Assignmnt #8 Poblm 9. Poblm 9.7 Poblm 9. Poblm 9.3 Poblm 9.4 LC 35 Nots St #8 Antnns gin nd fficincy Antnns dipol ntnn Hlf wv dipol Fiis tnsmission qution Fiis tnsmission qution Do this ssignmnt by Novmb 9. Mk-up Tutoil Tusdy Dcmb 4 8 Th mk-up tutoil will b t th sm tim nd in th sm oom s th usul Mondy tutoil. Not tht th will b tutoils on both Mondy Dcmb 3 nd on Tusdy Dcmb 4. Th finl xm in LC 35 is Dcmb 3 8 fom : to 5:.
Th F Filds of n Antnn ( ) ( ) + ( )
Find th Mgntic Fild In th f fild th lctic fild is: ( ) ( ) + ( ) Wht is th mgntic fild in th f fild? Fdy s Lw: so x ωµ H H ωµ Do th cul in sphicl coodints. Nglct th tms in / nd / 3 bcus thy n fild.
Cul in sphicl coodints: lctic fild: ( ) ( ) ( ) + ( ) sin sin ( ) + sin ( ) +
Th componnts of th f fild : ( ) sin sin sin sin ( ) ( ) ( ) ( ) sin sin ( ) ( ) sin sin Th componnt vis s so w cn nglct it. â Wok on th componnt: â
Th componnts of th f fild : ( ) ( ) Wok on th componnt: â ( ) () sin sin ( ) ( ) ( )
Th componnts of th f fild : ( ) ( ) Wok on th componnt: â ( ) () ( ) ( )
So th cul is vlutd s: + And th mgntic fild is: H ωµ + H ωµ H ωµ µ ε µ µε µ µε ωµ µε ω ωµ ωµ
So th mgntic fild is: H + ( ) ( ) + ( ) ( ) H + Hnc in th f fild of ny ntnn:
Pow Flow Dnsity ( ) ( ) ( ) + ( ) ( ) ( ) H + [ ] * R H S v + + * R S v + + S v * * R conugt conugt
+ + S v * * R S v * * R + S v * * R + R S v + S v Wtts p squ mt
3 Qusi-Pln Wvs ( ) ( ) ( ) + ( ) ( ) ( ) H + ( ) ( ) ( ) ( ) H S v S v ( ) ( ) ( ) ( ) H nd HH nd HH
Th Htzin Dipol Pul Whits nd Ns Fig. 9.3 4
Th Htzin Dipol << λ 5
N Filds nd F Filds 6
Th N Fild 7
Th F Fild 8
Angl Dpndnc I sin 4π ( ) ( ) + ( ) I 4π ( ) sin nd
Th Dipol Antnn
Th F Filds of Dipol Antnn It My B Shown tht: ( ) ( ) I π ( ) F( ) I π ( ) F( )
Hlf-Wv Dipol Antnn In gnl: I π ( ) F( ) Hlf-wv dipol: F F h ( ) ( ) π λ λ cos h π λ π h λ 4 λ 4 ( hcos ) cos( h) sin π π cos cos cos sin
F ( ) π π cos cos cos sin F ( ) π cos cos sin I π ( ) F( )
xmpl
Ointtion- vticl dipol nd hoizontl pln I π ( ) F( ) Th dipol is t th oigin ointd long th z xis which is th vticl xis. Th hoizontl pln is th xy pln 9.
Hlf-Wv Dipol Antnn Fom bov: I π ( ) F( ) F ( ) π cos cos sin
F π cos cos sin π π cos cos π sin cos ( )
wh F ( ) π cos cos sin
6 ππ 3 d F ( ) π F 3 π cos cos sin π π cos cos 3 π sin 3.865
Rviw: F Fild of n Antnn ( ) ( ) + ( ) ( ) H + + S v Th pow flow dnsity: Wtts/mt
Rviw: Th F Filds of Dipol Antnn It My B Shown tht: ( ) ( ) I π ( ) F( )
Rdition Pttns ( ) ( ) + ( ) Azimuth Pttn fo: 9 : nd vs. (xy pln) lvtion pttn fo : nd vs. (xz pln) lvtion pttn fo 9 : nd vs. (yz pln)
I π ( ) F( ) F ( ) π cos cos sin
π π π π I F I cos sin cos cos π π π π F so ( ) π sin cos cos F
I π ( ) F( ) I π π cos cos sin
Amplitud vs. Position 48
Ay of Two Dipols Fo ch individul dipol: ππ II ooff FF cos ππ cos sin In th zimuth o 9 dgs pln FF cos ππ cos ππ sin ππ cos Hnc w cn wit mo simply s CCII oo wh CC ππ And th distnc fom th dipol to th obsv.
Ay of Two Dipols continud II oo δδ # # II oo Fo dipol # t th oigin th cunt is II oo nd th fild stngth is CCII oo RR RR RR th distnc fom dipol # to th obsv. An ntnn y is md up of two vticl hlf-wv dipol ntnns. Antnn # is t th oigin nd cis cunt II oo. Antnn # is t xx dd nd cis cunt II oo δδ with phs shift of δδ ltiv to ntnn #. Find th f fild. Fo dipol # t xx dd th cunt is II oo δδ nd th fild stngth is: CCII oo δδ RR RR RR th distnc fom dipol # to th obsv. Fo two dipols cting togth us supposition: CCII oo RR RR RR δδ + CCII oo RR Cn w simplify this fo n obsv in th f fild?
Ay of Two Dipols: F Fild Appoximtion # # CI R R R R d cos + CI δ R wh is th distnc fom th oigin to th obsv. Fo ntnn # RR is smll thn : R Fo mplitud nglct dd cos compd to. But fo phs puposs w cnnot nglct dd cos bcus it my b significntly-lg phs ngl such s 9 dgs o 8 dgs. CI CI + CI + CI + δ δ ( d cos ) d cos ( d cos ) ( ) ( δ d cos CI )
nd Fi Ay: dition in th +x diction. + ( ) ( δ d cos CI ) Choos π δ λ d 4 π λ π d λ 4 CCII oo Ninty dgs out of phs. Spc th ntnns qut-wvlngth pt. + ππ ππ cos
In th Obsv t Zo Dgs + x diction fo cos + cos ( ) CI π π CI + + π π π π cos ( ) CI CI CI ( + ) CI CCII oo ππ ππ cos II oo CCII oo
In th Obsv t 8 Dgs + + π π π π cos8 ( ) π CI CI CI ( + ) x diction fo 8 8 cos8 cos ( ) CI + π π CI CCII oo ππ ππ cos ππ II oo CCII oo
Amplitud vs. Position
Cdioid Rdition Pttn
Bodsid Ay: dition in th +y nd y diction. + ( ) ( δ d cos CI ) Choos: δ λ d π λ d π λ + Opt th ntnns in phs Spc th ntnns hlf-wvlngth pt ( ) ( π cos CI ) δ
Obsv t 9 Dgs CI π cos9 ( 9) CI ( + ) CI ( + ) CI ( + ) + ( ) ( π cos CI ) 9 cos 9 Th filds in phs nd dd nd so th is mximum fild stngth fo 9 dgs.
Obsv t Zo Dgs + ( ) ( π cos CI ) cos ( ) ( π cos ) ( π CI + CI + ) CI ( ) Th filds out of phs nd subtct nd so th is zo fild fo dgs.
Amplitud vs. Position
Rdition Pttn
Dictionl Accss-Point Antnn
Th is blun on th oth sid: Blun blnc to unblnc tnsfom. Th ntnn is blncd Th coxil cbl is unblncd. 79
Rdition Pttn of th Dictionl AP Antnn