Lecture 27: The 180º Hybrid.

Transcription

1 Whits, EE 48/58 Lctur 7 Pag f 0 Lctur 7: Th 80º Hybrid. Th scnd rciprcal dirctinal cuplr w will discuss is th 80º hybrid. As th nam implis, th utputs frm such a dvic can b 80º ut f phas. Thr ar tw primary bjctivs fr this lctur. Th first is t shw that th S matrix f th 80º hybrid is j S (7.0),() with rfrnc t th prt dfinitins in Fig. 7.4: ( ) ( ) 4 80º Hybrid 3 Th scnd primary bjctiv is t illustrat th thr cmmn ways t prat this dvic. Ths ar:. In-phas pwr splittr: Input Islatin 4 80º Hybrid 3 Thrugh Cupld With input at prt and using clumn f [S], w can dduc that prt is matchd, th utputs ar prts and 3 (which ar in phas with ach thr) and prt 4 is th islatin prt. 06 Kith W. Whits

2 Whits, EE 48/58 Lctur 7 Pag f 0. Out-f-phas pwr splittr: Islatin Input 4 80º Hybrid 3 Thrugh Cupld With input at prt 4 and using clumn 4 f [S], w can dduc that prt 4 is matchd, th utputs ar prts and 3 (which ar cmpltly ut f phas with ach thr) and prt is th islatin prt. 3. Pwr cmbinr: Sum ( ) Diffrnc ( ) 4 80º Hybrid 3 Input A Input B With inputs at prts and 3 and using clumns and 3 f [S], w can dduc that bth prts and 3 ar matchd, prt will prvid th sum f th tw input signals and prt 4 will prvid th diffrnc. Bcaus f this, prts and 4 ar smtims calld th sum and diffrnc prts, rspctivly. Thr ar diffrnt ways t physically implmnt a 80º hybrid, as shwn in Fig W ll fcus n th ring hybrid and spcifically cnsidr th first tw applicatins dscribd abv. Thr is lss symmtry in th S matrix () fr th 80º hybrid

3 Whits, EE 48/58 Lctur 7 Pag 3 f 0 than th quadratur hybrid s w xpct lss physical symmtry as wll. Ring Hybrid Th ring hybrid (aka th rat rac) is shwn in Fig. 7.4a: W ll analyz this structur using th sam vn-dd md apprach w applid t th Wilkinsn pwr dividr and th branch lin cuplr in th prvius tw lcturs. In th prsnt cas, th physical symmtry plan biscts prts and frm 3 and 4 in th figur abv.. In-phas pwr splittr. Assum a unit amplitud vltag wav incidnt n prt :

4 Whits, EE 48/58 Lctur 7 Pag 4 f 0 Prt Prt B B Prt 3 B 3 Prt 4 B 4 As in Lctur 6, prpr symmtric and anti-symmtric xcitatins f this dvic ar rquird t prduc th vn and dd md prblms, as shwn in Fig. 7.44: B B3 B4 B B B3 B4 B Ntic that w r trating th curvd prtins f th rat rac dvic as straight sctins f TLs. Ignring this curvatur may b a rasnabl assumptin. Similar t what w drivd in Lctur 6,

5 Whits, EE 48/58 Lctur 7 Pag 5 f 0 B (7.0a),() B T T (7.0b),(3) B3 (7.0c),(4) B4 T T (7.0d),(5) Each f th vn and dd slutins fr B i ( i,,4) can b fund by cascading ABCD matrics, thn cnvrting t S paramtrs. Sinc th prts ar trminatd by matchd lads, w can dirctly dtrmin and T frm ths S paramtrs. As givn in th txt, j (7.04a,c),(6) j T T (7.04b,d),(7) Using ths valus in ()-(5) prducs B B4 0 (7.05a,d),(8) j B B3 (7.05b,c),(9) Ths rsults in (8) and (9) frm th first clumn f [S] in (). Thy indicat that with an input at prt and all utput prts trminatd by matchd TLs and lads, th signal is

6 Whits, EE 48/58 Lctur 7 Pag 6 f 0 qually dividd in phas at prts and 3, whil nn is dlivrd t prt 4. Using th physical symmtry f th circuit and xciting nw at prt 3, w can apprpriatly transps th rws f clumn t btain th third clumn f [S] in ().. Out-f-phas pwr splittr. Assum a unit amplitud vltag wav is incidnt n prt 4. Prt Prt B B B 3 Prt 3 B 4 Prt 4 T gnrat symmtric and anti-symmtric prblms, w ll xcit th circuit at prts and 4, as shwn in Fig. 7.45:

7 Whits, EE 48/58 Lctur 7 Pag 7 f 0 B B B3 B4 B B B 3 B4 Ths tw xcitatins sum t + at prt 4 and 0 at prt, as rquird. Frm Fig. 7.45a, th vn md prblm is T /4 Prt Prt /8.c. /8 Frm this figur (and th vn symmtry), w can writ B T B3 and B B4 (0),() Frm Fig. 7.45b, th dd md prblm is.c.

8 Whits, EE 48/58 Lctur 7 Pag 8 f 0 T /4 Prt Prt /8 /8 Frm this figur (and th dd symmtry), w can writ B T B3 and B B4 (),(3) Summing (0)-(3), w find B B B T T (7.06a),(4) B B B (7.06b),(5) B3 B3 B3 T T (7.06c),(6) B4 B4 B4 (7.06d),(7) Cascading ABCD matrics and cnvrting t S paramtrs, th txt shws that B B4 0 (7.09a,d),(8) j B B3 (7.09b,c),(9) Ths valus frm th furth clumn f [S] in (). Thy indicat that with xcitatin at prt 4 and all utput prts

9 Whits, EE 48/58 Lctur 7 Pag 9 f 0 trminatd by matchd TLs and lads, prt is islatd and th signal is qually split btwn utput prts and 3 with a 80º phas shift btwn thm. Onc again, using th physical symmtry f th circuit and xciting nw at prt, w can apprpriatly transps th rws f clumn 4 t btain th scnd clumn f [S] in (). Dsign f 80º Hybrid Th ring hybrid is xtrmly asy t dsign. On first cmputs th ffctiv prmittivitis and strip widths fr th Z 0 and Z 0 sctins f th dvic n a chsn substrat. Thn aftr chsing a cntr frquncy, th physical lngths f th /4 and 3 /4 prtins can b calculatd, again using th ffctiv prmittivitis. That s basically it. Typical S j rsults fr this dvic ar shwn in Fig. 7.46:

10 Whits, EE 48/58 Lctur 7 Pag 0 f 0 Can yu intrprt th maning f ths rsults? Hw d yu xpct S 4 and S 3 t bhav?