T-Match: Matching Techniques For Driving Yagi-Uda Antennas: T-Match. 2a s. Z in. (Sections 9.5 & 9.7 of Balanis)
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1 3/0/018 _mch.doc Pge 1 of 6 T-Mch: Mching Techniques For Driving Ygi-Ud Anenns: T-Mch (Secions 9.5 & 9.7 of Blnis) l s l / l / in The T-Mch is shun-mching echnique h cn be used o feed he driven elemen of Ygi-Ud nenn. I uses second shorer dipole h is plced smll disnce s (s << ) from he driven elemen (prllel, nd cenered in he plne of he Ygi-Ud nenn). As i is symmericl nd blnced, i is ypiclly used o connec winled rnsmission lines o Ygi-Ud nenns. Design nlysis nd procedure follows h for he folded dipole. Due o muul coupling wih he reflecor nd direcor elemens, he design of he T-Mch is pproxime. In prcice, lengh djusmens will usully be required. The chrcerisic impednce of he rnsmission line porion of he 1 s T-Mch is given by 0 cosh
2 3/0/018 _mch.doc Pge of 6
3 3/0/018 _mch.doc Pge 3 of 6 V where V, nd we define curren divisor fcor 1 1 v u 1 cosh 1 when ' v 1 when ' 1 v u 1 cosh 1 when ' vu s where u nd v. The curren divisor fcor hs big impc ' ' on he mgniude of in (i.e., when increses in increses nd vice vers). The curren divisor fcor is inversely reled o he spcing s (i.e., if s decreses increses nd vice vers).
4 3/0/018 _mch.doc Pge 4 of 6 Trnsmission line mode impednce: Definiion of rnsmission line inpu impednce where k = = /. 1 V ' j 0 n kl '/ I Noe, for 0 < l < 0.5, we ge 0 n(kl /) > 0, i.e., inducive recnce. This is ypiclly he cse encounered when using T-mch by iself or in Ygi-Ud nenn. When l = 0.5, = j 0 n(/). Anenn mode impednce nd curren: The nenn impednce is usully found numericlly using Mehod of Momens (MoM) progrm for dipole h hs rdius e (he equivlen rdius of he wo wires) over he lengh l nd rdius for he porion of he dipole exending beyond he T-Mch (l < l). [Noe: If T-Mch used o drive Ygi-Ud nenn, his equivlen dipole should be insered ino he Ygi-Ud nenn o deermine.] The equivlen rdius for wo closely spced (cener-o-cener disnce s) wires of rdii nd is deermined by 1 u u u v (1 u) ln( e) ln( ') ln ln Definiion of nenn inpu impednce V ' (1 ) I Tol impednce nd curren for T-Mch: The curren he erminls of he T-Mch is
5 3/0/018 _mch.doc Pge 5 of 6 1 V ' V ' I I I (1 ) 1 1 (1 ) V V (1 ) (1 ) 1 1 V 1 1 I V' (1 ) 1 (1 ) Solving for he inpu dmince nd impednce, yields nd Y I 1 1 V in (1 ) Y Y (1 ) V (1 ) I (1 ) in For he cse h l / (hlf-wve dipole), he rnsmission line impednce >>, herefore, he inpu impednce becomes in (1 ) If =, he curren division fcor = 1 nd we ge s before. in 4 Noe: If hs n inducive recnce (i.e., X > 0), i my no be possible o chieve relizble mch using sndrd T-Mch s will lso hve n inducive recnce. In h cse, eiher he lengh l needs o be shorened o mke hve cpciive recnce (i.e., X < 0) or modified T-Mch my be used.
6 3/0/018 _mch.doc Pge 6 of 6 Design Process: We desire o mch given Ygi-Ud nenn o rnsmission line chrcerisic impednce 0,feed. Usully, specificion in erms of he VSWR is given. 1) Selec driven elemen lengh l so h l 1 < l < l 3,, s, nd l (usully l < l /). These vlues my be chnged ler. ) Clcule he chrcerisic impednce 0 of he rnsmission line porion of he T-Mch. 3) Clcule he rnsmission line mode inpu impednce. 4) Clcule he prmeers u, v, nd. 5) Clcule he equivlen rdius e of he T-Mch secion. 6) Find inpu impednce of nenn mode. 7) Find overll inpu impednce in. 8) Deermine if in mees your specificion. If so, sop design process. If no, ry chnging l o l ' 1 n k Y Im (1 ) 1 0 o beer offse he nenn mode recnce, nd repe seps ) hrough 8). If necessry, l,, nd s cn be vried. Remember, he mgniude of he inpu impednce is grely ffeced by (i.e., when increses in increses nd vice vers). In urn, is inversely reled o s (i.e., if s decreses increses nd vice vers).
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