Circuits Op-Amp. Interaction of Circuit Elements. Quick Check How does closing the switch affect V o and I o?

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1 Crcuts Op-Amp ENGG st Semester, 01 Interactn f Crcut Elements Crcut desgn s cmplcated by nteractns amng the elements. Addng an element changes vltages & currents thrughut crcut. Example: clsng a swtch s equvalent t addng a new element. Dr. Kenneth Wng Department f Electrcal and Electrnc Engneerng [eference: MIT curse 6.01, March 01] 1st semester, 01 ENGG Dr. K. Wng Hw des clsng the swtch affect V and I? Start by cmputng V and I when the swtch s pen. 1. V decreases, I decreases. V decreases, I ncreases 3. V ncreases, I decreases 4. V ncreases, I ncreases 5. culd be any f abve, dependng n lamp resstance 1st semester, 01 ENGG Dr. K. Wng 3 Calculate V usng vltage dvder relatn: Ω V = 1V = 8V 1Ω+ Ω Calculate I by lumpng resstrs nt seres equvalent: 1V I = = 4A 1Ω+ Ω 1st semester, 01 ENGG Dr. K. Wng 4 1

2 Nw cmpute V and I when the swtch s clsed. Hw des clsng the swtch affect V and I? Assume the lamp can be represented by a resstr (0 < < ). Then s n parallel wth the Ω resstr. Ω V = 1V = 1V = 1V 8V 1Ω+ Ω 1Ω+ Ω+ 3 Ω Ω+ Ω Ω+ Ω Ω+ 1V 1V Ω+ I = = = 1A 4A 1Ω+ Ω 1Ω+ Ω+ 3 1st semester, 01 ENGG Dr. K. Wng 5 1. V decreases, I decreases. V decreases, I ncreases 3. V ncreases, I decreases 4. V ncreases, I ncreases 5. culd be any f abve, dependng n lamp resstance 1st semester, 01 ENGG Dr. K. Wng 6 Bufferng wth Op-Amps Interactns between elements can be reduced (r elmnated) by usng an p-amp as a buffer. Ths p-amp crcut prduces an utput vltage equal t ts nput vltage (8V) whle havng n effect n the left part f the crcut. Op-Amps An peratnal amplfer (p-amp) s an electrnc cmpnent that s easly cnfgured t perfrm a varety f useful functns. Op-amps allw us t desgn and analyze crcuts fr n slatng parts f crcuts: makng t easer d mdular desgn f crcuts and abstract ther detals, n amplfyng vltages, and n perfrmng mathematcal peratns (addtn and subtractn). Tday: hw t analyze and desgn p-amp crcuts 1st semester, 01 ENGG Dr. K. Wng 7 1st semester, 01 ENGG Dr. K. Wng 8

3 Op-Amp Mdel Here s an accurate crcut mdel f a µa709 p-amp. Vltage-cntrlled vltage surce An p-amp (peratnal amplfer) can be represented by a vltage-cntrlled vltage surce s a tw-prt. We wll cnsder tw dfferent, much smpler, mdels: n Vltage-cntrlled vltage surce n Ideal abstract mdel I 1 = 0 and V = KV 1 where K s large (typcally K > 10 5 ). 1st semester, 01 ENGG Dr. K. Wng 9 1st semester, 01 ENGG Dr. K. Wng 10 Op-Amp An p-amp can be represented by a vltage-cntrlled vltage surce. I + = I = 0 and V = K(V + V ) where K s large ( 10 5 ). N current flws thrugh the nput termnals r between nput and utput. What yu cnnect t the utput termnal des nt affect the vltage at the nput termnals. Op-Amp: Negatve feedback ( 1) V V + ( + ) ( V) K V = V K + 1 V V when K s large = V = V V = K V V = K V K + V = KV N current flws between V and V 1st semester, 01 ENGG Dr. K. Wng 11 1st semester, 01 ENGG Dr. K. Wng 1 3

4 What abut pstve feedback? D bth f these crcuts functn dentcally? Paradx Try analyzng the vltage-cntrlled vltage surce mdel. ( 1) V = K V V K + V = KV V V K = 1 K + 1 ( 1 ) V = K V V K V = KV V V K = 1 1 K 1st semester, 01 ENGG Dr. K. Wng 13 These crcuts seem t have dentcal respnses f K s large. Smethng s wrng! 1st semester, 01 ENGG Dr. K. Wng 14 Pstve and Negatve Feedback Negatve feedback (left) drves the utput tward the nput. Pstve feedback (rght) drves the utput away frm the nput. Paradx eslved Althugh bth crcuts have slutns wth V = V (large K), nly the frst s stable t changes n V. Feedback t the pstve nput f an p-amp s unstable. Use negatve feedback t get a stable result. 1st semester, 01 ENGG Dr. K. Wng 15 1st semester, 01 ENGG Dr. K. Wng 16 4

5 Abstractn: deal p-amp mdel As K, the dfference between V + and V ges t zer. Example: ( V V ) Ideal abstractn: V + = V + K V = V K + 1 K 1 1 V+ V = V V = V V = V = V K + 1 K + 1 K lm = 0 K + V = K V V = K V V 1st semester, 01 ENGG Dr. K. Wng 17 Bufferng wth Op-Amps Interactns between elements can be reduced (r elmnated) by usng an p-amp as a buffer. Ths p-amp crcut prduces an utput vltage equal t ts nput vltage (8V) whle havng n effect n the left part f the crcut. 1st semester, 01 ENGG Dr. K. Wng 18 n What happens f we add the thrd lamp? Clsng the swtch wll make: Buffers Op-amps can be used t parttn a crcut nt cnceptually separate peces. ecall that clsng the swtch adds a thrd lght lamp, and als alters the brghtness f the rgnal tw lamps. a. lamp 1 brghter b. lamp dmmer c. a. and b. d. lamps 1,, & 3 equally brght e. Nne f the abve 1st semester, 01 ENGG Dr. K. Wng 19 We can use an p-amp t elmnate the ladng effects f the thrd lamp. 1st semester, 01 ENGG Dr. K. Wng 0 5

6 What wll happen when the swtch s clsed? 1. #1 s brghtest. #3 s brghtest 3. #3 s dmmest 4. all 3 lamps equally brght 5. Nne f the abve 1st semester, 01 ENGG Dr. K. Wng 1 Clsng the swtch wll have n effect n the left lamps because n current wll flw (I L = 0) when swtch s pen O clsed. Ø Ths s half f the buffer dea: n nput current! When the swtch s clsed, V y = V x. Ø Ths s the ther half: utput vltage = nput vltage! 1st semester, 01 ENGG Dr. K. Wng What wll happen when the swtch s clsed? Pwer als The utput f an p-amp can prvde pwer t a crcut. Example: The battery prvdes the pwer t llumnate the left lamps. Pwer fr the thrd lamp cmes frm the pamp. 1. #1 s brghtest. #3 s brghtest 3. #3 s dmmest 4. all 3 lamps equally brght 5. Nne f the abve 1st semester, 01 ENGG Dr. K. Wng 3 But where des the p-amp get the pwer? 1st semester, 01 ENGG Dr. K. Wng 4 6

7 Pwer als Op-amps derve pwer frm cnnectns t a pwer supply. Cmmn p-amp patterns We wll analyze them usng the deal mdel. The pwer supply lmts the utput f an p-amp. Typcally, the utput vltage f an p-amp s cnstraned s that V EE < V < V CC. 1st semester, 01 ENGG Dr. K. Wng 5 1st semester, 01 ENGG Dr. K. Wng 6 Nn-nvertng amplfer eference vltage: V r Cncentrate n the resstr dvder In deal p-amp mdel V = V V Vr V V = 1 ( ) = ( ) ( ) V V V V V V r 1 r 1 V V = 1+ V V r r 1 Dfference frm reference vltage s amplfed Nn-nvertng amplfer examples V V = 1+ V V Let 1 =, V r = 0 V, V CC = +10 V, and V EE = 10 V. If V = +4 V, then V = +8 V If V = 3 V, then V = 6 V If V = +7 V, then V = +10 V r r 1 1st semester, 01 ENGG Dr. K. Wng 7 1st semester, 01 ENGG Dr. K. Wng 8 7

8 Nn-nvertng amplfer examples V V = 1+ V V Let 1 =, V r = +5 V, V CC = +10 V, and V EE = 0 V. If V = + V, then what s V? a. 6 V b. 1 V c. 0 V d. +10 V e. +11 V r r 1 If V = +8 V, then what s V? V = +10 V 1st semester, 01 ENGG Dr. K. Wng 9 Fr whch value(s) f 1 and/r s V = 4V? Fr example: = 300, 1 = 100 Can we arrange t s that V = 0.5V? 1st semester, 01 ENGG Dr. K. Wng 30 Invertng amplfer eference vltage: V r Cncentrate n the resstr dvder In deal p-amp mdel V = V r Vr V V Vr = 1 V V = V V r r 1 V V = V V r r 1 Dfference frm reference vltage s amplfed and nverted Invertng amplfer examples Let 1 =, V r = 0 V, V CC = +10 V, and V EE = 10 V. If V = +4 V, then V = 4 V If V = 3 V, then V = +3 V Let 1 =, V r = +5 V, V CC = +10 V, and V EE = 0 V. If V = +4 V, then V = +6 V. If V = +7 V, then V = +3 V. V V = V V r r 1 1st semester, 01 ENGG Dr. K. Wng 31 1st semester, 01 ENGG Dr. K. Wng 3 8

9 Determne the utput f the fllwng crcut. Determne the utput f the fllwng crcut. 1. V = V 1 + V. V = V 1 V 3. V = V 1 V 4. V = V 1 + V 5. Nne f the abve 1st semester, 01 ENGG Dr. K. Wng 33 Ideal p-amp apprxmatn: KCL at V : Slvng: V = V = V 0 V 0 V + + = V = V V 1 1st semester, 01 ENGG Dr. K. Wng 34 Determne the utput f the fllwng crcut. Determne s that V = (V 1 V ) 1. V = V 1 + V. V = V 1 V 3. V = V 1 V 4. V = V 1 + V 5. Nne f the abve 1st semester, 01 ENGG Dr. K. Wng = 0. = 1 3. = Nne f the abve 1st semester, 01 ENGG Dr. K. Wng 36 9

10 N current n pstve r negatve nputs: V+ = V V = V1+ ( V V1) 1+ 1 = V1 + V 3 3 Ideal p-amp: 1 V+ = V = V = V1+ V V = V V1 = = Ω st semester, 01 ENGG Dr. K. Wng 37 Determne s that V = (V 1 V ) 1. = 0. = 1 3. = Nne f the abve 1st semester, 01 ENGG Dr. K. Wng 38 In cnclusn Op-amps are useful! Amplfy Add and subtract Buffer Dfferent mdels are useful fr dfferent jbs 1st semester, 01 ENGG Dr. K. Wng 39 10