Department of Electrical and Computer Engineering FEEDBACK AMPLIFIERS

Transcription

1 Department o Electrcal and Computer Engneerng UNIT I EII FEEDBCK MPLIFIES porton the output sgnal s ed back to the nput o the ampler s called Feedback mpler. Feedback Concept: block dagram o an ampler wth eedback s shown n g. below. By means o a sutable samplng network, output voltage (or) current s appled to the nput through a eedback two-port network s shown n above g. t the nput the eedback sgnal s combned wth the sgnal source through a mxer network and s ed nto the ampler. Feedback Network: Feedback network s usually a passve two-port network whch may contan resstors, capactors and nductors. Very oten t s smply a resstve conguraton. Samplng Network: There are two types o samplng networks. ) Voltage Samplng Network ) Current Samplng Network The output voltage s sampled by connectng the eedback network s shunt across the output. The output current s sampled by connectng the eedback network n seres across the output. 1

2 Department o Electrcal and Computer Engneerng UNIT I EII Mxng Network: The commonly used seres nput and shunt nput connectons are shown below. Ideal Sngle-Loop Feedback mpler: - Gan o the ampler β - Feedback rato X - βxo βx /Xo - Gan o the ampler wth eedback There are two types o eedbacks. ) Postve Feedback: ) Postve eedback ) Negatve eedback I the eedback sgnal X s n phase wth nput sgnal Xs, then the type o eedback s sad to be postve (or) regeneratve eedback. Thereore, or postve eedback, XXs+X XsX -X X o Xo X X X β X βx o X o 2

3 Department o Electrcal and Computer Engneerng UNIT I EII Xo X o Xs X X Dvdng wth X both numerator and denomnator Here X o Xs X 1 X 1 β > The product o the open loop gan and the eedback actor s called the Loop gan β. I β 1 then, Hence the gan o the ampler wth postve eedback s nnte and the ampler gves an a.c. output wthout a.c. nput sgnal. Thus the ampler acts as an oscllator. Postve eedback ncreases the nstablty o an ampler, reduces the bandwdth and ncreases the dstorton and nose. ) Negatve Feedback: I the eedback sgnal X s out o phase wth nput sgnal Xs, then the type o eedback s sad to be Negatve (or) de-generatve eedback. Thereore, or Negatve eedback, X Xs-X Xs X +X X o Xo X X X β X βx o X o Xo X o Xs X + X Dvdng wth X both numerator and denomnator X o Xs X 1+ X 1 + β Here < I β >> 1 then 1 entrely n the eedback network. β, where β s a eedback rato. The gan may be made to depend I the eedback network contans only stable passve elements, the gan o the ampler usng Negatve eedback s also stable.

4 Department o Electrcal and Computer Engneerng UNIT I EII General characterstcs o Negatve Feedback mplers: ) Stablty to the gan: The transer gan o the ampler s not constant as t depends on the actors such as operatng pont, temperature, e.t.c. Ths lack o stablty n amplers can be reduced by ntroducng negatve eedback. I β>>1, then 1 1+ β β β The gan s dependent only on the eedback network. I the eedback network contans only stable passve elements, the mprovement n stablty s acheved. The gan o the ampler wth negatve eedback s Derentatng wth respect to the, we get Where ( 1+ β) β 1 ( 1+ β) ( 1+ β) d d 2 2 d d d d ( 1+ β ) d d 1 1+ β d d d ( 1+ β) ( 1+ β) ( ) 1 + β ractonal change n amplcaton wth eedback. ractonal change n amplcaton wthout eedback. The ractonal change n amplcaton wth eedback dvded by the ractonal change wth out eedback s called the Senstvty. Senstvty d d β The recprocal o senstvty s called Desenstvty. Increase o Bandwdth: D (1+β) The product o voltage gan and bandwdth o an ampler wthout eedback and wth eedback remans the same..e.,. ( B.W ). (B.W) 1 For Negatve eedback ampler the voltage changes by the actor ; so ts bandwdth 1+ β would be ncreased by (1+β). 4

5 Department o Electrcal and Computer Engneerng UNIT I EII Thereore, or negatve eedback ampler the upper cut-o requency 2 s ncreased by actor (1+β) and the lower cut-o requency s decreased by (1+β). Thereore, 2 2 (1+β) β Frequency Dstorton: I the eedback network does not contan reactve elements, the overall gan s not a uncton o requency. Under such condtons requency and phase dstorton s substantally reduced. Nose and Non-Lnear dstorton: Sgnal eedback reduces the amount o nose sgnal and non-lnear dstorton. Suppose that a large ampltude sgnal s appled to a stage o an ampler so that the operaton o the devce extends slghtly beyond ts range o lnear operaton and as a consequence the output sgnal s slghtly dstorted. By ntroducng negatve eedback the nput sgnal ncreased by the same amount by whch the gan s reduced, so that the output sgnal ampltude remans the same. D Thereore, by ntroducton o negatve eedback the dstorton wll reduce to D 1 + β 1 wth the use o negatve eedback the nose reduced by a actor Problems: 1+ β 1. n ampler has an open loop gan o 800 and a eedback rato o I the open loop gan changes by 20% due to temperature, nd the percentage change n closed loop gan. Soluton: Gven 800 Β 0.05 d d 20% 0.2?. d d 1 d β ( 1+ ) d 0.2 d d d d d 0.48% 2. n ampler has voltage gan wth eedback s 0. I the gan wthout eedback changes by 20% and the gan wth eedback should not vary more than 2%. Determne the values o the open loop gan and eedback rato β. Soluton: Gven 800 d d 20% 0.2 2%

6 Department o Electrcal and Computer Engneerng UNIT I EII? Β? d d 1 d β ( 1+ ) 1 ( 1+ β ) (1+β) We know that the gan wth eedback s 1 + β β β 9 β 9/00 (00) β n ampler has mdband gan o 125 and a bandwdth o 250kHz. ) 4% negatve eedback s ntroduced, nd the new band wdth and gan. ) band wdth s restrcted to 1MHz, nd the eedback rato. Soluton: Gven 125 Bandwdth (B.W) 250 KHz β 4% 0.04 BW? ) BW (1+β) B.W. (1+125x0.04) x 0.25x 1.5 MHz ) BW 1MHz 6 Hz β? BW (1+β) B.W. 6 (1+125.β) x 25x 1+125β 00/ β β / n ampler has a voltage gan o 400, 1 50Hz, KHz and a dstorton o % wthout eedback. Fnd the voltage gan, 1, 2 and D when a negatve eedback s appled wth eedback rato o Soluton: 400 6

7 Department o Electrcal and Computer Engneerng UNIT I EII 1 50Hz 2 200x Hz D % 0.1, β β β 1.4 ( 1 β ) Hz D 200x x KHz D β D 7.14 % 5. n ampler has a voltage gan o 00 wth negatve eedback, the voltage gan reduced to. Calculate the racton o the output that s eedback to the nput. Soluton: Gven: 00 β? For a negatve eedback β 1+ 00β + 4 β 1+ β 2 β 99 β 99/ β 99/ β The gan o an ampler s decreased to 00 wth negatve eedback rom ts gan o Calculate the eedback actor and the amount o negatve eedback n db. Soluton: Gven : 5000 Β? For a negatve eedback β β 00+5x 6 β 5x 7

8 Department o Electrcal and Computer Engneerng UNIT I EII 1+5x β 5 5x β 4 β 4/(5x ) β 0.8x - β β n db 20log (0.0008) n ampler wth negatve eedback gves an output o 12.5V wth an nput o 1.5V. When eedback s removed, t requres 0.25V nput or the same output. Fnd, ) Value o voltage gan wthout eedback. ) Value o β, the nput and output are n phase and β s real. Soluton: Gven: Vo 12.5V Vs 1.5V V o 8. V s 1.5 V 0.25 Vo 12.5 V 12.5 o 50 V 0.25 Hence 1 + β β 8.+8.x50β 50 β 41.67/(8.x50) β 0.1 β V /Vo V βxvo 1.25V Classcaton o Feedback mplers Feedback amplers can be classed on the bass o two mportant processes. 1. Samplng o output sgnal,.e., ether the output voltage s sampled (or) output current s sampled. 2. Mxng o source sgnal and eedback sgnal.e., the eedback network and the nput termnals o the basc amplers are n seres (or) n parallel. Based on the above eedback processes, the eedback amplers can be our types. 1. Voltage Seres eedback ampler. 2. Current Seres eedback ampler.. Voltage Shunt eedback ampler. 4. Current Shunt eedback ampler. 8

9 Department o Electrcal and Computer Engneerng UNIT I EII Eect negatve eedback upon nput and output resstances Voltage Seres Feedback mplers: block dagram o voltage-seres eedback s shown n g. below n whch a porton o the output voltage through the eedback network s appled n seres wth the nput voltage o the ampler resultng n an overall gan reducton. Ths ampler s also called as Voltage mpler. I there s no eedback, the voltage gan o the ampler s The voltage eedback actor β s gven by Vo/V β V /Vo Where V s the eedback voltage Vo s the output voltage. I a eedback sgnal V s connected n seres wth the nput then, V Vs-V V o V V o (V s -V ) V o (V s -βv o ) ( V βv o ) V o V s βv o V o + βv o V s Vo Vs 1 + β V o (1+ β) V s The voltage gan o the ampler wth eedback s gven by, Input and Output Impedances: 1 + β V o /V s Voltage Seres eedback crcut or the calculaton o nput and output resstances s shown n g. below. 9

10 Department o Electrcal and Computer Engneerng UNIT I EII By neglectng source resstance s The nput mpedance o the ampler wthout eedback s The nput mpedance o voltage-seres eedback ampler s, Consder V I Vs V I Vs βvo I V /I V s /I ( ) V V s V ( V βv o ) Vs β. V I ( V o V ) I Vs βv I Vs β I I + β I V s ( β ) 1+ I V s V s + I ( 1 β ) ( 1 β ) + Thereore, or voltage-seres eedback ampler, the nput mpedance s ncreased by a actor (1+β). For the measurement o output resstance, the load resstance L s dsconnected and the voltage source Vs s set to zero. Then an external voltage V s appled across the output termnals, whch delvers the current I. The output resstance o wth eedback s gven by, o V/I Wth Vs0, by applyng KVL to the nput sde V -V pplyng KVL to the output sde, we get V Io+V V Io -V (V -V )

11 Department o Electrcal and Computer Engneerng UNIT I EII V Io βv V+βV Io V(1+β) Io V o I 1 + β o o 1 + β (V βv) The output mpedance o the ampler wth negatve eedback or voltage-seres ampler s decreased by a actor (1+β). The shunt connecton o eedback network at the output reduces the output resstance. The seres connecton o the eedback network at the nput ncreases the nput resstance. Current Seres Feedback block dagram o current-seres eedback s shown n g. below. In ths eedback the output current Io returnng to the nput as a voltage proportonal to Io and s n seres opposton to the appled sgnal Vs. Feedback actor β V /Vo Ths type o ampler s also called Transconductance mpler. I there s no eedback, the gan o the ampler, Io/V I eedback sgnal V s connected n seres wth the nput. V Vs-V Io V Io (Vs-V ) Io (Vs-βIo) (V βio) Io(1+ β) Vs Io Vs 1 + β 1 + β Thereore, or current seres eedback the gan, 1 + β 11

12 Department o Electrcal and Computer Engneerng UNIT I EII Thereore, the voltage gan wth eedback, Input and Output Impedances. 1 + β Current Seres eedback crcut or the calculaton o nput and output resstances s shown n g. below. The nput mpedance o the ampler wthout eedback s V /I The nput mpedance o current-seres eedback ampler s, V s /I V Consder I Vs V ( ) I V V s V Vs βvo I ( V βv o ) Vs β. V I ( V o V ) I + β I V s ( β ) 1+ I V s V s + I ( 1 β ) ( 1 β ) + Thereore, or current-seres eedback ampler, the nput mpedance s ncreased by a actor (1+β). The output mpedance wth current-seres eedback can be determned by applyng a sgnal V to the output wth Vs shorted out, resultng n a current I, the rato o V to I beng the output mpedance. The output mpedance o wth eedback s gven by, o V/I Wth Vs0, by applyng KVL to the nput sde V -V V s 0 The current I due to the voltage V s gven by I (V/o) + V 12

13 Department o Electrcal and Computer Engneerng UNIT I EII I (V/o) - V I (V/o) βi I+βI V/o I(1+β) V/o V o ( 1+ β ) I o o ( 1+ β ) (V βi) For current-seres eedback the output mpedance ncreases by (1+β). Voltage Shunt Feedback mplers In ths eedback ampler a part o the output voltage s ed back n parallel wth the nput voltage through the eedback network. The eedback current I s proportonal to the output voltage Vo. block dagram o voltage-shunt eedback ampler s shown n g. below. I The eedback actor β V o Voltage-Shunt eedback ampler s called as Trasnconductance mpler. I there s no eedback the transresstance gan o the ampler Vo/V. The gan o the ampler wth eedback s, Vo/Is But, I Is-I V o V V o (I s -I ) V o (I s -βv o ) (I βv o ) V o +βv o I s V o (1+ β) I s Vo Vs 1 + β Thereore or voltage-shunt eedback ampler the gan, 1 + β 1

14 Department o Electrcal and Computer Engneerng UNIT I EII Input and Output Impedances Voltage-Shunt eedback crcut or the calculaton o nput and output resstances s shown n g. below. The nput mpedance o the ampler wthout eedback s V /I The nput mpedance o Voltage-Shunt eedback ampler s, V /I s V Consder ( ) I I I s I V Is I V Is βvo V Is β. I I s β I V I s V + β I I s V βv ( I V o ) β ( ) V o I + ( V I) ( 1 ) I s V + β V Is 1 + β 1 + β Thereore, or Voltage-Shunt eedback ampler, the nput mpedance s ncreased by a actor (1+β). The output mpedance wth Voltage-Shunt eedback can be determned by applyng a sgnal V to the output wth Vs shorted.e., Vs0. I Vs0, Is0 Then I +I 0 The output mpedance o wth eedback s gven by, o V/I 14

15 Department o Electrcal and Computer Engneerng UNIT I EII Wth Is0, I -I I -βv, pplyng KVL to the output sde, we get V Io+I V Io βv V+βV Io V(1+β) Io V o I 1 + β o o 1 + β For Voltage-Shunt eedback the output mpedance decreased by (1+β). Note: The shunt connecton o eedback network at the nput and output o ampler tends to decrease the nput and output mpedances. Current-Shunt Feedback mpler block dagram o current-shunt eedback ampler s shown n g. below. In ths eed back the output current Io returnng to the nput as a current I n parallel wth the nput current I. Feedback actor β I /Io Current-shunt eedback ampler s called as Current mpler. I there s no eedback, the gan o the ampler Io/I. The gan o the ampler wth eedback s Io/Is But I Is-I Io I Io (Is-I ) Io (Is-βIo) Io Is-βIo Io(1+ β) Is Io Is (I βio) 1 + β 1+ β Thereore or Current-shunt eedback ampler the gan, 1 + β 15

16 Department o Electrcal and Computer Engneerng UNIT I EII Input and Output Impedances Current-Shunt eedback crcut or the calculaton o nput and output resstances s shown n g. below. The nput mpedance o the ampler wthout eedback s V /I The nput mpedance o Voltage-Shunt eedback ampler s, V /I s V Consder I I Is I V Is I V Is β Io I s β I o V Is β I V ( I I o ) β ( V I) I s βv V I s V + βv ( 1 ) I s V + β V Is 1 + β 1 + β Thereore, or Current-Shunt eedback ampler, the nput mpedance s ncreased by a actor (1+β). The output mpedance wth Current-Shunt eedback can be determned by applyng a sgnal V to the output wth Vs shorted.e., Vs0. I Vs0, Is0 Wth I s 0, I +I 0, I -I The output mpedance o wth eedback s gven by, o V/I The current I due to the voltage V s gven by 16

17 Department o Electrcal and Computer Engneerng UNIT I EII I (V/o) + I I (V/o) - I (I -I ) I (V/o) βio (I βio) I+βI V/o I(1+β) V/o V o ( 1+ β ) I o o ( 1+ β ) For current-shunt eedback the output mpedance ncreases by (1+β). 8. Calculate the gan, nput mpedance, output mpedance o voltage seres eedback ampler havng 00, 1.5kΩ, o50kω and β1/12. Soluton: Gven: kΩ 0 50kΩ β 1/12 For a voltage-seres eedback ampler 1 + β ( 1+ β ) o o 1 + β ( 1 ) ( ) o 1.5X (1+25) 1.5X x26 9kΩ kΩ 1+ 00( 1 ) n ampler has a value o n 4.2kΩ, V 220 and β0.01, determne the value o nput resstance o the eedback ampler. Soluton: Gven: n 4.2kΩ V 220 β β kΩ ( ) 17

18 Department o Electrcal and Computer Engneerng UNIT I EII Methodology o Feedback mpler nalyss Step 1: Identy topology. (Type o eedback). a) To nd the type o samplng network ) By shortng the output.e., Vo0, eedback sgnal (X ) becomes zero then we can say that t s Voltage Samplng. ) By openng the output loop.e., Io0, eedback sgnal (X ) becomes zero then we can say that t s Current Samplng. b) To nd the type o mxng network. Step 2: Step : Step 4: ) I the eedback sgnal s subtracted rom the nput voltage source, then we can say that t s Seres Mxng. ) I the eedback sgnal s subtracted rom the nput current source, then we can say that t s Shunt Mxng. To nd the nput crcut. ) For voltage samplng Vo0 ) For current samplng Io0 To nd the output crcut. ) For seres mxng I 0 ) For shunt mxng V 0 eplace the actve devce by ts h-parameter model at low requency. Step 5: Fnd the open loop gan (wthout eedback), o the ampler. Step 6: X Indcate X and Xo on the crcut and evaluate β X o. Step 7: From and β nd,, o. Voltage Seres Feedback mpler The example or voltage-seres eedback s the emtter ollower crcut. Step 1: ) the Vo0, X 0 hence t s voltage samplng. ) Feedback sgnal X s subtracted rom the voltage source Vs, Thereore t s seres mxng. 18

19 Department o Electrcal and Computer Engneerng UNIT I EII Thereore, hence the gven crcut s a voltage-seres eedback ampler. Step 2: To nd the nput crcut V o 0 Step : To nd the output crcut I 0 By combnng nput and output crcuts, we obtan the crcut as shown n gure below. Step 4: eplacng the transstor by ts h-parameter (approxmate) model, the equvalent crcut s shown n gure below. 19

20 Department o Electrcal and Computer Engneerng UNIT I EII Step 5: Step 6: Step 7: Open loop gan V o Vs From the crcut, Vo h e b e V β V o β β s + h e ( 1+ β ) o o o 1+ β ' o e ' e o 1 + β ( ) Vs s + h b e h e b e s + h b e h e e s + h e ( ) both the voltages present across e.. For the crcut shown n gure below, calculate, β,,,, o and o. Soluton: h e e s + h e

21 Department o Electrcal and Computer Engneerng UNIT I EII V β 1 V o β s + h e kω ( 1+ β ). 2.1 ( 2.8) kω o o o 1+ β ' o e ' Ω o.8 Current-Seres Feedback mpler The example or current-seres eedback ampler s the common emtter ampler wth emtter resstor s unbypassed by a capactor. Step 1: ) the I o 0, eedback sgnal becomes zero, hence t s current samplng. ) Feedback sgnal X s subtracted rom the voltage source Vs, Thereore t s seres mxng. Thereore, the gven crcut s a current-seres eedback ampler. Step 2: To nd the nput crcut I o 0 21

22 Department o Electrcal and Computer Engneerng UNIT I EII Step : To nd the output crcut I 0 By combnng nput and output crcuts, we obtan the crcut as shown n gure below. Step 4: eplacng the transstor by ts h-parameter (approxmate) model, the equvalent crcut s shown n gure below. Step 5: Step 6: I Open loop gan o Vs From the crcut, Io h e b ( e ) Vs s + h b e + h e b ( s + h e + b e ) h e s + h e + e V β From the crcut, V I o e I o I β o e I e o 22

23 Department o Electrcal and Computer Engneerng UNIT I EII Step 7: 1 + β s + h e + e ( 1 β ) + o ( 1 β ) o + o v V I o o c. c Vs Vs 11. For the crcut shown n gure below, calculate, β,,,, o and o. Soluton: h e s + h e + e ( ) 50. β e -1.2x β x - s + h e + e. Ω ( 1 + β ).. ( ) kω o ' 2.2k o o Ω ' o ( 1 + β ) 2.2 ( ) ' o kΩ 2

24 Department o Electrcal and Computer Engneerng UNIT I EII 12. n ampler wth current seres eedback has the orm shown n gure below. The transstor has h e 0, h e 2kΩ, o470ω and e conssts o two 0Ω resstors. One s by passed by capactor C e. Calculate the values o voltage gan and nput resstance wthout eedback. Soluton: Gven current-seres eedback ampler. To nd the nput crcut, I o 0 To nd the output crcut, I 0 By combnng the nput and output crcuts, we obtan the crcut as shown n gure below kΩ 5.6kΩ 4.07kΩ kΩ 2kΩ 1.kΩ eplacng the transstor by ts h-parameter model, the equvalent crcut s shown n gure below. 24

25 Department o Electrcal and Computer Engneerng UNIT I EII h e ( h 4.07k ) e e Ω + + β e -0Ω khz 1 + β kΩ ( 1+ β ). 1.4 ( ) 1.4 ( 8.1) o o ' o 0Ω ' 0 8. o ( 8.1) Current-Shunt Feedback mpler 1140 The example or current-shunt eedback ampler s the two transstors n cascade connecton wth eedback rom second emtter to rst base through resstor. Step 1: ) I the Io0, eedback sgnal becomes zero, hence t s current samplng. ) Feedback sgnal X s subtracted rom the current source, Thereore t s seres mxng. Thereore, the gven crcut s a current-shunt eedback ampler. Step 2: To nd the nput crcut I o 0 25

26 Department o Electrcal and Computer Engneerng UNIT I EII Step : To nd the output crcut V 0 By combnng nput and output crcuts, we obtan the crcut as shown n gure below. Open loop gan, We know that b To nd 2 c 1 c 2 b 2 c 2 b 2 c 2 s c 2 b c 2 1 b 1 c b s 2 1 b1 current gan o a CE mpler h e 26

27 Department o Electrcal and Computer Engneerng UNIT I EII c c From the above crcut, 1 1 b 2 c b c 2 1 c c Where s the nput mpedance o a CE ampler wth emtter resstor s un 2 bypassed by a capactor, and s gven by ( 1 )( e ) 2 h e + + h e2 ' c We know that 1 s the current gan o a CE ampler b 1 c 1 h e b 1 c 1 h e b 1 b1 To nd s s b1 + 1 b 1 s + 1 Where s ( ' + e2 ) and h 1 e c 1 h h e c e Calculatng β I β I o e2 I e 2 ' + e2 I e2 I o ' e2 ( Io c e )

28 Department o Electrcal and Computer Engneerng UNIT I EII I Io β e2 ' + e2 e2 ' + e2 1 + β s h e o ( 1 β ) o o + ' o c β ' o ' o ( 1+ β ) 1. For the crcut shown n gure below, calculate, β,,,, o and o. c Soluton: 1 h h e c e kΩ 1.2kΩ h ( 1 h )( e ' 2 e + e 2 ) kΩ+ 1.2kΩ,.55kΩ 2 ( ) 1.2k 1.25k s ' + e2 1.2k k c 1 c (-50)(-0.457)(50)(0.58)406 β e ' + e 2 50k 1.2k + 50k kΩ 28

29 Department o Electrcal and Computer Engneerng UNIT I EII 1 + β k 1.1k h e 0.612k + 1.1k 0.94kΩ 0.94 k 1 + β Ω o ( 1 β ) o + o ' o c 500Ω 2 ' ' o o ( 1+ β ) 500( ) 500( ) ' kΩ o Voltage-Shunt Feedback mpler The example or voltage-shunt eedback ampler s a common emtter ampler wth collector-to-base bas crcut. Step 1: ) Vo0, eedback sgnal becomes zero, V V o Vo >> V ' hence t s current samplng. V o ' 29

30 Department o Electrcal and Computer Engneerng UNIT I EII ) Feedback sgnal X s subtracted rom the current source, Thereore t s shunt mxng. Thereore, the gven crcut s a voltage-shunt eedback ampler. Step 2: To nd the nput crcut I o 0 Step : To nd the output crcut V 0 By combnng nput and output crcuts, we obtan the crcut as shown n gure below. Vo Open loop gan, Is From the crcut, V ( ' ) o c c Vo c Where L L ' c c L. c b. L s b s 0

31 Department o Electrcal and Computer Engneerng UNIT I EII We know that c current gan o a CE mpler b c b h e To nd b s : Where s ' s ' s + ' From the above crcut, s b + h e b s + h e Open loop gan,. c b. L b s h. e h L + e Calculatng β I β V o But Vo ' I 1 β I ' ' 1 + β h h e e + h e 1 + β 1

32 Department o Electrcal and Computer Engneerng UNIT I EII o o o 1+ β ' o c ' ' ' o o 1 + β Vo Vo v Vs Iss s 14. For the crcut shown below, determne open loop gan, β,,,, o and o. Soluton: o s ' s ' 500 s + ' β -0.02x ' 50 - h e + h L e L ' c L 2.1 kω ( 50) ( 2.1 ) ( 50) ( 2.1 ) 9.4 Open loop gan ( ). 8. kω 2

33 Department o Electrcal and Computer Engneerng UNIT I EII β h e kω Ω 1 + β o o o 1+ β ' o L 2.1kΩ ' L o 75.8 Ω 1 + β