School of lctical ngining Lctu : Wi Antnnas
Wi antnna It is an antnna which mak us of mtallic wis to poduc a adiation. KT School of lctical ngining www..kth.s
Dipol λ/ Th most common adiato: λ Dipol 3λ/ KT School of lctical ngining www..kth.s 3
Fding Balanc o unbalanc? - If w ty to fd a balanc antnna with unbalanc fding, th adiation pattn can b distotd and asymmtic. - Th unbalancd cunts can b liminatd using a balun (balancd to unbalancd tansfom) KT School of lctical ngining www..kth.s 4
Infinitsimal dipol It is an lctically small antnna. Its dimnsions a much small than th wavlngth (l<<λ, l λ/5). Cunt: I( z) I KT School of lctical ngining www..kth.s 5
Th magntic potntial is: wh R is: and thn: Infinitsimal dipol: Cunt KT School of lctical ngining www..kth.s 6 / / ' ') ', ', ( 4 ),, ( l l jk dl z y x I z y x A z y x jk l l z jk z l I a dz I a z y x A / / 4 ' 4 ),, ( ') ( I z I
Infinitsimal dipol: Filds (I) If w know th magntic potntial, w can obtain th Filds (,). A j j A ( And changing th coodinats to sphical: A) A A A sin cos cos cos sin sin sin cos sin cos cos A sin A A x y z KT School of lctical ngining www..kth.s 7
Infinitsimal dipol: Filds (II) W know that: A x A y So thn: A A A jk Il 4 Il 4 cos jk sin Rmmb that: A j j A ( A) j KT School of lctical ngining www..kth.s 8
Infinitsimal dipol: Filds (III) So, th magntic fild will b: A / sin A / A sin / sin A jki l sin 4 jk jk And th lctic fild will b: I ki j l cos l sin 4 jk jk jk ( k) jk KT School of lctical ngining www..kth.s 9
omwok To div th magntic fild fom th magntic potntial vcto fo an infinitsimal dipol: jki l sin 4 jk jk KT School of lctical ngining www..kth.s
Th pow is coming fom th Poynting vcto: Fo this paticula cas: Infinitsimal dipol: Radiatd pow KT School of lctical ngining www..kth.s W W W W W
Infinitsimal dipol: Radiatd pow Thn: W 8 sin j I l 3 k and: W jk I l cos sin 3 6 k So, th pow is: P S Wds W W sin dd W sin dd P 3 I l j 3 k KT School of lctical ngining www..kth.s
omwok Div th total pow fom th point vcto: P S Wds W W sin dd W sin dd P 3 I l j 3 k KT School of lctical ngining www..kth.s 3
Infinitsimal dipol: Radiatd pow P P tot _ ad ~ j W m ~ W Th tim-avag adiatd pow: P tot _ ad Il 3 Th tim-avag activ pow: ~ W m ~ W Il 3 k 3 KT School of lctical ngining www..kth.s 4
Infinitsimal dipol: Na Fild W hav: I jki l sin 4 ki j l cos l sin 4 jk jk jk jk jk ( k) jk Dominant lmnts k k Il sin 4 jk Il cos j 3 k Il sin j 3 4k jk jk KT School of lctical ngining www..kth.s 5
W hav: Infinitsimal dipol: Fa Fild I jki l sin 4 ki j l cos l sin 4 jk jk jk jk jk ( k) jk Dominant lmnts k k jkil sin 4 ki j l sin 4 jk jk TM Mod: tansvsal lctic and magntic KT School of lctical ngining www..kth.s 6
Impdanc: Fa fild W hav a plan wav: jkil sin 4 ki j l sin 4 jk TM Mod: tansvsal lctic and magntic jk Z wav Z wav KT School of lctical ngining www..kth.s 7
Dictivity: Infinitsimal dipol Th adiatd pow is: P ad sin j 3 8 I l k In fa fild, it is: 8 And th adiation intnsity is: P ad Il sin kil sin j 4 jk U kil kil sin Pad sin 8 4 KT School of lctical ngining www..kth.s 8
Dictivity: Infinitsimal dipol Th maximum adiation intnsity is: / U max 8 kil So, th dictivity is: D max U P max 4 tot _ ad Il 8 4 Il 3 3 KT School of lctical ngining www..kth.s 9
Infinitsimal dipol Simulatd sults: -fild Radiation Pattn KT School of lctical ngining www..kth.s
Dipol Lt s suppos th following cunt distibution in th dipol: zi I( x', y', z') zi sin k sin k l z' z' l l z' z' l l / l KT School of lctical ngining www..kth.s
Dipol Sinc th dipol is not infinitsimally small, w can t tak as distanc to th dipol. If w hav a dipol ointd in z axis. R z'cos KT School of lctical ngining www..kth.s
Dipol W calculatd bfo th fa filds fo a small dipol: Thn, th diffntial is: jki( x', y', z')sin 4R ki( x', y', z')sin j 4R jkr l jkr l d d jki( x', y', z')sin 4R ki( x', y', z')sin j 4R jkr dz' jkr dz' KT School of lctical ngining www..kth.s 3
Whn fa fild: thn: Dipol d jkr ki( x', y', z')sin jk jkz' cos j dz' 4 and th lctic fild is: R jk( z'cos ) jk jkz'cos d k j sin 4 jk l / l / I( x', y', z') jkz'cos dz' I j jk cos kl cos cos sin kl j I jk cos kl cos cos sin kl KT School of lctical ngining www..kth.s 4
omwok 3 Undstanding of: R jkr jk( z'cos ) jk jkz'cos Plot fo lag valus of th magnitud and phas of: ) ) jk R jk jkz'cos What is a lag valu of? (choos an abitay valu of angl and fquncy) KT School of lctical ngining www..kth.s 5
Dipol Radiatd pow: P ad R I 8 cos kl cos cos sin kl Radiation intnsity: U P ad I 8 cos kl cos cos sin kl KT School of lctical ngining www..kth.s 6
Whn l = λ/: Dictivity: Dipol λ/ KT School of lctical ngining www..kth.s 7 sin cos cos 8 sin cos cos cos 8 U I I.5 dbi.64 4 _ max max ad P tot U D _ sin cos cos 4 P d I ad tot 3 sin 8 U I
Dipol λ/ Simulatd sults: Fa filds -fild Radiation Pattn KT School of lctical ngining www..kth.s 8
Plot (fo instanc in Matlab), th adiation pattn fo dipols of diffnt sizs: l=λ/5 l=λ/3 l=λ l=3λ/ l=λ omwok 4 Calculat numically th maximum dictivity fo ach cas. kl kl D max 4 max U U sin dd max U U sin d U U cos cos cos sin KT School of lctical ngining www..kth.s 9
Imag Thoy (I) Whn ou antnna is placd na to a lctic o magntic fild: lctic lctic Magntic Magntic h h σ= (lctic conducto) lctic lctic Magntic Magntic KT School of lctical ngining www..kth.s 3
Imag Thoy (II) Whn ou antnna is placd na to a lctic o magntic fild: lctic lctic Magntic Magntic h h σ m = (Magntic conducto) lctic lctic Magntic Magntic KT School of lctical ngining www..kth.s 3
Infinit pfct conducto W could gt a cohnt contibution fom a dipol and its gound plan to poduc a cohnt adiation. KT School of lctical ngining www..kth.s 3
Infinit pfct conducto Fo a singl infinitsimal dipol (fa fild): d kil sin j 4 jk With th Imag thoy: kil sin jrv 4 jk Fo a pfct conducto (σ= ): R v KT School of lctical ngining www..kth.s 33
Infinit pfct conducto Th contibutions will b summd: TOT TOT d z z and in fa fild, fo th amplituds: but not fo th phass:, hcos hcos KT School of lctical ngining www..kth.s 34
Infinit pfct conducto Th total fa fild (θ componnt): TOT TOT ki j ki j l sin 4 l sin 4 jk( hcos ) jk cos( khcos) jk( hcos ) Th dictivity is: D max 3 cos(kh) (kh) sin(kh) 3 (kh) KT School of lctical ngining www..kth.s 35
Infinit pfct conducto Dictivity vsus th distanc to th gound plan: KT School of lctical ngining www..kth.s 36
Infinit pfct conducto λ/4 distanc. Simulations of adiation pattn: KT School of lctical ngining www..kth.s 37
Infinit pfct conducto 5λ distanc. Simulations of adiation pattn: KT School of lctical ngining www..kth.s 38
Monopol A vy common antnna, bcaus it is quivalnt to a full λ/ dipol: KT School of lctical ngining www..kth.s 39
Monopol λ/4 lngth. Simulations: Radiation Pattn Fa filds KT School of lctical ngining www..kth.s 4