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Fields and Waves I
Lecture 26Intro to Antennas & Propagation
K. A. ConnorElectrical, Computer, and !stems Engineering "epartment
#ensselaer Pol!tec$nic Institute, %ro!, '
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%$ese lides Were Prepared (! Pro). Kennet$ A. Connor *sing+riginal aterials Written ostl! (! t$e Follo-ing
Kennet$ A. Connor / ECE "epartment, #ensselaerPol!tec$nic Institute, %ro!, '
0. "arr!l ic$ael / 1E 1lo(al #esearc$ Center,isa!una, '
%$omas P. Cro-le! / ational Institute o) tandards and %ec$nolog!, 3oulder, C+
$eppard 0. alon / ECE "epartment, #ensselaerPol!tec$nic Institute, %ro!, '
Lale Ergene / I%* In)ormatics Institute, Istan(ul, %ure!
0e4re! 3raunstein / C$ung5Ang *niversit!, eoul, Korea
aterials )rom ot$er sources are re)erenced -$ere t$e! areused. %$ose listed as *la(! are gures )rom *la(!7ste8t(oo.
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E8amples o) Antennas
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Antennas
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moteiv %mote !Inverted FAntenna
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moteiv %mote !
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moteiv %mote !
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moteiv %mote !
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moteiv %mote !
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%ransmission Lines &Antennas
#evie- %ransmission Lines
#evie- 3oundar! Conditions
#evie- 9oltage, Current, Electric andagnetic Fields
Etc.
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%E Waves on %ransmissionLines
Connecting *ni)orm Plane Waves -it$ 9oltages andCurrents on %ransmission Lines
E z E e E e x j z j z( ) = ++
−−
+β β
H z E e E e y
j z j z
( ) = −+−
−
+β β
η
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%E Waves
%$ese elds can e8ist in t$e region (et-een t$e conductingplates i) t$e (oundar! conditions on t$e plates arereasona(l! satised. ince t$e electric eld $as onl! an x component, it is totall! normal to t$e conducting(oundaries. %$is can occur i) t$ere is a sur)ace c$arge ont$e (oundar!, ρ ε ε ε β β s x
j z j z E z E e E e= = ++−
−+( )
%$e magnetic eld is totall! tangent to t$e conducting(oundar!, -$ic$ can occur i) t$ere is a sur)ace current
densit! given (!
J H z E e E e
s y
j z j z
= = −+
−−
+
( )β β
η
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%E Waves
%$en, assuming t$at t$e lo-er plate is grounded, t$e voltageon t$e upper plate -ill (e
( )v z E z d x s E e s E e V e V e
x
s j z j z j z j z= = + = +
∫ +
−
−
+
+
−
−
+( )0
β β β β
-$ere -e $ave integrated t$e electric eld along t$evertical :red; pat$ s$o-n.
s
w
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%E Waves
%o connect t$e magnetic eld -it$ t$e current, -e mustintegrate along a closed pat$ t$at encloses one o) t$e t-oconductors. %$e (ottom pat$ s$o-n includes t$e $ori
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%E Waves
For a parallel plate -aveguide :stripline;, t$e inductance andcapacitance per unit lengt$ and intrinsic impedance are
l
s
w=
µ
c
w
s=
ε
Z l
c
s
ww s
s
w
s
wo = = = =
µ
ε
µ
ε η
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%E Waves
so t$e current e8pression is
i z V e V e
Z
j z j z
o
( ) = −+
−−
+β β
We could $ave determined t$is current )rom t$e sur)acecurrent densit! so -e s$ould c$ec to (e sure t$at t$e t-oresults agree. %$e total current at an! z s$ould (e given (!
i z J w E e E e w V e V eZ
s
j z j z j z j z
o
( ) = = − = −+−
−+
+−
−+β β β β
η
as (e)ore.
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%E Waves
Finall!, -e can c$ec to see i) t$e c$arge per unit lengt$ :asdetermined )rom t$e (oundar! condition; gives us t$e usualcapacitance per unit lengt$.
( ) ( )q w w E e w E e w s
V e V e c v z s j z j z j z j z
= = + = + =+−
−+
+−
−+ ρ ε ε
ε β β β β
as e8pected.
%$e same anal!sis can (e done )or coa8ial ca(les and t-o5-ire lines. %$e general results are t$e same.
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tanding Waves9oltage tanding Wave -it$ $ort Circuit Load
ConstructiveInter)erence
"estructiveInter)erence
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tanding Waves9oltage tanding Wave -it$ +pen Circuit Load
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0ava Applet o) Waves
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tanding Wave
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imple Antennas
Currents on Wire Antennas
1eneral %!pes o) Antennas
%$e ?ert
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imple Wire AntennaCurrents
From C%A 0o$n EngineeringElectromagnetic Fields & Waves
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imple Wire AntennaCurrents
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imple Wire AntennaCurrents
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imple Wire AntennaCurrents
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imple Wire AntennaCurrents
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%!pes o) Antennas
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?ert
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?ert
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ote t$at t$e-aves(ecomeplanar atlarge
distances
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?ert
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$ort "ipole
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Aperture Antennas
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Antenna Parameters
Calculate t$e Electric and agnetic Fields )rom
t$e Antenna Currents / usuall! re@uires t$euse o) potentials
Far Fields are Products o) terms lie t$e)ollo-ing / :depends on current and inversel!
on position;, sp$erical -ave, eld pattern "etermine t$e Po!nting 9ector / Po-er "ensit!
is product o) E and ? / average goes inversel!-it$ position s@uared and -it$
1ain is t$e ratio o) po-er densit! to isotropicvalue
#adiation #esistance is t-ice t$e average totalpo-er divided (! t$e current s@uared
( ) F θ
( ) F 2 θ
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Antenna Anal!sis
?ert
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Antenna Anal!sis
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Antenna Anal!sis
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Antenna Anal!sis
Keep +nl! %$e Largest %erms in t$e Far
Field
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Antenna Anal!sis( ) F 2 θ
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Antenna Anal!sis
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ote t$at t$e-aves(ecomeplanar atlarge
distances
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?ert
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?al) Wave "ipole
( ) F 2 θ
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#adiation Patterns
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Antenna
Patterns
' i A
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'agi Antenna
D.1?<
B El t ' i
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B Element 'agi
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P t $ A t
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Patc$ Antenna
P t $ A t
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Patc$ Antenna
P t $ A t
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Patc$ Antenna
P t $ A t
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Patc$ Antenna
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$ttp==Hournals.tu(ita.gov.tr=eletri=issues=el5D5BG5B=el5BG5B555
Antenna Polari
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Antenna Polari
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?ori
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In t$e earl! da!s o) F radio in t$e 5B ?< spectrum,t$e radio stations (roadcasted $ori
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Circular polari
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Antenna Polari
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Antennas
%$e simplest antenna is t$e ?ert
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Antennas
%$e electric eldaround t$e?ert
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Antennas
Po-er is radiated$ori
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Antennas ?al) Wave "ipole vs uarter Waveonopole
Antennas / ?al) Wave "ipole vs uarter Wave
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Antennas ?al) Wave "ipole vs uarter Waveonopole
Antennas / ?al) Wave "ipole vs uarter Wave
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p onopole
3ertoni lides
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3ertoni lides
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