherical aes

+IEL) E!6IBALE24E PRI24IPLE

a )ield in a lossy reion is 'ni;'ely speci)ied y The so'rces ithinthe reion pl's the tanential components o) the electric )ield oer

the o'ndary, or the tanential components o) the manetic )ield

oer the o'ndary, or the )ormer oer part o) the o'ndary and the

latter oer the rest o) the o'ndary

Aperture Antennas+IEL) E!6IBALE24E PRI24IPLE

The e;'ialence principle is deeloped y considerin an act'al

radiatin so'rce hich electrically is represented y c'rrent densities



radiatin so'rce, hich electrically is represented y c'rrent densities

J1 and (1 as shon in /i're12.1a9.

The so'rce radiates )ields E1 and "1 eeryhere. To accomplish this,

a closed s'r)ace - is chosen, shon dashed in /i're12.1a9, hich

encloses the c'rrent densities J1 and (1 .

Aperture Antennas+IEL) E!6IBALE24E PRI24IPLE

The ol'me ithin - is denoted y K1 and o'tside - y K2.



!rod'ce the oriinal )ields E1, "19 only o'tside -.

Aperture AntennasRE4(A26LAR APER(6RE&

#n practice, the rectan'lar apert're is proaly the most common

microae antenna. Beca'se o) its con)i'ration, the rectan'lar



coordinate system is the most conenient system to e>press the)ields at the apert're and to per)orm the interation.

-hon in /i're12. are the three most common and conenient

coordinate positions 'sed )or the sol'tion o) an apert're antenna.

/i're12.


#n /i're12.a9 the apert're lies on the y6 plane, in /i're12.9

on the >6 plane and in /i're12 c9 on the >6y plane



on the > plane, and in /i're12.c9 on the > y plane.

/i're12.


/or a ien )ield distri'tion, the analytical )orms )or the )ields )or

each o) the arranements are not the same "oeer the comp'ted



each o) the arranements are not the same. "oeer the comp'ted

al'es ill e the same, since the physical prolem is identical in all

cases. /or each o) the eometries shon in /i're12., the only

di))erence in the analysis is in the )orm'lation o)

1. the components o) the e;'ialent c'rrent densities J>, Jy, J,(>, (y, (9

2. the di))erence in paths )rom the so'rce to the oseration point

r7cos9

$. the di))erential area ds7


#n eneral, the non ero components o) Js and (s are



The di))erential paths ta*e the )orm o)


and the di))erential areas are represented y




.%6niform )istribution on an Infinite round Plane























































Aperture Antennas



Aperture Antennas



Aperture Antennas4IR46LAR APER(6RE&

A idely 'sed microae antenna is the circ'lar apert're.



3ne o) the attractie )eat'res o) this con)i'ration is its simplicity in

constr'ction.

#n addition, closed )orm e>pressions )or the )ields o) all the modes

that can e>ist oer the apert're can e otained.

The proced're )olloed to determine the )ields radiated y a circ'lar

apert're is identical to that o) the rectan'lar, as s'mmaried in

-ection12.$. The primary di))erences lie in the )orm'lation o) the

e;'ialent c'rrent densities J>, Jy, J, (>, (y, (9 the di))erentialpaths )rom the so'rce to the oseration point

Aperture Antennas4IR46LAR APER(6RE&

f..do onsel)ff



Aperture Antennas/A/I2E(C& PRI24IPLE

o that ire and apert're antennas hae een analyed, one may

in;'ire as to hether there is any relationship eteen them.



This can e ansered etter y )irst introd'cin Bainet7sprinciple

hich in optics states that hen the )ield ehind a screen ith an

openin is added to the )ield o) a complementary str'ct're, the s'm

is e;'al to the )ield hen there is no screen.

Bainet7s principle in optics does not consider polariation, hich is

soitalin antenna theoryZ it deals primarily ith asorin screens.

An e>tension o) Bainet7s principle, hich incl'des polariation and

the more practical cond'ctin screens, as introd'ced y Boo*er\1$], \1+]. Re)errin to /i're12.22a9,

ffffffffdo onsel)ffff

CONTENTS Antennas

/ d t l ! t ) A t




Arrays

Apert're, Horn and Re)lector antennas


Horn Antennas3ne o) the simplest and proaly the most idely 'sed microae

antenna is the horn.



The horn is nothin more than a hollo pipe o) di))erent cross

sections, hich has een tapered )lared9 to a larer openin.

The horn is idely 'sed as a )eed element )or lare radio astronomy,

satellite trac*in, and comm'nication dishes )o'nd installedthro'ho't the orld.

#n addition to its 'tility as a )eed )or re)lectors and lenses, it is a

common element o) phased arrays and seres as a 'niersal

standard )or caliration and ain meas'rements o) other hih6ainantennas.

Horn Antennas



Horn AntennasE * PLA2E &E4(9RAL H9R2

The E6plane sectoral horn is one hose openin is )lared in the

direction o) the E6)ield, and it is shon in /i're1$.2a9.



H*PLA2E &E4(9RAL H9R2/larin the dimensions o) a rectan'lar ae'ide in the direction o)

the "6)ield, hile *eepin the other constant, )orms an "6plane

sectoral horns hon in /i're1$.19

CONTENTS Antennas

/ d t l ! t ) A t




Arrays

Apert're, "orn and Reflector antennas


Reflector antennasI2(R9)64(I92

The 'se o) re)lector antennas )or deep space comm'nication, s'ch

as in the space proram and especially their deployment on the

s'r)ace o) the moon res'lted in estalishin the re)lector antenna



s'r)ace o) the moon, res'lted in estalishin the re)lector antennaalmost as a ho'sehold ord d'rin the 1^0s.

Altho'h re)lector antennas ta*e many eometrical con)i'rations,

some o) the most pop'lar shapes are the plane, corner, and c'red

re)lectors especially the paraoloid9, as shon in /i're1X.1, each

o) hich ill e disc'ssed in this chapter.

Reflector antennasI2(R9)64(I92



Reflector antennasPLA2E RE+LE4(9R:

The simplest type o) re)lector is a plane re)lector introd'ced to direct

enery in a desired direction.



Reflector antennasPARA/9LI4 RE+LE4(9R



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