antenna engineering for ete(lpu)
TRANSCRIPT
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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
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CONTENTS Antennas
/'ndamental !arameters o) Antennas
Arrays
Apert're Antennas and Re)lector antenna
Radio Wae propaation
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CONTENTS Antennas
/'ndamental !arameters o) Antennas
Arrays
Apert're, "orn and Re)lector antennas
Radio Wae propaation
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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
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#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
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#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.
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#TR3%4CT#3 A transmission6line Theenin e;'ialent o) the antenna
system
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#TR3%4CT#3 A transmission6line Theenin e;'ialent o) the antenna
system
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.
#TR3%4CT#3
.
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#TR3%4CT#3
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Antennas
#ntrod'ction
Types o) Antenna
Radiation (echanism
!hysical concept o) Radiation in sinle ire, to ire
C'rrent %istri'tion on a Thin Wire Antenna
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T<!E- 3/ ATEA-
Wire antennas
Apert're antennas
(icrostrip antennas
Array antennas
Re)lector antennas=ens antennas
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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
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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
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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
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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
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atc! Antenna attern
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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
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Arra" o# patc!
Antennas
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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
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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
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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.
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'(
=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".
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Antennas
#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
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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
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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
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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.
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Radiation $echanism
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Radiation $echanism
(hin wire
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Radiation $echanism&in'le wire:
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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.
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Radiation $echanism(wo*#ires:
@ 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
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Radiation $echanism(wo*#ires:
@ #) 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.
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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
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Radiation $echanism /ormation and detachment o) electric )ield line )or short %ipole Antenna
)ipo&e
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)ipo&e
C t )i t i% ti t!i i
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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.
C t )i t i% ti t!i i
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Current )istri%ution on a t!in *ireantenna
C t )i t i% ti t!i i
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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
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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 *ire
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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 *ire
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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.
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CONTENTS Antennas
+undamental Parameters of Antennas
Arrays
Apert're, "orn and Re)lector antennas
Radio Wae propaation
+undamental Parameters of Antennas
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+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
+undamental Parameters of Antennas
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+undamental Parameters of Antennas #ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
#ntrod'ction
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#ntrod'ction
To descrie per)ormance o) an antenna
%e)inition o) ario's parameters
+undamental Parameters of Antennas
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+undamental Parameters of Antennas #ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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 pattern
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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
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Radiation pattern
Coordinate system )or antenna analysis
Radiation pattern
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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
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Radiation pattern
Radiation pattern
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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
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Radiation pattern
ario's parts o) a radiation pattern are re)erred to as a loes
To dimensional polar pattern
Radiation pattern lobes
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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
+undamental Parameters of Antennas
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+undamental Parameters of Antennas #ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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 !oer %ensity
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Radiation !oer %ensity
!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 %ensity
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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
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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
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Radiation !oer %ensity The aerae poer radiated y an antenna radiated poer9
can e ritten as
Radian and -teradian
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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
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#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
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#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
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#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
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#sotropic antenna
)irectiona&
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)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&
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/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
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The space s'rro'ndin an antenna is 's'ally s'diided into three
reions5
2ie&3Re4ions
2ie&3
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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
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The space s'rro'ndin an antenna is 's'ally s'diided into threereions5
Re4ions
+undamental Parameters of Antennas
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#ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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 #ntensity
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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
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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
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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
+undamental Parameters of Antennas
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#ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
)irecti"it-%irectiity %95
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%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
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The eneral e>pression )or the directiity and ma>im'm
directiity %09 'sin
%irectiity
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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:
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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:
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)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:
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)irectional Patterns:
With this appro>imation, ma>im'm directiity can e appro>imated y
+undamental Parameters of Antennas
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#ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
Antenna Hain
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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
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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
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Antenna Hain
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!artial ain o) an antenna
/or a ien polariation in a ien direction
Total ain
Antenna Hain
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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
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#ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
Antenna
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Ecienc"#n eneral, the oer all
E))iciency can e ritten as
Ra3iation Resistance 6 Antenna
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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
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#ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
Bea*i3t
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! 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
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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.
+undamental Parameters of Antennas #ntrod'ction
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#ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
Bandwid
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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!
+undamental Parameters of Antennas #ntrod'ction
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#ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
Polarizati
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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
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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!"
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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!"
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"oriontal polariation
Kertical polariation
Circ'lar polariation
RC!9
Circ'lar polariation
=C!9
Wa!"
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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
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+undamental Parameters of Antennas #ntrod'ction
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#ntrod'ction
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
o ar za on oWa!"
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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#
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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!"
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)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]
+undamental Parameters of Antennas #ntrod'ction
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t od'ct o
Radiation !attern
Radiation !oer %ensity
Radiation intensity
%irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
Cir&'lar Polarization#
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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
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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!#
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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
+undamental Parameters of Antennas #ntrod'ction
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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
Elli%ti&al Polarization#A ti h i i lli ti ll l i d i) th ti
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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
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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
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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
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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
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(-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.
+undamental Parameters of Antennas #ntrod'ction
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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
o ar za on o"" a& orE)&i!n&$
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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&$
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!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-
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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
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!=/ )or transmittin and receiin apert're antennas
E)&i!n&$
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!=/ )or transmittin and receiin linear ire antennas
+undamental Parameters of Antennas #ntrod'ction
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Radiation !attern
Radiation !oer %ensity
Radiation intensity %irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
-od!,I i d
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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
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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
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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
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C'rrent deeloped ithin the loop is
In%'t I-%!dan&!( it d ) t d l d ithi th l i
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(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
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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
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The poer s'pplied y the enerator d'rin conN'ate
matchin is
Mod!
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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
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!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=
+undamental Parameters of Antennas #ntrod'ction
Radiation !attern
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Radiation !attern
Radiation !oer %ensity
Radiation intensity %irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
+undamental Parameters of Antennas #ntrod'ction
Radiation !attern
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Radiation !attern
Radiation !oer %ensity
Radiation intensity %irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
Ant!nna Radiation E)&i!n&$
R th t t ))i i th t t * i t t th
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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&$
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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
+undamental Parameters of Antennas #ntrod'ction
Radiation !attern
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Radiation !attern
Radiation !oer %ensity
Radiation intensity %irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
Equi"alent areasWith each antenna, e can associate an 'mer o) e;'ialent areas.
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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
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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
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ect e a ea e
4nder conN'ate matchin
The ma>im'm e))ectie area Aem
Equi"alent areas
(he scatterin' area As
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' 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.
4nder conN'ate matchin
As
Equi"alent areas
(he loss area AL
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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=
4nder conN'ate matchin
Equi"alent areas
4apture area Ac
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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
4nder conN'ate matchin
#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
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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
+undamental Parameters of Antennas #ntrod'ction
Radiation !attern
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Radiation !attern
Radiation !oer %ensity
Radiation intensity %irectiity, Hain, Antenna e))iciency, Beamidth
Bandidth
!olariation, =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
Antenna Temperat're
The rihtness temperat're emitted y the di))erent so'rces is
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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
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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 %
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Antenna 2oise Power .Pr %
Antenna Temperat'reAntenna temperature at the recei"er terminals
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Antenna Temperat're(he effecti"e antenna (emperature .(a% at the recei"er
t i l i i b
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terminals is 'i"en b-
Antenna Temperat're(he antenna noise power
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(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
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Antenna Temperat're
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CONTENTS Antennas
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/'ndamental !arameters o) Antennas
Arra-s
Apert're, "orn and Re)lector antennas
Radio Wae propaation
Arra-s Introduction
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(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
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(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
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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)
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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
$. The e>citation amplit'de o) the indiid'al elements
+. The e>citation phase o) the indiid'al elements
X. The relatie pattern o) the indiid'al elements
Arra-sApplications
An array that is idely 'sed
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as a ase6station antenna )or
moile comm'nication.
#t is a trian'lar array consistin
o) tele dipoles, ith )o'r
dipoles on each side o) the
trianle.
Each )o'r element array, on
each side o) the trianle, is
asically 'sed to coer anan'lar sector o) 120 )ormin
hat is 's'ally re)erred to as a
sectoral array
Arra-s Introduction
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(wo*Element Arra-
2*Element Linear Arra-: 6niform Amplitude and &pacin' /roadside Arra-
9rdinar- End*+ire Arra-
Hansen*#ood-ard End*+ire Arra-
2*Element Linear Arra- : 6niform &pacin', 2on 6niformAmplitude
Anal-sis of /inomial and )olph*(scheb-scheff Arra-
&cannin' Arra-, &uperdirecti"e arra-
Arra-s(#9*ELE$E2( ARRA;:
To in)initesimal horiontal dipoles positioned alon the 6
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a>is, as shon in )i're .1a9
/i're .1 Heometry o) a to element array positioned alon
the 6a>is.
Arra-s(#9*ELE$E2( ARRA;:
The total )ield radiated y the to elements, ass'min no
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co'plin eteen the elements, is e;'al to the s'm o) the
to and in the y6 plane it is ien y
b!hase di))erence eteen the elements adNacentelement
*D2π?λ
The manit'de e>citation o) the radiators is identical #09
!hase di))erenceD2π?λ)x Path difference
Arra-s(#9*ELE$E2( ARRA;:
Ass'min )ar6)ield oserations and
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re)errin to /i're .19
E;'ation 61red'ces to
Arra-s(#9*ELE$E2( ARRA;:
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The total )ield o) the array is e;'al to the )ield o) a sinleelement positioned at the oriin m'ltiplied y a )actor
hich is idely re)erred to as the array )actor.
Th's )or the to6element array o) constant amplit'de, theArra- +actor is ien y
hich in normalied )orm can e ritten as
Arra-s(#9*ELE$E2( ARRA;:
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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.
Arra-s(#9*ELE$E2( ARRA;:
Pattern $ultiplication:
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The )ar6one )ield o) a 'ni)orm to element array o)
identical elements is e;'al to the prod'ct o) the )ield o) asinle element, at a selected re)erence point 's'ally the
oriin9, and the array )actor o) that array. That is,
Arra-s Introduction
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(wo*Element Arra-
2*Element Linear Arra-: 6niform Amplitude and &pacin' /roadside Arra-
9rdinar- End*+ire Arra-
Hansen*#ood-ard End*+ire Arra-
2*Element Linear Arra- : 6niform &pacin', 2on 6niformAmplitude
Anal-sis of /inomial and )olph*(scheb-scheff Arra-
&cannin' Arra-, &uperdirecti"e arra-
Arra-s2*ELE$E2( LI2EAR ARRA;: 6niform Amplitude and
&pacin'
= t li th th d t i l d l t R ) i t
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=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
Arra-s2*ELE$E2( LI2EAR ARRA;: 6niform Amplitude and
&pacin'
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Arra-s2*ELE$E2( LI2EAR ARRA;: 6niform Amplitude and
&pacin'
(he Arra- factor .A+%
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(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
Arra-s2*ELE$E2( LI2EAR ARRA;: 6niform Amplitude and
&pacin'
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('ltiplyin oth sides y e N
s'tractin E; . )rom E; .8
Which can also e ritten as
.
Arra-s2*ELE$E2( LI2EAR ARRA;: 6niform Amplitude and
&pacin'
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A/
#) the re)erence point is the physical center o) the array, the array
)actor o) 6109 red'ces to
i) is small
Arra-s2*ELE$E2( LI2EAR ARRA;: 6niform Amplitude and
&pacin'
ma>im'm al'e o) array )actor is e;'al to
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ma>im'm al'e o) array )actor is e;'al to
2ormali3ed Arra- +actor
Arra-s2*ELE$E2( LI2EAR ARRA;: 6niform Amplitude and &pacin'
2ulls of the Arra-:
To )ind the n'lls o) the array
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.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
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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-
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(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-s3n the asis o) the main loe array
/roadside Arra-
9rdinar- End*fire Arra-
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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
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, ' ' ,
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.
Arra-s/roadside Arra-:
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
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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-
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(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-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
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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
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Arra-s Introduction
(wo*Element Arra-
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(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-sHansen*#ood-ard End*+ire Arra-:
To enhance the directiity o) an end6)ire array itho't
destroyin any o) the other characteristics.
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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
Arra-sHansen*#ood-ard End*+ire Arra-:
To realie the increase in directiity as a res'lt o) the "ansen6
Woodyard conditions, it is necessary that, in addition to the
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y y
conditions o) 62$a9 and 62$9. ass'mes al'es o)
/or ma>im'm radiation alon O0D00
/or ma>im'm radiation alon O0D1800
Arra-sHansen*#ood-ard End*+ire Arra-:
/or an array o) elements, the condition o) D π is satis)ied
y 'sin e;n 62$a9 )or O D0 and e;n 62$9 )or OD180 and
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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-:
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where L is the o"erall len'th of the arra-
Arra-s/roadside Arra-:
)irecti"it-:
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here = is the oerall lenth o) the array
Arra-s
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Arra-s Introduction
(wo*Element Arra-
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(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-s2*Element Linear Arra- : 6niform &pacin', 2on 6niform
Amplitude
Introduction
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#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.
Arra-s2*Element Linear Arra- : 6niform &pacin', 2on 6niform
Amplitude
Introduction
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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.
Arra-s2*Element Linear Arra- : 6niform &pacin', 2on 6niform
Amplitude
Introduction
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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
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number of
elements .$%
.% +or oddnumber of
elements
.$5%
Arra-s
.% +or e"en number of elements .$%
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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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
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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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
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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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
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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-
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-
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/inomial Arra-:
The array )actor )or the inomial array is represented y 61a9F61c9
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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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-:
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( 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-:
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)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-:
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(hese expressions can be used effecti"el- to desi'n binomial
arra-s with a desired half*power beamwidth or directi"it-
Arra-s
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Arra-s)olph*(scheb-scheff Arra-:
.A% Arra- +actor:
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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. % -
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,
Arra-s)olph*(scheb-scheff Arra-:
.A% Arra- +actor:
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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. % -
Arra-s)olph*(scheb-scheff Arra-:
.A% Arra- +actor:
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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. % -
Arra-s)olph*(scheb-scheff Arra-:
.A% Arra- +actor:
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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. % -
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
Arra-s)olph*(scheb-scheff Arra-:
.A% Arra- +actor:
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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-
properties o) the Tscheysche)) polynomials are
Arra-s)olph*(scheb-scheff Arra-:
./% Arra- )esi'n:&tatement:
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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%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-s)olph*(scheb-scheff Arra-:
./%Arra- )esi'n:
2*Element Linear Arra- : 6niform &pacin', 2on 6niform Amplitude
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Arra-s Introduction
(wo*Element Arra-
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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&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.
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#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
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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.
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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
Arra-s)esi'ns #ith 4onstraints:
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
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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.
Arra-s)esi'ns #ith 4onstraints:
Cominin 68$9 and 68$c9 red'ces to
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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
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/'ndamental !arameters o) Antennas
Arrays
Aperture, "orn and Re)lector antennas
Radio Wae propaation
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
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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.
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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
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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
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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.
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!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
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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.
Aperture AntennasRE4(A26LAR APER(6RE&
#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
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on the > plane, and in /i're12.c9 on the > y plane.
/i're12.
Aperture AntennasRE4(A26LAR APER(6RE&
/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
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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
Aperture AntennasRE4(A26LAR APER(6RE&
#n eneral, the non ero components o) Js and (s are
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The di))erential paths ta*e the )orm o)
Aperture AntennasRE4(A26LAR APER(6RE&
and the di))erential areas are represented y
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture AntennasRE4(A26LAR APER(6RE&
.%6niform )istribution on an Infinite round Plane
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Aperture Antennas
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Aperture Antennas
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Aperture Antennas4IR46LAR APER(6RE&
A idely 'sed microae antenna is the circ'lar apert're.
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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
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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.
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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$], \1+]. Re)errin to /i're12.22a9,
ffffffffdo onsel)ffff
CONTENTS Antennas
/ d t l ! t ) A t
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/'ndamental !arameters o) Antennas
Arrays
Apert're, Horn and Re)lector antennas
Radio Wae propaation
Horn Antennas3ne o) the simplest and proaly the most idely 'sed microae
antenna is the horn.
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The horn is nothin more than a hollo pipe o) di))erent cross
sections, hich has een tapered )lared9 to a larer openin.
The horn is idely 'sed as a )eed element )or lare radio astronomy,
satellite trac*in, and comm'nication dishes )o'nd installedthro'ho't the orld.
#n addition to its 'tility as a )eed )or re)lectors and lenses, it is a
common element o) phased arrays and seres as a 'niersal
standard )or caliration and ain meas'rements o) other hih6ainantennas.
Horn Antennas
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Horn AntennasE * PLA2E &E4(9RAL H9R2
The E6plane sectoral horn is one hose openin is )lared in the
direction o) the E6)ield, and it is shon in /i're1$.2a9.
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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
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/'ndamental !arameters o) Antennas
Arrays
Apert're, "orn and Reflector antennas
Radio Wae propaation
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
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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
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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.
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Reflector antennasPARA/9LI4 RE+LE4(9R
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All th B t