CHPTER 3: FEEDBCK Dr. Wan Mahan Hafzah bnt Wan Mahmud
Feedback ntrductn Types f Feedback dvantages, Characterstcs and effect f Negatve Feedback mplfers Crcuts wth negatve feedback Pstve feedback and Oscllatr Operatn 2
Example f Negatve Feedback n Everyday Lfe djustng the shwer T ht, turn t dwn T cld, turn t up Drvng a car T slw, put yur ft dwn T fast, ease yur ft ff Blng kppers Water s bubblng, turn heat dwn Water ges ff the bl, turn heat up Standng up straght Start fallng t the left, shft weght t the rght 3
Feedback: alve Example s the water nears the specfed level, the valve s clsed Negatve feedback s mst cmmnly used t cntrl systems 4
n Techncal Terms Summng Nde mplfer nput - Errr Feedback Netwrk Feedback s a technque t feed back a prtn f the utput sgnal (current r vltage) t the nput surce thrugh a feedback netwrk m f the crcut s t mnmse the errr 5
Type f Feedback Tw types f feedback Pstve (regeneratve) Negatve (degeneratve) The basc dea f negatve feedback s t trade ff gan fr ther desrable prpertes 6
Type f Feedback (cnt.) n negatve feedback systems, the feedback tends t reduce the nput t the frward path n pstve feedback systems, the feedback tends t ncrease the nput t the frward path Negatve feedback: Pstve feedback: β s pstve β s negatve and less than 1 ( pen-lp gan, β feedback netwrk) 7
mplfer wthut Feedback X can be current r vltage sgnals s called an pen lp gan 8
mplfer wth Feedback Fgure 3.2: X S X XO X f Feedback netwrk: Gan wthut feedback: Gan wth feedback: β F X X X X F X X s F s called an 9 clse lp gan
n Fg. 3.2: Gan wth Feedback X f β X X X S X f X S β X X X ( X S β X ) X ( 1 β) X S f X X s 1 β mplfer s gan wth feedback s reduced by the factr (1 β) Deselectvty D 1 β 10
Why Feedback? (dvantages) Desenstze the gan: make the value f the gan less senstve t varatns n the value f crcut cmpnents, such as mght be caused by changes n temperature better stablzed gan Overall gan wth negatve feedback: f 1 β f β >> 1 then: f β 1 β Gan wth feedback ( f ) s ndependent f amplfer gan (). f depends n feedback netwrk (β) 11
Why Feedback? (dvantages) Reduce nnlnear dstrtn: make the utput prprtnal t the nput mre lnear peratn Reduce the effect f nse: mnmze the cntrbutn t the utput f unwanted electrc sgnals generated, ether by the crcut cmpnents themselves, r by extraneus nterference reduced dstrtn f the utput sgnal Extend the bandwdth f the amplfer mprved frequency respnse 12
Frequency Respnse lthugh gan s reduced, BW s ncreased f Lf f L 1 β f Hf f 1 H 13 ( β )
Gan Bandwdth Prduct (GBP) GBP fr amplfer wth r wthut prduct s equal: ( BW ) ( BW ) f f Cutff frequences wth feedback: f Lf f L f f ( ) 1 Hf H 1 β β Bandwdth wth feedback: BW f f Hf f Lf snce f Hf >> f Lf then BW f f Hf BW f f f 1 Hf H ( β ) 14
Gan Bandwdth Prduct (GBP) GBP fr amplfer wth feedback: f x BW f β 1 β ( f H ( 1 ) ) f H Fr amplfer wthut feedback, the bandwdth: BW f H f L f The GBP fr amplfer wthut feedback: H Prven that: xbw f H ( BW ) ( BW ) f f 15
Why Feedback? (dvantages) Better nput and utput mpedances: rase r lwer the nput and utput mpedance by the selectn f an apprprate feedback tplgy accrdng t the type f amplfer hgher r lwer nput mpedance (Z ) hgher r lwer utput mpedance (Z ) Type f mplfer ltage mplfer Transmpedance mplfer Transcnductance mplfer Current mplfer Feedback Cnnectn ltage seres (shunt-seres) ltage shunt (shunt-shunt) Current seres (seres-seres) Current shunt (seres-shunt) 16
Feedback Cnnectn Types Bth vltage and current can be fed back t the nput ether n seres r parallel (shunt) 4 basc ways f cnnectng the feedback sgnal: ) vltage seres feedback (Fg.3.4(a)) ) vltage-shunt feedback (Fg.3.4(b)) ) current-seres feedback (Fg.3.4(c)) v) current-shunt feedback (Fg.3.4(d)) 17
ltage mplfer (a) vltage-seres feedback (shunt-seres) ƒ / s Transmpedance/ transresstance mplfer (b) vltage-shunt feedback (shunt-shunt) ƒ / s 18
Trancnductance mplfer (c) current-seres feedback (seres-seres) ƒ / s Current mplfer (d) current-shunt feedback (seres-shunt) ƒ / s 19
n Fg. 3.4, the terms vltage refers t cnnectng the utput vltage (Fg. a & b) as nput t the feedback netwrk whle current refers t tappng ff sme utput current (Fg. c & d) thrugh the feedback netwrk Seres refers t cnnectng the feedback sgnal n seres wth the nput sgnal vltage (Fg. a & c); whle shunt refers t cnnectng the feedback sgnal n shunt (parallel) wth an nput current surce (Fg. b & d) 20
mplfer Fundamentals 21
mplfers Type f mplfer ltage mplfer Transmpedance mplfer Transcnductance mplfer Current mplfer Feedback Cnnectn ltage seres ltage shunt Current seres Current Shunt deal nput mpedance (Z) deal Output mpedance (Z) Gan wthut Feedback 0 0 0 0 t tc 22
Fg. 3.5(a) ltage-seres Feedback 23
ltage-seres Feedback Fndng f Output f the crcut: O t the nput: s f and β f Hence: O ( ) ( β ) s f s f s f ( 1 β ) s O s 1 β 24
ltage-seres Feedback ) f s (1 β β β Fndng Z 25 ) 1 ( v s F Z Z β Z nput mpedance s ncreased ( ) s 1 Z β
Fndng Z ltage-seres Feedback Fr the crcut: Wth s 0 Z v - f Therefre Z v f Z v (β) Rewrtng the equatn v β Z Then the utput mpedance: Z f 1 Z v β 26
ltage-shunt Feedback Transmpedance mplfer 27
ltage-shunt Feedback ) (1 t t t t t s t f F β β β t 1 β F F s reduced 28 1 β t ) / ( / / f s F Z β β t F 1 Z Z β Z F s reduced
ltage-shunt Feedback Crcut n fndng utput mpedance 29
ltage-shunt Feedback Z F can be fund n smlar manner as the vltage amplfer wth vltage seres feedback When s 0 - f Z t Therefre Z t f f β, s ( 1 β ) t Z Z t ( β) Z F Z 1 β t Z F s reduced 30
Current-Seres Feedback Transcnductance mplfer 31
Current-Seres Feedback tc F 1 β F s reduced tc β β β 1 tc f s Fndng gan wth feedback 32 tc f F β β β 1 tc tc tc tc tc s S tc 1 β nther way:
Current-Seres Feedback tc s s f s Z - Z - Z - Z β β tc s - Z β Fndng nput mpedance 33 ( ) tc s F 1 Z Z β Z F s ncreased tc s ( ) tc tc tc s 1 Z Z Z Z β β β
Current-Seres Feedback Crcut t fnd utput mpedance Wth s 0: - f 34
Current-Seres Feedback Fndng utput mpedance tc Z Wth s 0: - f and f β Z f tc (- f ) - tc β Z Z (1 β ) Z tc Z (1 βtc ) Z F s ncreased 35
Current-Shunt Feedback Current mplfer 36
Current-Shunt Feedback F β β 1 S F O F β 37 S F 1 β F s reduced F 1 β β β 1 s
Current-Shunt Feedback f s F Z Z Z / / β β F 1 Z Z β Z F s decreased 38 Z F s ncreased Z Z Z ) - (- f β ) (1 f Z Z β Z ) (1 β
Current-Shunt Feedback Crcut t fnd utput mpedance 39
Effect f Feedback n nput and Output mpedances Feedback Tplgy mplfer ltage ltage Current Current seres shunt seres shunt ltage Transmpe- Transcnduc- Current mplfer Transcnduc- Transmpedance mplfer tance mplfer mplfer Z F Z ( 1 β) 1Z β Z ( 1 β) 1Z β Z F Z β Z β 1 1 Z ( 1 β) Z ( 1 β) 40
mplfer & Feedback Tplgy 41
PRCTCL FEEDBCK CRCUTS 42
Feedback n Crcuts T determne the type f feedback emplyed by a crcut, a test can be dne t check ether the utput vltage ( ) r utput current ( ) s taken at the utput t be fed back Ths s dne usng test fr vltage r test fr current Then at the nput sectn, check the way the surce (X s ), nput (X ) and feedback (X f ) sgnals are cnnected: ether n seres r parallel (shunt) 43
Test fr ltage r Current Test fr vltage Shrt crcut the lad s that the utput vltage becmes zer f the sgnal returned t the amplfer nput by the feedback netwrk becmes zer, then the amplfer has a vltage feedback Test fr current Open crcut the lad s that the utput current becmes zer f the sgnal returned t the amplfer nput by the feedback netwrk als becmes zer, then the amplfer has a current feedback 44
Example 1 Determne the feedback tplgy used n the crcut Fnd the feedback netwrk (β), and gan fr ths crcut 45
Example 1 : Test fr ltage Shrt crcut the utput The utput vltage ( 0 ) s zer; and n utput sgnal s beng fed t the feedback netwrk Snce the sgnal returned t the amplfer nput by the feedback netwrk becmes zer, then the amplfer has a vltage feedback t the nput: Surce sgnal s n seres wth nput and feedback sgnals Thus t s a vltage seres feedback 46
Example 1 : Test fr Current Open crcut utput There s a current () beng fed t the feedback netwrk Snce the sgnal returned t the amplfer nput by the feedback netwrk s nt zer, then the utput sgnal beng taken s nt current, s the amplfer has a vltage feedback t the nput: Surce sgnal s n seres wth nput and feedback sgnals Thus t s a vltage seres feedback 47
Example 1 Fndng the feedback factr (β): 2 1 2 F R R R 48 2 1 2 R R R β 2 1 2 F R R R S the feedback netwrk( β):
Example 1 Fndng the gan wth feedback s But - s F s F Thus: F O S O F 1 β R R 1 1 2 F R 2 R1 R 2 49
Example 2 Determne the feedback tplgy used n the crcut Fnd the feedback netwrk (β), and gan fr ths crcut 50
Test fr vltage Shrt crcut the utput The utput vltage ( 0 ) s zer; but there s a sgnal beng fed t feedback netwrk Snce the sgnal returned t the amplfer nput by the feedback netwrk s nt zer, then t s nt the utput vltage beng taken t be fed back Example 2 Hence the amplfer has a current feedback 51
Test fr current Open crcut the utput There s n utput sgnal beng fed t feedback netwrk Snce the sgnal returned t the amplfer nput by the feedback netwrk s zer, then t s the utput current beng taken t be fed back Example 2 Hence the amplfer has a current feedback 52
Example 2 t the nput: Surce sgnal s n seres wth nput and feedback sgnals Thus t s a current seres feedback The amplfer s a transcnductance amplfer 53
Example 2 O F But 0 O F R F F F R F β O Feedback netwrk F - S F F F R F O R O S 1 R F tc mplfer s gan 54
Example 3 Determne the feedback tplgy used n the crcut 55
Test fr vltage Shrt crcut utput Output vltage wll be zer; n utput sgnal s beng fed t the feedback netwrk Snce the sgnal returned t the amplfer nput by the feedback netwrk becmes zer, then the amplfer has a vltage feedback Example 3 t the nput: Surce sgnal s parallel wth nput and feedback sgnals Thus t s a vltage shunt feedback 56
Test fr current Open crcut utput There s a current beng fed t the feedback netwrk Snce the sgnal returned t the amplfer nput by the feedback netwrk s nt zer, then the utput sgnal beng taken s nt current; t s the utput vltage Hence the amplfer has a vltage feedback Example 3 t the nput: Surce sgnal s parallel wth nput and feedback sgnals Thus t s a vltage shunt feedback 57
Example 3 Exercse: Fnd the feedback netwrk (β), and the gan fr ths crcut Ths crcut has a vltage shunt feedback Thus t s a transmpedance amplfer 58
Slutn fr Exercse (Example 3) F S 0 S F O O R 0 59 O O F R 1 β O S O F R O O R
POSTE FEEDBCK ND OSCLLTOR OPERTON 60
Oscllatr n scllatr s a crcut that prduces a perdc wavefrm n ts utput wth nly the dc supply vltage as an nput The utput vltage can be ether snusdal r nn- snusdal, dependng n the type f scllatr Fg. 3.9 dc supply vltage scllatr ut 61
Pstve Feedback Pstve feedback s used n a range f bth analgue and dgtal crcuts t prduce a varety f effects Pstve feedback Mst cmmnly used n the prductn f scllatrs Pstve feedback s characterzed by the cndtn wheren an n-phase prtn f the utput vltage f an amplfer s fed back t the nput wth n net phase shft 62
Pstve Feedback & Oscllatn ttal phase shft f 360 s ntrduced nvertng mplfer (θ 180 ) and f are n phase β O Fg. 3.10 Feedback netwrk (θ 180 ) 63
Pstve Feedback : nvertng mplfer Fg. 3.10 64
Pstve Feedback : Nnnvertng mplfer n-phase f v Nnnvertng amplfer Feedback crcut 65
Oscllatn Frm the shwn fgure, the n-phase feedback vltage, f, s amplfed t prduce the utput vltage, whch n turn prduces the feedback vltage lp s created n whch the sgnal sustans tself and a cntnuus snusdal utput s prduced Ths phenmenn s called scllatn 66
Cndtns fr Oscllatn Tw cndtns are requred t sustan a state f scllatns: The phase shft arund the feedback lp must be effectvely 0 (r 360 ) The vltage gan, cl, arund the clsed feedback lp (lp gan) must equal t 1 (unty) These 2 cndtns are knwn as Barkhausen Crtern 67
Barkhausen Crtern f v f v Phase shft 0 cl v β 1 Feedback crcut Feedback crcut n-phase (a) (b) Fg. 3.11 : General cndtns t sustan scllatn : (a) The phase shft arund the lp s 0 (b) The clsed lp gan s 1 68
Start-up Cndtns t cc v cl v β t β cl > 1 cl 1 When scllatn starts at t, the cndtn cl > 1 causes the snusdal utput vltage ampltude t buld up t a desred level. Then cl decreases t 1 and mantans the desred ampltude. 69
Effects f v β n Oscllatr Operatn Fg. 3.12: (a) The utput s drven nt clppng when v β > 1 70
Effects f v β n scllatr peratn Fg. 3.12: (b) The utput fades ut when v β < 1 Dampng; The fadng and lss f scllatns that ccur when vβ < 1 71
Effects f v β n scllatr peratn Fg. 3.12: (c) cnstant-ampltude utput s prduced when v β 1 72
Q & 73