55:041 Electronic Circuits
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1 55:04 Electrnc Crcuts Feedback & Stablty Sectns f Chapter 2. Kruger Feedback & Stablty
2 Cnfguratn f Feedback mplfer S S S S fb Negate feedback S S S fb S S S S S β s the feedback transfer functn Implct ssumptns Made T s the lp gan f T Input sgnal s transmtted thrugh amplfer and nt thrugh β netwrk Output sgnal s transmtted thrugh β netwrk nly There are n ladng effects β netwrk des nt lad amplfer mplfer (wth/wthut β netwrk) des nt lad surce S S. Kruger Feedback & Stablty 2
3 β s the feedback transfer functn T s the lp gan = β f Prfund result: Clsed-lp gan s ndependent frm pen-lp gan, and we can cntrl the clsedlp gan wth the amunt f feedback. Kruger Feedback & Stablty 3
4 Example Hw gd s the /β apprxmatn? ssume pen-lp gan s = 0 5, and the clsed-lp gan s f = 50. Then f f / ssume pen-lp gan s =0 6, wth the same β f Practcally the same clsed-lp gan. Kruger Feedback & Stablty 4
5 Gan Senstty f d f d d f d Ddng bth sdes wth clsed-lp gan yelds d f f d 2 d d f f d Ths shws that the % change n clsed-lp gan s smaller, by a factr +β, than the % change n pen-lp gan.. Kruger Feedback & Stablty 5
6 Gan Senstty n engneer desgned a feedback amplfer β = , and = 0 5. By hw much des the clsed-lp gan change when the same feedback netwrk s used, but an amplfer wth pen-lp gan = 0 6 s used? d f f d % In ther wrds, the pen-lp gan changed by a factr 0, whle the clsed lp gan changed abut 0.5%.. Kruger Feedback & Stablty 6
7 . Kruger Feedback & Stablty 7 Gan Versus Frequency ssume we can characterze the frequency respnse f an amplfer wth a sngle ple (ths s true fr many p-amps) H s s ) ( ) ( ) ( ) ( s s s f H f s s. ) ( We assume the feedback netwrk s ndependent frm frequency The clsed-lp gan s smaller than the pen-lp gan by a factr (+β) The 3 db bandwdth s larger by a factr (+β)
8 Gan-Bandwdth Prduct Gan-bandwdth prduct f a feedback amplfer s cnstant We can ncrease bandwdth at the expense f gan. Kruger Feedback & Stablty 8
9 Nse Senstty n S N S N 00 0 n n S N S 0 N Cnclusns. Negate feedback can reduce nternallygenerated addte amplfer nse Same clsed-lp gan as preus amplfers 2 2 n S (mpre S/N) 2 2 N 2. Negate feedback per 00se wll 0. nt reduce S/N wth respect t external nse n n S N S N 000 S N. Kruger Feedback & Stablty 9
10 eductn f Nnlnear Dstrtn Open-Lp Gan Nn-lnear because the gan depends n the sgnal f Clsed-lp gan, β = Kruger Feedback & Stablty 0
11 dantages f Negate Feedback. Gan Senstty aratns n gan s reduced 2. Bandwdth Extensn larger than that f basc amplfer 3. Nse Senstty may ncrease S/N rat 4. eductn f Nnlnear Dstrtn 5. Cntrl f Impedance Leels nput and utput mpedances can be ncreased r decreased Dsadantages f Negate Feedback. Crcut Gan reduced cmpared t that f basc amplfer 2. Stablty pssblty that feedback crcut wll becme unstable and scllate at hgh frequences. Kruger Feedback & Stablty
12 Ideal Basc Feedback Cnfguratns Vltage mplfer Very Cmmn Current mplfer Transcnductance mplfer (ltage n-current ut) Cnerts current t ltage Transresstance mplfer (current n-ltage ut) Cnerts ltage t current. Kruger Feedback & Stablty 2
13 . Kruger Feedback & Stablty 3
14 ecap: Cnfguratn f Feedback mplfer Negate feedback β s the feedback transfer functn Implct ssumptns Made T s the lp gan f T Input sgnal s transmtted thrugh amplfer and nt thrugh β netwrk Output sgnal s transmtted thrugh β netwrk nly There are n ladng effects β netwrk des nt lad amplfer mplfer (wth/wthut β netwrk) des nt lad surce. Kruger Feedback & Stablty 4
15 ecap-ideal Basc Feedback Cnfguratns Vltage mplfer Current mplfer Transcnductance mplfer (ltage n-current ut) Cnerts current t ltage Transresstance mplfer (current n-ltage ut) Cnerts ltage t current. Kruger Feedback & Stablty 5
16 . Kruger Feedback & Stablty 6 Ideal Seres-Shunt Feedback f Vltage mplfer V I x Sample utput ltage and feed t back t nput Ideal: assume feedback netwrk des nt lad utput/nput 0 x x V I V x x I I x I x x f I V KVL: V x
17 . Kruger Feedback & Stablty 7 Seres-Shunt Feedback Output esstance Hw d we determne utput resstance?. Turn ff ndependent surces 2. dd test ltage V x 3. See what test current I x flws 4. Determne V x /I x V V x x x V V I x x V V x V x x f I V KCL Fast
18 Equalent Crcut: Seres-Shunt Feedback Crcut f f f Useful t thnk f ths as the mprement factr BW f BW. Kruger Feedback & Stablty 8
19 Ideal Basc Feedback Cnfguratns Vltage mplfer Current mplfer Transcnductance mplfer (ltage n-current ut) Cnerts current t ltage Transresstance mplfer (current n-ltage ut) Cnerts ltage t current. Kruger Feedback & Stablty 9
20 . Kruger Feedback & Stablty 20 Ideal Shunt-Seres Feedback f Current mplfer Sample utput current and feed t back t nput Ideal: assume feedback netwrk des nt lad utput, s that I s unaffected e I I I I I I I V I I f I V Feedback = Subtract, educe, Steal Frm Fast
21 Ideal Shunt-Seres Feedback Hw d we determne utput resstance?. Turn ff ndependent surces 2. dd test current I x utput 3. See what test current V x results 4. Determne V x /I x I I x V x I I x x x I I I x f V I x x Fast. Kruger Feedback & Stablty 2
22 Equalent Crcut: Shunt-Seres Feedback Crcut Current mplfer f Useful t thnk f ths as the mprement factr f f V I x x. Kruger Feedback & Stablty 22
23 ecap - Ideal Basc Feedback Cnfguratns Vltage mplfer Current mplfer Transcnductance mplfer (ltage n-current ut) Cnerts current t ltage Transresstance mplfer (current n-ltage ut) Cnerts ltage t current. Kruger Feedback & Stablty 23
24 . Kruger Feedback & Stablty 24 Ideal Seres-Shunt Feedback f Vltage mplfer V I x Sample utput ltage and feed t back t nput Ideal: assume feedback netwrk des nt lad utput/nput x V I V x x x I I x I x x f I V Fast
25 Ideal Seres-Seres Feedback Crcut Sample utput current and feed t back t nput as a ltage Ideal: assume feedback netwrk des nt lad utput, s that I s unaffected Transcnductance mplfer (ltage n-current ut) gf g z g Unts f β Z? V/ Fast f? (neglect S ) I I I f I z z gv z I g I z g Cnerts utput current t a ltage. Kruger Feedback & Stablty 25
26 Ideal Seres-Seres Feedback Crcut I x V x Fast I I x I I x x f V x V x V V I z gv g x I x I z z x x g f? (neglect S ). Kruger Feedback & Stablty 26
27 Equalent Crcut: Seres-Seres Feedback Crcut Transcnductance mplfer (ltage n-current ut) f z g gf f z g Useful t thnk f ths as the mprement factr g z g. Kruger Feedback & Stablty 27
28 ecap-ideal Basc Feedback Cnfguratns Vltage mplfer Current mplfer Transcnductance mplfer (ltage n-current ut) Cnerts current t ltage Transresstance mplfer (current n-ltage ut) Cnerts ltage t current. Kruger Feedback & Stablty 28
29 Ideal Shunt-Shunt Feedback Crcut Sample utput ltage and feed t back t nput as a current Ideal: assume feedback netwrk des nt lad utput, s that V s unaffected Transresstance mplfer (current n-ltage ut) zf z g z f f g g z z Cnerts utput ltage t a current. Kruger Feedback & Stablty 29
30 Equalent Crcut: Shunt-Shunt Feedback Crcut Transresstance mplfer (current n-ltage ut) Useful t thnk f ths as the mprement factr f f g z z g. Kruger Feedback & Stablty 30 g z zf z
31 Summary f Feedback mplfer Functns. Kruger Feedback & Stablty 3
32 Ntes n Unts and Subscrpts Transresstance mplfer (current n-ltage ut) z V I Unts f resstance/mpedance (Z) I fb g I V fb Unts f cnductance (g) Cnerts utput ltage t current f z zf f g z g z g z Prduct shuld be dmensnless. Kruger Feedback & Stablty 32
33 . Kruger Feedback & Stablty 33 Op-mp Seres-Shunt Feedback Crcut Seres-shunt feedback Input mpedance wll ncrease Output mpedance wll decrease Bandwdth wll ncrease Seres-shunt feedback Take sme f the utput ltage Feed t back n seres wth nput ssume ery large fb V V V f f 2 2 f 2 f
34 Op-mp Seres-Seres Feedback Transcnductance amplfer (ltage n, current ut) Feedback: ltage n seres wth nput ltage Feedback ltage s a functn f utput current E cnerts current t ltage Ideal p-amp, neglect base current: gf I V Seres-Seres Feedback E Z E. Kruger Feedback & Stablty 34
35 Op-mp Shunt-Seres Feedback f F /. Kruger Feedback & Stablty 35
36 Op-mp Shunt-Shunt Feedback Current-n, ltage-ut Transresstance Z Output ltage and 2 generate a feedback current that reduces current flwng nt p-amp Ideal p-amp, neglect nput current: g 2 Feedback reduces nput mpedance Shunt-Shunt Feedback. Kruger Feedback & Stablty 36
37 Dscrete Shunt-Seres Transstr Crcut. Kruger Feedback & Stablty 37
38 Dscrete Transstr Crcut Vltage ut Current n Nte that C2 E 2 E 2 s that ths crcut s really samplng the utput ltage Output ltage and F generate a feedback current that reduces current flwng nt amplfer Shunt-Seres Feedback. Kruger Feedback & Stablty 38
39 Dscrete Transstr Crcut Current-n, ltage-ut Transresstance Z Output ltage and F generate a feedback current that reduces current flwng nt transstr base Feedback reduces nput mpedance Shunt-Shunt Feedback g F. Kruger Feedback & Stablty 39
40 Multstage Feedback Crcut I fb I Output ltage and F generate a feedback current that reduces current flwng nt transstr base Feedback reduces nput mpedance Skp Shunt-Shunt Feedback. Kruger Feedback & Stablty 40
41 ecap-cnfguratn f Feedback mplfer Negate feedback β s the feedback transfer functn Implct ssumptns Made T s the lp gan f T Input sgnal s transmtted thrugh amplfer and nt thrugh β netwrk Output sgnal s transmtted thrugh β netwrk nly There are n ladng effects β netwrk des nt lad amplfer mplfer (wth/wthut β netwrk) des nt lad surce. Kruger Feedback & Stablty 4
42 Stablty ecall defntn f lp gan: T = β We assume β s nt a functn f frequency Hweer, the amplfer gan,, s a functn f frequency = (s), and we nrmally set s = jω, s = (jω). Thus T(jω) = β(jω). Clsed-lp gan: If T(jω) = -, then f f ( j) ( j) ( j) T( j) ( j) Instablty We can wrte T( j) T( j) Equalent cndtns fr stablty T( j) r less than 80 Gan margn: when the amplfer phase shft s80, hw much headrm/margn befre the gan s and the amplfer becmes unstable? Phase margn: when the amplfer gan s, hw much mre headrm/margn befre the phase shft s80 amplfer becmes unstable?. Kruger Feedback & Stablty 42
43 . Kruger Feedback & Stablty 43 ja T 2 a ja T ja T 2 a ja T tan a a a tan tan jb ja K T 2 2 b a K jb ja K T ) ( tan ) ( tan tan tan b a b a Cmplex Number eew
44 . Kruger Feedback & Stablty 44? ), ( tan 80 b b M 2 0 ) ( f j K f T 2 0 ) ( f j K f T?, 0 0 ) ( f f K f j K f T M b 80 tan f K
45 . Kruger Feedback & Stablty ) ( f j f j K f T ) ( f f K f T?, 0 0 ) ( f f f K f T Numercal slutn, tral-and-errr
46 (jω). Kruger Feedback & Stablty 46
47 . Kruger Feedback & Stablty 47
48 . Kruger Feedback & Stablty 48
49 . Kruger Feedback & Stablty 49
50 . Kruger Feedback & Stablty 50
51 Bde Plt: Phase and Gan Margns Lp Gan T(jω) = β ( jω) = 0 db gan margn 0 T( f ) 80 db f f 80 phase margn 80 ( f). Kruger Feedback & Stablty 5
52 Bde Plt: Phase and Gan Margns Stable r unstable?. Kruger Feedback & Stablty 52
53 Plttng Lp Gan If β s ndependent f frequency, then the lp gan T(jω) = β(jω) s smply a scaled ersn f the pen-lp gan.. Kruger Feedback & Stablty 53
54 Plttng Lp Gan If β s ndependent f frequency, then the lp gan T(jω) = β (jω)s smply a scaled ersn f the pen-lp gan. T( j) 20lg 20lg 20lg db 20lg 20lg We can determne the lp gan by graphcally subtractng a plt f 20lg(/β ) frm the pen lp Bde plt. pwerful aratn f the graphcal subtractn technque s the fllwng. Often 20lg s aalable n graphcal frm. It s ery cnenent t plt 20lg(/β ) n ths graph, and cnsder ths the new frequency axs.. Kruger Feedback & Stablty 54
55 Graphcal Subtractn n amplfer has pen-lp gan shwn belw. The amplfer s used n a feedback cnfguratn and the clsed-lp gan s 4,000. What are the phase- and gan margns? Ths s where lp gan s (0 db) 0 db New axs clsedlp 32 db clsedlp 4,000 20lg 72 db Gan margn s 32 db 87 Phase margn s 87 mplfer s stable. Kruger Feedback & Stablty 55
56 Graphcal Subtractn n amplfer has pen-lp gan shwn belw. The amplfer s used n a feedback cnfguratn and the clsed-lp gan s,000. What s the phase margn? clsedlp clsedlp,000 20lg 60 db Phase margn s 90. Kruger Feedback & Stablty 56
57 n amplfer has pen-lp gan shwn left. The amplfer s used n a feedback cnfguratn and the clsed-lp gan s 00. What are the phase- and gan margns? What s the clsed-lp bandwdth? 45 db clsedlp clsedlp 00 20lg 40 db 90 Phase margn s 90 Gan margn s 45 Bandwdth ~ MHz. Kruger Feedback & Stablty 57
58 Nyqust Stablty Crtern (Sectn 2.9.3) Nt Cered. Kruger Feedback & Stablty 58
59 eew: Lp Gan/Stablty N frequency dependence f ( s) ( s ) ( s) ( s) ( s) f ( s) ( s) T( s) Gan depends n frequency Gan and feedback depend n frequency T( s) T( j) T(jω) s a cmplex functn T( j) T( j) s j f ( j) ( j) T( j) If T(jω) = and the phase s 80 then T(jω) = - f ( j) ( j) Instablty. Kruger Feedback & Stablty 59
60 Lp Gan The term (+β) s used frequently n feedback amplfer analyss Lp gan T = β s mprtant n determnng stablty Step : Break the feedback lp Step 2: Termnate s that prts see same mpedances Step 3: Insert a test current/ltage and measure respnse: T = -V r /V t Can be used as an analyss technque, n SPICE, as well as n sme actual crcuts. Kruger Feedback & Stablty 60
61 V T V r t. Kruger Feedback & Stablty 6
62 p n Lp gan? t t 0. t n t n 20 p 3 n 60 t p 60, p n 3,000 t T t 00. Kruger Feedback & Stablty 62
63 . Kruger Feedback & Stablty 63
64 mplfer has an pen-lp gan 5 0 f j 3 0 f j 0 5 Is amplfer stable f used s that clsed-lp gan - 00? clsed lp 00, 0.0 Lp gan T s T ( f ) (0.0) T( f ) 3 0 f j 3 0 f j 0 5 Stable? examne phase- and gan margns T ( f ) f tan tan f Sle fr f 62 Hw? f = 30 khz 8 phase margn => amplfer s stable. Kruger Feedback & Stablty 64
65 Bde Plt: Phase and Gan Margns Lp Gan T(jω) = β ( jω) = 0 db gan margn 0 T( f ) 80 db f f 80 phase margn 80 ( f). Kruger Feedback & Stablty 65
66 Bde Plt: Phase and Gan Margns Stable r unstable?. Kruger Feedback & Stablty 66
67 Plttng Lp Gan If β s ndependent f frequency, then the lp gan T(jω) = β s smply a scaled ersn f the pen-lp gan.. Kruger Feedback & Stablty 67
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55:041 Electronic Circuits
55:04 Electronc Crcuts Feedback & Stablty Sectons of Chapter 2. Kruger Feedback & Stablty Confguraton of Feedback mplfer Negate feedback β s the feedback transfer functon S o S S o o S S o f S S S S fb
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