Microelectronic Circuits. Feedback. Ching-Yuan Yang

Transcription

1 Mcrelecrnc rcu Feedback hng-yuan Yang Nanal hung-hng Unvery Deparmen Elecrcal Engneerng Oulne The General Feedback Srucure Sme Prpere Negave Feedback The Fur Bac Feedback Tplge The Sere-Shun Feedback mpler The Sere-Sere Feedback mpler The Shun-Shun and Shun-Sere Feedback mpler Deermnng he Lp Gan The Sably Prblem Eec Feedback n he mpler Ple Sably udy Ung Bde Pl Frequency mpenan 8- hng-yuan Yang / EE, NHU

2 The General Feedback Srucure 8- hng-yuan Yang / EE, NHU General rucure he eedback ampler x x, x x, x x x : eedback acr : lp gan : amun eedback >>, hen /. The gan he eedback ampler alm enrely deermned by he eedback newrk. Feedback gnal: x x Fr >> we ee ha x x, whch mple ha x 0. x : errr gnal x x 8-3 hng-yuan Yang / EE, NHU

3 Sme Prpere Negave Feedback 8-4 hng-yuan Yang / EE, NHU Sme Prpere Negave Feedback Deenze he gan Exend he bandwdh he ampler educe he eec ne educe nnlnear drn 8-5 hng-yuan Yang / EE, NHU

4 Gan Deenvy ume ha cnan. x x d d d d d d The percenage change n due varan n me crcu parameer maller han he percenage change n by amun eedback. The amun eedback,, al knwn a he deenvy acr. 8-6 hng-yuan Yang / EE, NHU Bandwdh Exenn nder an ampler whe hgh-requency repne characerzed by a ngle ple. M M : he mdband gan ω H : he upper 3-dB requency ω H pply he negave eedback wh a requency-ndependen acr : M M le - lp gan ωh M The eedback ampler: hgh-requency repne M Mdband gan M M Upper 3-dB requency ω H ω H M The ampler band wdh ncreaed by he ame acr, M, by whch mdband gan decreaed, manan he gan-bandwdh prduc cnan. Smlarly, he lw-requency repne he eedback ampler ha a lwer 3-dB requency ωl ωl M 8-7 hng-yuan Yang / EE, NHU

5 Ne educn The ampler uer rm ne and he ne can be aumed be nrduced a he npu he ampler. Negave eedback appled mprve SN: : npu gnal : upu gnal n : ne r nererence : gan Sngal - - ne ra S N n clean amp. n S N n 8-8 hng-yuan Yang / EE, NHU educn n Nnlnear Drn The pen-lp vlage raner characerc he ampler change rm and hen 0. [curve a] pply negave eedback wh 0.0 he ampler [curve b] : he lpe he eepe egmen: he lpe he nex egmen: urve a hw he ampler raner characerc whu eedback. urve b hw he characerc wh negave eedback 0.0 appled The rder--magnude change n lp cnderably reduced. The prce pad a reducn n vlage gan hng-yuan Yang / EE, NHU

6 The Fur Bac Feedback Tplge 8-0 hng-yuan Yang / EE, NHU Fur bac eedback plge Bae n he quany be ampled vlage r curren and n he dered rm he upu vlage r curren, ampler can be claed n ur caegre. lage ampler urren ampler Trancnducance ampler Tranreance ampler Fur bac eedback plge: lage-amplng ere-mxng ere-hun plgy urren-amplng hun-mxng hun-ere plgy urren-amplng ere-mxng ere-ere plgy lage-amplng hun-mxng hun-hun plgy 8- hng-yuan Yang / EE, NHU

7 lage mpler haracerc: npu gnal: vlage upu gnal: vlage lage-cnrlled vlage urce Hgh npu mpedance Lw upu mpedance Feedback plgy lage-amplng ere-mxng ere-hun plgy The eedback newrk ample he upu vlage, and he eedback gnal x a vlage ha can be mxed wh he urce vlage n ere. Sere reer he cnnecn a he npu and hun reer he cnnecn a he upu. haracerc: Sablze he vlage gan Hgher npu reance ere cnnecn a he npu Lwer upu reance parallel cnnecn a he upu 8- hng-yuan Yang / EE, NHU lage-amplng ere-mxng ere-hun plgy Example v v v negave eedback 8-3 hng-yuan Yang / EE, NHU

8 urren mpler haracerc: npu gnal: curren upu gnal: curren urren-cnrlled curren urce Lw npu mpedance Hgh upu mpedance Feedback plgy urren-amplng hun-mxng hun-ere plgy The eedback newrk ample he upu curren, and he eedback gnal x a curren ha can be mxed n hun wh he urce curren. Shun reer he cnnecn a he npu and ere reer he cnnecn a he upu. haracerc: Sablze he curren gan Lwer npu reance hun cnnecn a he npu Hgher upu reance ere cnnecn a he upu 8-4 hng-yuan Yang / EE, NHU urren-amplng hun-mxng hun-ere plgy Example b c c c e /α b negave eedback 8-5 hng-yuan Yang / EE, NHU

9 Trancnducance mpler haracerc: npu gnal: vlage upu gnal: curren lage-cnrlled curren urce Hgh npu mpedance Hgh upu mpedance Feedback plgy urren-amplng ere-mxng ere-ere plgy The eedback newrk ample he upu curren, and he eedback gnal x a vlage ha can be mxed wh he urce vlage n ere. Sere reer he cnnecn a he npu and ere reer he cnnecn a he upu. haracerc: Sablze he rancnducance gan Hgher npu reance ere cnnecn a he npu Hgher upu reance ere cnnecn a he upu 8-6 hng-yuan Yang / EE, NHU urren-amplng ere-mxng ere-ere plgy Example v v be c v c c v c /α v negave eedback 8-7 hng-yuan Yang / EE, NHU

10 Tranreance mpler haracerc: npu gnal: curren upu gnal: vlage urren-cnrlled vlage urce Lw npu mpedance Lw upu mpedance Feedback plgy lage-amplng hun-mxng hun-hun plgy The eedback newrk ample he upu vlage, and he eedback gnal x a curren ha can be mxed n wh hun he urce curren. Shun reer he cnnecn a he npu and hun reer he cnnecn a he upu. haracerc: Sablze he ranreance gan Lwer npu reance hun cnnecn a he npu Lwer upu reance hun cnnecn a he upu 8-8 hng-yuan Yang / EE, NHU lage-amplng hun-mxng hun-hun plgy Example Nrn herem negave eedback 8-9 hng-yuan Yang / EE, NHU

11 Tw-Pr Newrk Parameer y parameer Equvalen crcu: 8-0 hng-yuan Yang / EE, NHU z parameer Equvalen crcu: 8- hng-yuan Yang / EE, NHU

12 h parameer Equvalen crcu: 8- hng-yuan Yang / EE, NHU g parameer Equvalen crcu: 8-3 hng-yuan Yang / EE, NHU

13 The Sere-Shun Feedback mpler 8-4 hng-yuan Yang / EE, NHU The deal Suan he Sere-Shun Feedback mpler deal rucure crcu: a unlaeral pen-lp ampler : npu reance : vlage gan : upu reance crcu: an deal vlage-amplng ere-mxng eedback newrk The urce and lad reance are ncluded nde he crcu. The crcu de n lad he crcu. D n change /. 8-5 hng-yuan Yang / EE, NHU

14 8-6 hng-yuan Yang / EE, NHU Equvalen crcu The cle-lp gan and have recprcal un npu reance The ere-mxng ncreae he npu reance by. General rm Z Z [ ] / 8-7 hng-yuan Yang / EE, NHU Oupu reance 0 Oupu reance where The vlage-amplng eedback reduce he upu reance by. General rm 0 r and Z Z

15 The Praccal Suan Dervan he crcu and crcu r he ere-hun eedback ampler. Blck dagram a praccal ere-hun eedback ampler and are he npu and upu reance, repecvely, he eedback ampler, ncludng and L. The acual npu and upu reance he eedback ampler uually exclude and L : n and u L 8-8 hng-yuan Yang / EE, NHU The crcu n wh he eedback newrk repreened by h parameer. h parameer The urce and lad reance huld be lumped wh he bac ampler. n addn, he reance n he eedback huld be al lumped wh he bac ampler. h-parameer w-pr eedback newrk: Neglec h, he rward ranmn eec he eedback newrk, and hu m he cnrlled urce h. 8-9 hng-yuan Yang / EE, NHU

16 The crcu n aer neglecng h. h negleced. Deermne : h 0 pr pen-crcued 8-30 hng-yuan Yang / EE, NHU Summary he Sere-Shun Feedback mpler 8-3 hng-yuan Yang / EE, NHU

17 Example 8. n p amp cnneced n he nnnverng cnguran The p amp ha an pen-lp gan μ, a derenal npu reance d, and an upu reance r. Fnd expren r,, he cle-lp gan /, he npu reance n, and he upu reance u. μ 0 4, d 00kΩ, r kω, L kω, kω, MΩ, and 0kΩ. The eedback newrk cn and. Th newrk ample he upu vlage and and prvde a vlage gnal acr ha mxed n ere wh he npu urce. 8-3 hng-yuan Yang / EE, NHU crcu: ' [ L ] d μ ' [ ] r 6000 / L d crcu: ' ' 3 0 / 8-33 hng-yuan Yang / EE, NHU

18 6000 lage gan 857 / 7 npu reance where he npu reance he crcu. d kω 7 777kΩ n 739kΩ Oupu reance where he upu reance he crcu. r L 667 Ω Ω 7 u L u 00 Ω 8-34 hng-yuan Yang / EE, NHU The Sere-Sere Feedback mpler 8-35 hng-yuan Yang / EE, NHU

19 The deal Suan he Sere-Sere Feedback mpler deal rucure crcu: a unlaeral pen-lp ampler : npu reance : rancnducance gan : upu reance crcu: an deal curren-amplng ere-mxng eedback newrk The urce and lad reance are ncluded nde he crcu. The crcu de n lad he crcu. D n change / hng-yuan Yang / EE, NHU Equvalen crcu The cle-lp gan and have recprcal un npu reance / The ere-mxng ncreae he npu reance by. General rm Z Z [ ] 8-37 hng-yuan Yang / EE, NHU

20 Oupu reance 0 Oupu reance n h cae, r 0 The vlage-amplng eedback ncreae he upu reance by. General rm Z Z [ ] 8-38 hng-yuan Yang / EE, NHU The Praccal Suan Dervan he crcu and crcu r he ere-ere eedback ampler. Blck dagram a praccal ere-hun eedback ampler and are he npu and upu reance, repecvely, he eedback ampler, ncludng and L. The acual npu and upu reance he eedback ampler uually exclude and L : n and u L 8-39 hng-yuan Yang / EE, NHU

21 The crcu n wh he eedback newrk repreened by z parameer. z parameer The urce and lad reance huld be lumped wh he bac ampler. n addn, he reance n he eedback huld be al lumped wh he bac ampler. z-parameer w-pr eedback newrk: Neglec z, he rward ranmn eec he eedback newrk, and hu m he cnrlled urce z hng-yuan Yang / EE, NHU The crcu n aer neglecng z. z negleced. Deermne : z 0 pr pen-crcued 8-4 hng-yuan Yang / EE, NHU

22 Summary he Sere-Sere Feedback mpler 8-4 hng-yuan Yang / EE, NHU Example 8. eedback rple cmped hree gan age wh ere-ere eedback ume ha he ba crcu caue 0.6m, m, and 3 4m. Ung hee value and aumng h e 00 and r, nd he pen-lp gan, he eedback acr, he cled lp gan /, he vlage gan /, he npu reance n, and he upu reance beween nde Y and Y. Nw, r Q 3 5kΩ, emae an apprxmae value he upu reance u hng-yuan Yang / EE, NHU

23 8-44 hng-yuan Yang / EE, NHU crcu: Deermne : 4.9 / ] [ ' E F E e c r r π α { } / 3. ] [ 3 E F E e e m c c r h g 0.6 m/ ' E F E e b e c r 0.7 / ' ' ' ' ' c c c 8-45 hng-yuan Yang / EE, NHU crcu: led-lp gan: lage gan: npu reance he crcu: npu reance he eedback ampler: Oupu reance he crcu: The reance lkng beween Y and Y. Oupu reance he eedback ampler: Ω.9 ' ' E E F E E 83.7 m/ / c Ω k 3.65 ] [ E F E e e r h Deermne : Ω M 3.34 Ω 43.9 ] [ 3 e e E F E h r Ω k 35.6

24 Fnd he upu reance rm he equvalen crcu. u r r 3 3 g [ g m3 m3 3 π 3 5[ MΩ r r ] r π hng-yuan Yang / EE, NHU Hmewrk # Prblem 6, 4, 4, 5, 7, hng-yuan Yang / EE, NHU

25 The Shun-Shun Feedback mpler 8-48 hng-yuan Yang / EE, NHU The deal Suan he Shun-Shun Feedback mpler deal rucure crcu: a unlaeral pen-lp ampler : npu reance : ranreance gan : upu reance crcu rancnducance: an deal vlage-amplng hun-mxng eedback newrk The urce and lad reance are ncluded nde he crcu. The crcu de n lad he crcu. D n change / hng-yuan Yang / EE, NHU

26 8-50 hng-yuan Yang / EE, NHU Equvalen crcu The cle-lp gan and have recprcal un npu reance The hun-mxng reduce he npu reance by. General rm Z Z 8-5 hng-yuan Yang / EE, NHU Oupu reance 0 Oupu reance where The vlage-amplng eedback reduce he upu reance by. General rm 0 r and Z Z

27 The Praccal Suan Dervan he crcu and crcu r he ere-hun eedback ampler. Blck dagram a praccal hun-hun eedback ampler and are he npu and upu reance, repecvely, he eedback ampler, ncludng and L. The acual npu and upu reance he eedback ampler uually exclude and L : n and u L 8-5 hng-yuan Yang / EE, NHU The crcu n wh he eedback newrk repreened by y parameer. y parameer The urce and lad reance huld be lumped wh he bac ampler. n addn, he reance n he eedback huld be al lumped wh he bac ampler. y-parameer w-pr eedback newrk: Neglec y, he rward ranmn eec he eedback newrk, and hu m he cnrlled urce y hng-yuan Yang / EE, NHU

28 The crcu n aer neglecng y. y negleced. Deermne : y 0 pr hr-crcued 8-54 hng-yuan Yang / EE, NHU Summary he Shun-Shun Feedback mpler 8-55 hng-yuan Yang / EE, NHU

29 Example 8.3 eedback crcu he hun-hun ype Deermne he mall-gnal vlage gan /, he npu reance n, and he upu reance u. The ranr ha 00. dc analy: 0.7 B B B m,.5m, and 4.5 B 8-56 hng-yuan Yang / EE, NHU Small-gnal analy crcu: npu reance he crcu r π.4 kω Oupu reance he crcu 4.7 kω Traner gan: π ' ' g ' ' g rπ m m π kω r π 8-57 hng-yuan Yang / EE, NHU

30 Deermne : ' ' 47kΩ Deermne he cled-lp characerc: led - lp gan Snce npu reance wh eedback Oupu reance wh eedback, kω 358.7/ hu he vlage gan 4.6 / Ω Ω 8-58 hng-yuan Yang / EE, NHU The Shun-Sere Feedback mpler 8-59 hng-yuan Yang / EE, NHU

31 8-60 hng-yuan Yang / EE, NHU deal rucure crcu: a unlaeral pen-lp ampler : npu reance : curren gan : upu reance crcu : an deal curren-amplng hun-mxng eedback newrk The urce and lad reance are ncluded nde he crcu. The crcu de n lad he crcu. D n change /. The deal Suan he Shun-Sere Feedback mpler 8-6 hng-yuan Yang / EE, NHU Equvalen crcu The cle-lp gan and have recprcal un npu reance The ere-mxng reduce he npu reance by. General rm Z Z

32 Oupu reance 0 Oupu reance n h cae, r 0 The curren-amplng eedback ncreae he upu reance by. General rm Z Z [ ] 8-6 hng-yuan Yang / EE, NHU The Praccal Suan Dervan he crcu and crcu r he ere-hun eedback ampler. Blck dagram a praccal hun-ere eedback ampler and are he npu and upu reance, repecvely, he eedback ampler, ncludng and L. The acual npu and upu reance he eedback ampler uually exclude and L : n and u L 8-63 hng-yuan Yang / EE, NHU

33 The crcu n wh he eedback newrk repreened by g parameer. g parameer The urce and lad reance huld be lumped wh he bac ampler. n addn, he reance n he eedback huld be al lumped wh he bac ampler. g-parameer w-pr eedback newrk: Neglec g, he rward ranmn eec he eedback newrk, and hu m he cnrlled urce g hng-yuan Yang / EE, NHU The crcu n aer neglecng g. g negleced. Deermne : g 0 pr hr-crcued 8-65 hng-yuan Yang / EE, NHU

34 Summary he Shun-Sere Feedback mpler 8-66 hng-yuan Yang / EE, NHU Example 8.4 eedback crcu he hun-ere ype Fnd he curren gan u / n, he npu reance n, and he upu reance u. The ranr ha 00 and 75. dc analy: neglec he eec ne ranr and B E E m 0.87 E E m hng-yuan Yang / EE, NHU

35 8-68 hng-yuan Yang / EE, NHU Small-gnal equvalen crcu crcu: ] [ ' π π r B E { } [ E m b r r g π π ' E e b r / 0.45 ' ' 8-69 hng-yuan Yang / EE, NHU Fnd npu/upu mpedance: Fnd he requred curren gan: Deermne : Deermne he cled-lp characerc: 0.54 ' ' E E Ω k.535 π r B E Ω 9.5 Ω 9.5 / / n Ω k.69 e E r r Ω k 40. Ω M 8. [ m u r g r π 3.44 / L c L u n u

36 Summary elanhp r he Fur Feedback_mpler Tplge 8-70 hng-yuan Yang / EE, NHU Deermnng The Lp Gan 8-7 hng-yuan Yang / EE, NHU

37 Deermnng he Lp Gan Lp gan a very mpran quany ha characerze a eedback lp. Fnd he lp gan: Le he exernal urce x 0. Open he eedback lp by breakng he cnnecn x he eedback newrk and apply a e gnal x. Deermne he lp gan: x x x x x x x x Lp gan x /x The lp gan gven by he negave he ra he reurned gnal he appled e gnal. 8-7 hng-yuan Yang / EE, NHU cncepual eedback lp brken a XX and a e vlage x appled. The mpedance Z equal ha prevuly een lkng he le XX. The lp gan r /, where r he reurned vlage. r an alernave, can be deermned by ndng he pen-crcu raner uncn T c and he hr-crcu raner uncn T c and cmbnng hem a ndcaed. T c T c pen-crcu raner uncn T c hr-crcu raner uncn T c 8-73 hng-yuan Yang / EE, NHU

38 led-lp crcu: x x x x X Y Break XX deermne he lp gan : X Y x x x x r r x r x x x 8-74 hng-yuan Yang / EE, NHU Break YY deermne T c and T c : Open-crcu raner uncn T c x x x x c T c c x c x Shr-crcu raner uncn T c x x x x c T x and c c c x x x x x x x Thu, T c T c x x x 8-75 hng-yuan Yang / EE, NHU

39 8-76 hng-yuan Yang / EE, NHU Equvalence rcu rm a Feedback-Lp Pn ew Break XX deermne he lp gan : r d d d d d L d L r ] [ ]} [ { ]} [ { μ r L d d d d d L d L r r ] [ ]} [ { ]} [ { μ 8-77 hng-yuan Yang / EE, NHU The Sably Prblem

40 Sably Prblem a Feedback mpler The cled-lp raner uncn a eedback ampler Fr phycal requence jω, r jω 0, Ljω 0, hen he cled-lp gan apprache nny a ω 0. Under h cndn, he crcu ample wn ne cmpnen a ω 0 ndenely. Barkhauen crera: a negave-eedback crcu ha a lp gan ha ae w cndn: Ljω 0 and Ljω 0 80, hen he crcu may cllae a ω 0. n rder enure cllan n he preence emperaure and prce varan, we ypcally che he lp gan be a lea wce r hree me he requred value. where : he pen-lp raner uncn : he eedback raner uncn jω jω L jω jω jω jω jω e jφω jω jω Ocllan culd ccur n a negave-eedback ampler, we wh nd mehd preven her ccurrence hng-yuan Yang / EE, NHU Nyqu Pl Nyqu crern: he nerecn ccur he le, 0, he magnude lp gan a h requency greaer han uny and he ampler wll be unable. he nerecn ccur he rgh, 0, he ampler wll be able hng-yuan Yang / EE, NHU

41 Eec O Feedback On The mpler Ple 8-80 hng-yuan Yang / EE, NHU Sably and Ple Lcan nder an ampler wh a ple par a σ 0 ± jω n. v e σ 0 [e jωn e jωn ] e σ 0 c ω n elanhp beween ple lcan and ranen repne: The exence any rgh-hal-plane ple reul n nably. 8-8 hng-yuan Yang / EE, NHU

42 Ple he Feedback mpler The cled-lp raner uncn a eedback ampler where : he pen-lp raner uncn : he eedback raner uncn Fnd ple: The ple he eedback ampler are he zer. 0 he characerc equan he eedback lp. huld herere be apparen ha applyng eedback an ampler change ple. 8-8 hng-yuan Yang / EE, NHU mpler wh Sngle-Ple epne n ampler whe pen-lp raner uncn characerzed by a ngle ple: 0 /ω p 0 / 0 The cled-lp raner uncn / ω Mdband Gan Ple pen - lp cled - lp Eec eedback n he ple lcan and he requency repne: ω 0 P p ω P 0 0 ω P 8-83 hng-yuan Yang / EE, NHU

43 0ω P Fr requence ω >> ω P 0, uch hgh requence he lp gan much maller han uny and he eedback neecve. Eec eedback n he requency repne: pplyng negave eedback an ampler reul n exendng bandwdh a he expene a reducn n gan. Snce he ple he cled-lp ampler never ener he rgh hal he plane, he ngle-ple ampler able r any value. Uncndnally able 8-84 hng-yuan Yang / EE, NHU mpler wh Tw-Ple epne n ampler whe pen-lp raner uncn characerzed by w ple: le-lp ple / ω / ω P P 0 ωp ωp 0 ωpω P ω ω -lcu dagram 0 P P ± ω P ωp 4 0 ω P ω P The eedback ampler al uncndnally able. The maxmum phae h per ple, bu h value reached a ω. The pen-lp ampler mgh have a dmnan ple, bu h n necearly he cae r he cledlp ampler. he cae wh ecnd-rder repne generally, he cled-lp repne can hw a peak hng-yuan Yang / EE, NHU

44 The characerc equan a ecnd-rder newrk: ω0 ω0 0 ω 0 : ple requency Q : ple Q acr Q Denn ω 0 and Q a par cmplex cnjugae ple: Deermne Q acr: Q ω ω P 0 ω P P ω P Nrmalzed magnude repne: Q > 0.7, peakng. Q 0.7, n peakng. Q 0.7 ple a 45, maxmally la hng-yuan Yang / EE, NHU Example 8.5 Pve-eedback crcu Open-lp crcu: Fnd he lp ranmn L and he characerc equan. Skech a r-lcu dagram r varyng K, and nd he value K ha reul n a maxmally la repne, and he value K ha make he crcu cllae. ume ha he ampler ha nne npu mpedance and upu mpedance. Slun The lp ranmn: r L KT where T he raner uncn he w-pr newrk. r / T 3/ / K / Thu L 3/ / The characerc equan: L 0 3 K Ple requency: ω 0 3 K 0 Q acr: Q 3 K hng-yuan Yang / EE, NHU

45 -lcu dagram: ω 0 Q 3 K The maxmally la repne: Q K.586 The ple are a 45. K 3, he crcu unable. The eedback n ac pve, and he crcu wll cllae a he requency r whch he phae T jω zer hng-yuan Yang / EE, NHU mpler wh Three r Mre Ple value 0 ex a whch h par cmplex-cnjugae ple ener he rgh hal he plane, hu caung he ampler becme unable. n ampler wh hree ple: -lcu dagram Snce he ampler wh hree ple ha a phae h ha reach 70 a ω reache, here ex a ne requency ω 80, a whch he lp gan ha 80 phae h. Frequency cmpenan There ex a maxmum value r abve whch he eedback ampler becme unable. lernavely, here ex a mnmum value value r he cled-lp gan 0 belw whch he ampler becme unable. T ban lwer value he cled-lp gan ne need aler he lp raner uncn L. Th he prce requency cmpenan hng-yuan Yang / EE, NHU

46 Sably Sudy Ung Bde Pl 8-90 hng-yuan Yang / EE, NHU Gan and Phae Margn Gan margn: The derence beween he value a ω 80 and uny n db. Phae margn: The derence beween he phae angle a he 0-dB requency and 80. The gan margn repreen he amun by whch he lp gan can be ncreaed whle ably mananed. a he requency uny lp-gan magnude, he phae lag n exce 80, he ampler wll be unable. Feedback ampler are uually degned have ucen gan margn and phae margn allw r he nevable change n lp gan wh emperaure, me, and n. 8-9 hng-yuan Yang / EE, NHU

47 Eec Phae Margn n led-lp epne jω e where θ 80 jθ le-lp gan a ω : phae margn jω / e jω jω e jθ jθ jω / e jθ Fr a phae margn 45, θ 35, j ω.3 Gan peakng The peakng ncreae a he phae margn reduced, evenually reachng when he phae margn zer. The cled-lp gan a lw requence apprxmaely /. 8-9 hng-yuan Yang / EE, NHU n lernave pprach r Sably naly Ung Bde Pl ume ha ndependen requency, we can pl 0lg/ a a hrznal ragh lne n he ame plane ued r 0lg. 0 lg jω 0 lg 0 lg expreed n db Sudy ably by examnng he derence beween he w pl. we wh evaluae ably r a deren eedback acr we mply draw anher hrznal ragh lne a he level 0lg/ hng-yuan Yang / EE, NHU

48 Example: Sably naly Ung Bde Pl The pen-lp gan he ampler 0 lg jω 0 lg 0 lg We can nd j j 0 6 j Hz and 00 0 lg 0 lg φ an an 0 lg an hng-yuan Yang / EE, NHU Frequency mpenan 8-95 hng-yuan Yang / EE, NHU

49 Thery Frequency mpenan :nrduce an addnal ple a D. ple: D, P, P, P3, 0 :Mve he rgnal lwrequency ple D..e., P D ple: D, P, P3, 8-96 hng-yuan Yang / EE, NHU mplemenan Frequency mpenan Tw-acaded gan age a mulage ampler Equvalen crcu r he nerace The crcu wh a cmpenang beween he w age capacr added P π x x ' D π x x 8-97 hng-yuan Yang / EE, NHU

50 8-98 hng-yuan Yang / EE, NHU Mller mpenan and Ple Splng gan age n a mulage ampler bere cmpenan gan age n a mulage ampler wh a cmpenang capacr n he eedback lp 8-99 hng-yuan Yang / EE, NHU ] [ ] [ g g m m ' ' ' ' ' ' ' ' ' P P P P P P P P P D ω ω ω ω ω ω ω ω ω ω P << ω P ' g g m m P ω ' g m P ω Ple plng ρ jω Bere mpenan ρ jω er mpenan

51 Example 8.6: Frequency mpenan The pen-lp raner uncn he peranal ampler: j j 0 j 0 We wh cmpenae he p amp ha he cled-lp ampler wh reve eedback able r any gan ha, r up uny and PM phae margn 45. ume ha he p amp crcu nclude a age uch a ha Fg.a wh 00pF, 5pF, and g m 40m/, ha he ple a P caued by by he npu crcu ha age, and ha he ple cnneced eher beween he npu nde B and grund r n he eedback pah he ranr. 6 7 Fg.a: 8-00 hng-yuan Yang / EE, NHU Fnd he cmpenang capacr cnneced acr he npu ermnal he ranr age. a Deermne and : 5 0 P 0.MHz Ω π π 5 0 P MHz Ω π π b Deermne D : ple rm P D : ' D and he nd ple reman unchanged. π PM 45 : The requred value r D deermned by drawng a 0dB/dec lne rm he -MHz pn n he 0lg/ 0lg 0dB lne. Th lne wll nerec he 00-dB dc gan lne a 0Hz. Thu ' 0Hz π D μf 8-0 hng-yuan Yang / EE, NHU

52 Fnd he cmpenang capacr cnneced n he eedback pah he ranr. By Eq and 8.59: gm ' P and ' P πg m π [ ] gm Deermne P : ume >>, hen ' P 60.6 MHz π The ple P mve a requency hgher han P3 0MHz. The new nd ple a P3. Th requre ha he ple be lcaed a 00Hz r PM 45 : ' P 00Hz 78.5pF πg m nclun: Ung Mller cmpenan n nly reul n a much maller cmpenang capacr bu, wng ple plng, al enable u place he dmnan ple a decade hgher n requency. 8-0 hng-yuan Yang / EE, NHU 8-03 hng-yuan Yang / EE, NHU

53 Hmewrk # Prblem 4, 58, 6, 67, 70, hng-yuan Yang / EE, NHU