haptr 7 ntrl Sytm Dgn by th t Lu Mthd 7. Intrdutn! Prfrman Spfatn: h rqurmnt mpd n th ntrl ytm ar plld ut a prfrman pfatn, whh gnrally rlat t auray, rlatv tablty, and pd f rpn.! Sytm mpnatn: Sttng th gan th frt tp n adjutng th ytm fr atfatry prfrman. In many pratal a, hwvr, adjutmnt f th gan aln may nt prvd uffnt altrnatn f th ytm bhavr t mt th gvn pfatn. A rdgn r addtn f a utabl dv alld mpnatn. h dv alld a mpnatr.! Sr mpnatn and fdbak (r paralll) mpnatn # Sr mpnatn: Fgur 7- (a). h mpnatr G () plad n r wth th plant. $ Smplr than fdbak mpnatn. $ Frquntly rqur addtnal amplfr t nra th gan and/r t prvd latn. # Fdbak mpnatn: Fgur 7- (b). It fd bak th gnal() frm m lmnt() and pla a mpnatr n th rultng nnr fdbak path.! mpnatr # Lad mpnatr: If a nudal nput appld t th nput f a ntwrk and th tady-tat utput ha a pha lad wth th am frquny, thn th ntwrk alld a lad ntwrk. h mpnatr havng a haratrt f a lad ntwrk a lad mpnatr. # Lag mpnatr: h mpnatr wth a pha lag haratrt. # Lag-lad mpnatr: Pha lag ur n th lw-frquny rgn and pha lad n th hgh-frquny rgn.! Dgn prdur: # St up a mathmatal mdl f th ntrl ytm # Adjut th paramtr f a mpnatr by tral and rrr ung mputr mulatn, n rdr t mt th dgn pfatn. # ntrut a prttyp and tt th pn-lp ytm. If ablut tablty f th ld-lp aurd, th dgnr l th lp and th prfrman f th ld-lp ytm. If th prfrman nt atfd, g t th frt tp, agan. 7-
7. Prlmnary Dgn ndratn! W aum that th plant gvn and unaltrabl. h dgn prblm bm th f mprvng ytm prfrman by nrtn f a mpnatr. mpnatn f a ntrl ytm rdud t th dgn f a fltr wh haratrt tnd t mpnat fr th undrabl and unaltrabl haratrt f th plant.! t-lu apprah t ntrl ytm dgn: In th dgn, th rt l f th ytm ar rhapd thrugh th u f a mpnatr that a par f dmnant ld-lp pl an b plad at th drd latn. (Oftn, th dampng rat and undampd natural frquny f a par f dmnant ld-lp pl ar pfd.)! fft f th addtn f pl: h addtn f a pl t th pn-lp tranfr funtn ha th fft f pullng th rt lu t th rght, tndng t lwr th ytm rlatv tablty and t lw dwn th ttlng f th rpn (Fgur 7- ).! fft f th addtn f zr: h addtn f a zr t th pn-lp tranfr funtn ha th fft f pullng th rt lu t th lft, tndng t mak th ytm mr tabl and t pd up th ttlng f th rpn (Fgur 7-). 5.8 ltrn ntrllr (rvw)! Opratnal amplfr: Fr th rut n Fgur 5-4, w hav ( ) ( ) 0 Whr th nput and may b d r a gnal and th dffrntal gan r vltag gan. h magntud pf apprxmatly 0 5 ~0 6 fr d gnal and a gnal wth frquny l than apprxmatly 0Hz. (h dffrntal gan dra wth th gnal frquny and bm abut unty fr frqun f MHz ~50MHz.) In th dal OP amp, th nput mpdan nfnty (n urrnt nput) and th utput mpdan zr.! Invrtng amplfr: Fr Fgur 5-44 lt u btan th utput vltag 0. 0 7-
7- Sn nly a nglgbl urrnt flw nt th amplfr, Sn ( ) 0 0 and ff, mut b almt zr. Hn w hav r If, thn th p-amp rut at a a gn nvrtr.! Nn-nvrtng amplfr: Fr Fgur 5-45(b), whh quvalnt t Fgur 5-45(a), w hav fr >>. hu Sn and hav th am gn, th p amp rut nn-nvrtng. xampl 5-) Fr Fgur 5-46 lt u dfn Sn th urrnt flwng nt th amplfr nglgbl, w hav Sn 0, w hav akng th Lapla tranfrm, 0 0 0 ( ) dt d ( ) dt d dt d () () () ()
h p-amp rut hwn n Fgur 5-46 a frt-rdr lag rut. S abl 5-.! Impdan apprah fr btanng tranfr funtn: Fr th rut hwn n Fgur 5-47, w hav () () () () xampl 5-4) h mplx mpdan () and () fr th rut n Fgur 5-46 ar Hn, h tranfr untn! Lad r lag ntwrk ung pratnal amplfr: Fr th rut n Fgur 5-48, w hav whr () () dv dt () I() I () V() () () I() () () () () α 4 7-4
7. Lad mpnatn! Lad mpnatr: Fgur 7-4 hw an ltrn rut ung pratnal amplfr. h tranfr funtn fr th rut btand a fllw: whr () () α # Lad ntwrk: > ; Fgur 7-5(a) # Lag ntwrk: < ; Fgur 7-5(b) 4! Lad mpnatn thnqu bad n th rt-lu apprah: ndr a dgn prblm n whh th rgnal ytm thr untabl fr all valu f gan r tabl but undrabl trannt-rpn haratrt. In uh a a, th rhapng f th rt lu nary n th brad nghbrhd f th jω ax and th rgn n rdr that th dmnant ld-lp pl b at drd latn n th mplx plan. h prblm may b lvd by nrtng an apprprat lad mpnatr n aad wth th fd-frward tranfr funtn.! h prdur fr dgnng a lad mpnatr fr th ytm hwn n Fgur 7-6 by th rt-lu mthd may b tatd a fllw:. Frm th prfrman pfatn, dtrmn th drd latn fr th dmnant ld-lp pl.. By drawng th rt-lu plt, artan whthr r nt th gan adjutmnt aln an yld th drd ld-lp pl. If nt, alulat th angl dfny φ. h angl mut b ntrbutd by th lad mpnatr f th nw rt lu t pa thrugh th drd latn fr th dmnant ldlp pl.. Aum th lad mpnatr G () t b G () α ( 0 < α < ) Whr α and ar dtrmnd frm th angl dfny. dtrmnd frm 7-5
th rqurmnt f th pn-lp gan. 4. If tat rrr ntant ar nt atfd, dtrmn th latn f th pl and zr f th lad mpnatr that th lad mpnatr wll ntrbut th nary angl φ. If n thr rqurmnt ar mpd n th ytm, try t mak th valu f α a larg a pbl. A larg valu f α gnrally rult n a largr valu f v, whh drabl. 5. Dtrmn th pn-lp gan f th mpnatd ytm frm th magntud ndtn. xampl 7-) h rt-lu plt fr th ytm n Fgur 7-7(a) hwn n Fgur 7-7(b). h ld-lp tranfr funtn bm () 4 () 4 h ld-lp pl ar latd at (Fgur 7-7 (b)) ± j hu ξ 0.5 ω n h dampng rat dtrmn th angular latn f th pl, whl th dtan f th pl frm th rgn dtrmnd by th undampd natural frquny (Fgur 7-8). It drd t mdfy th ld-lp pl that r ξ 0.5 ω n 4 ± j If th rgnal ytm ha th pn-lp tranfr funtn G(), thn th mpnatd ytm wll hav th pn-lp tranfr funtn. G () G() G() Nt that thr ar many pbl valu fr and α that wll yld th nary angl ntrbutn at th drd ld-lp pl. In th prnt ytm, th angl f G() at th drd ld-lp pl (S Fgur 7-0) 7-6
4 j ( ) 0 hu, f w nd t fr th rt lu t g thrugh th drd ld-lp pl, th lad mpnatr mut ntrbut φ0 at th pnt. Frt, draw a hrzntal ln pang thrugh pnt P, th drd latn fr n f th dmnant ld-lp pl. h hwn a ln PA n Fgur 7-9. Draw al a ln nntng pnt P and th rgn. Bt th angl btwn th ln PA and PO. Draw tw ln P and PD that mak angl ±φ/ wth th btr PB. h ntrtn f P and PD wth th ngatv ral ax gv th nary latn fr th pl and zr f th lad ntwrk. By fllwng th dgn prdur, w dtrmn th zr and pl f th lad mpnatr, a hwn n Fgur 7-0, t b 90 0 r r at -.9,.9 0.45 Pl at -5.4-5.4 α 0.57 hu th pn-lp tranfr funtn f th mpnatd ytm bm G () G().9 5.4 4.9 ( ) ( )( 5.4) whr 4. h rt-lu plt fr th mpnatd ytm hwn n Fgur 7-0. h gan valuatd frm th magntud ndtn a (.9) ( )( 5.4) 8.7 j It fllw that G () G() 8.7(.9) ( )( 5.4) h lad mpnatr ha th tranfr funtn G () (.9) 0.45 4.68.5 0.85 5.4 If th ltrn rut ung pratnal amplfr a hwn n Fgur 7-4 ud a 7-7
th lad mpnatr, thn th paramtr valu f th lad mpnatr ar dtrmnd frm () 4 0.45.5 () 0.85 In Fgur 7- w hav arbtrarly hn 0µF and 0Ω.! mparn f tp rpn f th mpnatd and unmpnatd ytm: S Fgur 7-. 7-8