GU (r. Hay Hamma) 4/0/06 Lctur # 0 Filtr sig y Th srti Lss Mth sig Stps Lw-pass prttyp sig. () Scalig a cvrsi. () mplmtati. Usig Stus. Usig High-Lw mpac Sctis. Thry f priic structurs. mag impacs a Trasfr fuctis fr tw-prt twrks. r. Hay Hamma, Grma Uivrsity i air Stpp mpac Lw-Pass Filtrs y usig altratig sctis f vry high a vry lw charactristic impac lis. Kw as Stpp-impac r hi-, lw- filtrs. cs l j si l l j si l cs l, Rciprcal twrk j ct l j si l li j ct l j si l j si l j l ct OMM (603) Lctur #0
GU (r. Hay Hamma) 4/0/06 Stpp mpac Lw-Pass Filtrs T-Equivalt ircuit cs l j j si l j j si l si cs l / l X j ta j l / Stpp mpac Lw-Pass Filtrs X l ta si l l 4 f w hav a shrt lgth f li a larg charactristic impac f w hav a shrt lgth f li a small charactristic impac X l 0 highimpac X 0 Yl lwimpac h l l LR h (iuctr) l R l (capacitr) h l Rati shul as high as pssil OMM (603) Lctur #0
GU (r. Hay Hamma) 4/0/06 Exampl 8.6 sig a stpp-impac lw-pass filtr havig a maximally flat rsps a a cutff frqucy f.5 GHz. t is cssary t hav mr tha 0 isrti lss at 4 GHz. Th filtr impac is 50 ; th highst practical li impac is 0, a th lwst is 0. sir th ffct f lsss wh this filtr is implmt with a micrstrip sustrat havig =0.58 cm, r =4., ta = 0.0, a cppr cuctrs f 0.5 mil thickss. aswr c.5 GHz R 50 L 0 h 0 4 @ 4GHz 0.6 c.5 h l 0 6 l Exampl 8.6 6 OMM (603) Lctur #0 3
GU (r. Hay Hamma) 4/0/06 Exampl 8.6 g 0.57 g g g g g 3 4 5 6.44 L.93.93 L.44 3 4 5 0.57 L 6 Exampl 8.6 l l L R 0.57 0 50 l R.4450 0 h 0.068 0.589.849 33.759 OMM (603) Lctur #0 4
GU (r. Hay Hamma) 4/0/06 Exampl 8.6 Thry f priic structurs Priic structurs ifiit trasmissi li priically la with ractiv lmts is rfrr t as a priic structur. OMM (603) Lctur #0 5
GU (r. Hay Hamma) 4/0/06 alysis f ifiit priic structurs Lt k,k Y Whr k is th prpagati cstat f th ula li l cs kl jy si kl j si kl cs kl Y 0 ls assum rmaliz valu t alysis f ifiit priic structurs cs j si 0 cs j si si cs j j j si cs cs j si cs j si j si cs j cs j si si cs cs si cs si jcs si j si jcs si si cs cs si cs si cs si j j j cs cs si si cs si cs j j cs cs si cs si cs si jcs si j si cs si cs si cs cs si cs OMM (603) Lctur #0 6
GU (r. Hay Hamma) 4/0/06 OMM (603) Lctur #0 7 alysis f ifiit priic structurs si cs cs si cs si si cs j j alysis f ifiit priic structurs z z z z (0) ) ( (0) ) ( Or 0 Fr a wav prpagatig i th +v ircti. 0 0
GU (r. Hay Hamma) 4/0/06 alysis f ifiit priic structurs Fr a Rciprcal twrk i trms f S-paramtrs S S trm f Trasmissi paramtrs, usig cvrsi tals Fr a trivial sluti, th trmiat f th matrix must vaish 0 0 ( ) 0 ( ) 0 ivi y 0 csh ut a cs si hc alysis f ifiit priic structurs csh cs si assum j csh csh cs j sih si cs si Th ccrigly, Must hav ithr =0, r =0 as 0, 0, as 0, 0 j -attuatig (pass-a) (mplx ) cs cs si ttuatig (stp-a) (Ral ) csh cs si Sic cs Sic csh cs si cs si t li is lsslss, s pwr is t issipat it is just rflct ack t th iput. OMM (603) Lctur #0 8
GU (r. Hay Hamma) 4/0/06 alysis f ifiit priic structurs ttuatig (stp-a) (Ral ) -attuatig (pass-a) (mplx ) alysis f ifiit priic structurs OMM (603) Lctur #0 9
GU (r. Hay Hamma) 4/0/06 OMM (603) Lctur #0 0 alysis f ifiit priic structurs alysis f ifiit priic structurs haractristic impac (lch mpac) at th uit cll trmials is giv y 0 0 0 0 ) ( 4 ) ( ) ( 4 Fr symmtrical clls + Fr psitiv travlig wavs. Fr gativ travlig wavs. Frm th trmiat f th matrix 0 ) ( x x 4 t: th valus wr rmaliz
GU (r. Hay Hamma) 4/0/06 alysis f ifiit priic structurs t that is always imagiary Hc as 0, 0, as 0, 0 -attuatig (pass-a) jsi cs cs si ttuatig (stp-a) cs si cs si magiary Ral Ral magiary Similar t Prpagatig Ms Similar t Evasct ms ( prpagatig ms) Trmiat Priic Structurs j z z j z j (ssum passa) 0 z Scti j j j Th icit a rflct vltags at th th uit cll j j j OMM (603) Lctur #0
GU (r. Hay Hamma) 4/0/06 OMM (603) Lctur #0 Trmiat Priic Structurs t th la whr = L L (=) i cas f symmtrical clls L L L T avi trmial rflctis yu must hav L & als L & Hc L L Exampl 9. priic la li, if =50, =.0 cm, a =.666 pf, sktch th k- iagram a cmput th prpagati cstat, phas vlcity, a lch impac at f = 3.0 GHz. ssum k=k. swr si cs cs k k k k si cs cs is rmaliz t Y k k si cs cs Y Y & t k is fucti f S w will rwrit th fucti i trm f k
GU (r. Hay Hamma) 4/0/06 Exampl 9. k c k c c cs cs k k si k c.6660 5030 0 cs cs k k si k 8 Passa Stpa cs k k si k cs k k si k Th av quati ca valuat umrically fr giv valus f k k c Sic c a ar cstats yu ar plttig agaist frqucy Exampl 9. 0 0.96 k OMM (603) Lctur #0 3
GU (r. Hay Hamma) 4/0/06 Exampl 9. t 3.0 GHz, w hav 9 3 0 k (0.0) 0.683 36 8 30 cs cs(36) (0.683) si(36 ). 5 50 kc 0.683 vp 0. 4c.5 lch impac.56 k 0.683 cs si 0.0707 jsi cs j0.3479 j0.347950 0.0707 7. 4 j mag impacs & Trasfr fuctis f tw prt twrk Fi mag mpac a trasfr fucti if a tw prt twrk? mag mpac as fucti f th Paramtrs i = iput impac at prt wh prt is trmiat with i i = iput impac at prt wh prt is trmiat with i t that th rfrc ircti fr th currt at prt has chs accrig t th cvti fr trasmissi paramtrs. r. Hay Hamma, Grma Uivrsity i air OMM (603) Lctur #0 4
GU (r. Hay Hamma) 4/0/06 mag impacs & Trasfr fuctis f tw prt twrk hc put impac at prt, with prt trmiat with i i caus i i i i r. Hay Hamma, Grma Uivrsity i air mag impacs & Trasfr fuctis f tw prt twrk Rciprcal twrk i u t th currt ircti Slvig fr a y vrtig matrix r. Hay Hamma, Grma Uivrsity i air i i i OMM (603) Lctur #0 5
GU (r. Hay Hamma) 4/0/06 mag impacs & Trasfr fuctis f tw prt twrk W sir that i i & i i Frm i i & i i i i r. Hay Hamma, Grma Uivrsity i air ii i i i i Sutractig th quatis i i i i i i i i i ii i i i i i i & sic i i i f symmtrical twrk i i i i mag mpac as fucti f th Paramtrs mag impacs & Trasfr fuctis f tw prt twrk Th trasfr fucti f th twrk i trm f Similarly frm r. Hay Hamma, Grma Uivrsity i air i i t: x y x y t: x yx y x y x y Fr a symmtrical T r twrks th cfficit is uity OMM (603) Lctur #0 6
GU (r. Hay Hamma) 4/0/06 mag impacs & Trasfr fuctis f tw prt twrk (Rati) Fr rciprcal twrks this factr ca qual t uity. Prpagati factr f th twrk r. Hay Hamma, Grma Uivrsity i air mag impacs & Trasfr fuctis f tw prt twrk Lt j t: x y x y x yx y x y x y csh csh Symmtrical T r twrks ca us t sig th filtrs / / twrk r. Hay Hamma, Grma Uivrsity i air T twrk OMM (603) Lctur #0 7
GU (r. Hay Hamma) 4/0/06 mag mpac Prpagati stat Paramtrs mag impacs & Trasfr fuctis f tw prt twrk / / i csh i i 4 T r. Hay Hamma, Grma Uivrsity i air 4 csh 4 it 4 4 csh 4 mag impacs & Trasfr fuctis f tw prt twrk xt stp is t vlp th lw-pass a high-pass filtr scti. Shrt Lw frqucy Lw Pass Rsps Shrt High Frqucy Highpass Rsps r. Hay Hamma, Grma Uivrsity i air OMM (603) Lctur #0 8