Operational Amplifier

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Operational Amplifier

  1. 1. Operational Amplifier Electronic Circuits CHO, Yong Heui
  2. 2. Electronic Circuits1. Ideal OP amp OP amp  OP amp 의 어떤 terminal 도 ground 에 연결되어 있지 않음 .  3 signal terminals and 2 power terminals (Not displayed) Ideal OP Amp  Differential input voltage, single- ended output voltage  Infinite input impedance i i = 0  Zero output impedance  Zero common-mode gain (v2=v1  vo=0)  Infinite open-loop gain A  Infinite bandwidth : A is constant at any frequencies. *Differential input voltage, single-ended output voltage 2 EM Wave Lab
  3. 3. Electronic Circuits1. Ideal OP amp Differential and common mode v Id = v 2 – v 1 v I cm = ½(v 1 + v 2 ) v 1 = v Icm - v Id /2 v 2 = v Icm + v Id /2 v 3 = mv d v d = (G m v 2 – G m v 1 ) R v 3 = mG m R (v 2 – v 1 ) Gain A = mG m R = 100·10·10 = 10 4 = 80 dB 3 EM Wave Lab
  4. 4. Electronic Circuits2. Inverter Closed loop gain i2 For ideal OP amp, finite v o means v 2 - i1 v 1 =0 v 2 – v 1 = v o /A = 0 v1 v2 v 2 ≒ v 1 : Virtual short circuit if v 2 is grounded, v 1 is a virtual ground i 1 = (v I – v 1 ) /R 1 = v I /R 1 terminal. vo = v1 – i2 R2 = v1 – i1 R2 = 0 – vI R2 / R1 ∵ infinite input impedance of ideal OP amp vo / vI = - R2 / R1 Closed-loop gain G ≡ v o / v I = - R 2 / R 1 R2 에 의해 negative feedback 회로로 동작 (positive feedback if connected between 2 and 3) Closed-loop gain 은 외부 수동 소자에 의해 결정  stable and predictable, but gain loss is inevitable 4 EM Wave Lab
  5. 5. Electronic Circuits2. Inverter Equivalent circuit 5 EM Wave Lab
  6. 6. Electronic Circuits2. Inverter Finite open loop gain = vx 6 EM Wave Lab
  7. 7. Electronic Circuits2. Inverter Example R 1 should be large as a input impedance, but large R 1 causes low voltage gain 7 EM Wave Lab
  8. 8. Electronic Circuits2. Inverter Summer Output is a weighted sum of input signals v o = v 1 (R a /R 1 )·(R c /R b ) + v 2 (R a /R 2 )·(R c /R b ) – v 3 ·(R c /R 3 ) – v 4 ·(R c /R 4 ) Different summing coefficients are possible 8 EM Wave Lab
  9. 9. Electronic Circuits3. Noninverter Closed loop gain 등가회로 9 EM Wave Lab
  10. 10. Electronic Circuits3. Noninverter Finite open loop gain vo = A ( vI - vx ) i1 = - vx / R1 i 2 = ( v x – v o )/ R 2 A 1 + (R 2 / R 1 ) v o / v I = --------------- 1 + (R 2 / R 1 ) Inverting 경우 1 + --------- A 와 분모 부분 같 음 A ≫ 1 + (R 2 / R 1 ) 이면 infinite gain 의 경우와 등가회로 같음 v I 와 v x 가 같은 값이 아니므로 (finite gain) → v x = R1 / (R1+ R2) · v o v o = A ( v I - v x ) ∵ Op amp 동작 특 성 위 두식을 이용하면 같은 결과를 얻는다 . 10 EM Wave Lab
  11. 11. Electronic Circuits3. Noninverter Voltage follower Non-inverting closed-loop 에서 R1=∞, R2=0 인 경우와 동일함 Ideal Op amp 의 infinite input impedance 를 이용하여 source inpedance 가 큰 source 에 연결할 수 있 고 , ideal Op amp 의 zero output impedance 를 이용하여 load inpedance 가 적은 load 에 연결할 때 사용 Buffer Amp 가 Voltage Source 와 Load impedance 에 연결 11 EM Wave Lab
  12. 12. Electronic Circuits4. Difference Common mode rejection ratio For practical circuits, Common-mode voltage gain A cm ≠ 0 v o = A d ·v Id + A cm ·v Icm 현재까지 두 input voltage 의 차이만 증폭된다고 가정하였음 . 하지만 , 실제로는 공통 부분도 A cm 만큼의 gain 을 가지고 증폭된다 . |Ad | CMRR = 20 Log | A cm | 12 EM Wave Lab
  13. 13. Electronic Circuits4. Difference Difference amplifier 지금까지는 inverting/noninverting 의 경우 input 이 없는 한쪽은 GND 였지만 , difference amp 에서 는 두 input 의 차이만을 증폭하고자 함 . (why don’t you use Op amp itself ?) Output port 에서 Common-mode signal 을 없애기 위해선 , inverting gain 과 noninverting gain 의 magnitude 는 같고 부호는 반대이어야 함 . (v I1 = v I2 일때 v 0 =0 이어야 함을 생각해 보면 됨 ) Inverting Noninverting i = 0 ≡ v O1 / v I 1 = - R 2 / R 1 13 EM Wave Lab
  14. 14. Electronic Circuits4. Difference Difference amplifier ᅵᅵ inverting gain ᅵᅵ ᅵᅵ = noninverting gain ᅵᅵ R4 R2 R2 / R1 = R3 + R4 [1 R1 ] + R4 R2 R2 R4 → R3 + R4 = R1 + R2 → R1 = R3 R4 R2 R2 vO2 = vΙ 2 R3 + R4 [1 R1 ] = vΙ 2 R1 + R2 R2 By superposition, v O = v O1 + ( vI 2 - vI 1 ) = v Id v O2 = R1 R1 R2 → Ad = R1 14 EM Wave Lab
  15. 15. Electronic Circuits4. Difference Difference amplifier 1 R4 1 R3 i1 = R1 [ v Icm - v R3 + R4 Icm ] = v Icm R1 R3 + R4 R4 R4 R2 R3 vO = v Icm – i2R2 = v - v R3 + R4 R3 + R4 Icm R1 R3 + R4 Icm R4 R2 R3 = R3 + R4 1- [ R1 R4 ]v Icm vO R4 R2 R3 For R1 = R3 , R2 = R4 Acm ≡ vΙcm = R +R 1- 3 4 [ R1 R4 ] v Id R id ≡ iI v Id = R 1 i I + 0 + R 1 i I ∵ vertual short R id = 2R 1 : low input resistance for high differential gain 15 EM Wave Lab
  16. 16. Electronic Circuits4. Difference Instrumentation amplifier R2 R2 [1 R1 ] ( vΙ 2 − vΙ 1 ) = 1 R1 [ ]v Ιd + + R4 R2 vΟ = R3 + 1 R1 [ ] vΙd = Ad vΙd R4 R2 Ad = R3 [ 1 R1 ] = + High input impedance and high differential gain Issues  A cm is equal to 1+R 2 /R 1 at the first stage.  Issues of imperfect match at the first two Op amps.  Two R 1 resistors should be simultaneously varied : Not easy job 16 EM Wave Lab
  17. 17. Electronic Circuits4. Difference Instrumentation amplifier 2R1 2R2 (vO2 – vO1) v 2R1 + 2R2 = Ιd → vO2 – vO1 = [1 2R ]v Ιd + 1 R4 R4 R2 vO R4 R2 vO = R3 (vO2 – vO1) = R3 [1 R1 ] vΙd → Ad ≡ vΙd = R3 [1 R1 ] + + 17 EM Wave Lab
  18. 18. Electronic Circuits5. Nonideal OP amp Nonideal OP amp Differential open-loop gain  Noninfinite CMRR, noninfinite input resistance, nonzero output resistance : Closed-loop circuits 에서 Not critical A0 A(jw) = 1+ jw/w b For w = 0 For w ≫ w b 18 EM Wave Lab
  19. 19. Electronic Circuits5. Nonideal OP amp Frequency response ← = vx − R2 / R 1 Vo(s)/Vi(s) ≈ s 1 + ωT / (1 + R2 / R1 ) For A0 ≫ 1+R2/R1 ωT ω3dB = −−−−−−−− − + R2 / 1 R1 For noninverting closed-loop case, only DC gain (1 + R 2 /R 1 ) is different 19 EM Wave Lab
  20. 20. Electronic Circuits5. Nonideal OP amp Frequency response Closed-loop gain R2/R1 f3dB=ft/(1+R2/R1) +1000 999 1kHz 1 + R2 / +100 99 10kHz Constant gain-BW product R1 +10 9 100kHz +1 0 1MHz -1 1 0.5MHz − R 2 / R1 -10 10 90.9kHz -100 100 9.9kHz -1000 1000 0.99kHz ωT = A0 · ωb 20 EM Wave Lab
  21. 21. Electronic Circuits6. Large signal Output voltage saturation 21 EM Wave Lab
  22. 22. Electronic Circuits6. Large signal Slew rate 22 EM Wave Lab
  23. 23. Electronic Circuits6. Large signal Slew rate 23 EM Wave Lab
  24. 24. Electronic Circuits6. Large signal Full power bandwidth Unity-gain voltage follower 의 input 에 sine wave 를 인가하고 출력 전압의 진폭이 최대 가 되도록 할 경우 , slew 현상이 발생하지 않는 입력신호의 최대 주파수 24 EM Wave Lab
  25. 25. Electronic Circuits7. DC effect Offset voltage 25 EM Wave Lab
  26. 26. Electronic Circuits7. DC effect Equivalent model DC biasing issue DC signal issue Inverting Noninverting 26 EM Wave Lab
  27. 27. Electronic Circuits7. DC effect Capacitive coupling Only for DC Only for AC A ≠ 1 + R 2 /R 1 STC HPF 27 EM Wave Lab
  28. 28. Electronic Circuits7. DC effect Input bias current 두 전류 I B1 , I B2 는 거의 같은 값을 가지지만 OP amp 내부의 mismatch 로 인해 약간 차이가 남 Only for DC B2 28 EM Wave Lab
  29. 29. Electronic Circuits7. DC effect Input bias current V O = I B1 R 2 ≈ I B R 2  limits on R 2 V O = -I B2 R 3 + R 2 (I B1 – I B2 R 3 /R 1 ) (for I B1 = I B2 = I B3 ) 두 input 단자에서 본 저항 값이 같다 . 29 EM Wave Lab
  30. 30. Electronic Circuits7. DC effect Input bias current For R 3 = ( R 1 ∥R 2 ) and I B1 ≠ I B2 ≠ I B3 I B1 = I B + I OS /2 I B2 = I B - I OS /2 → V O = I OS R 2 (compare with V O = I B1 R 2 in case of without R 3 ) AC coupled inverting amp AC coupled non-inverting amp 30 EM Wave Lab
  31. 31. Electronic Circuits8. Integrator Impedance characteristics 31 EM Wave Lab
  32. 32. Electronic Circuits8. Integrator Example 32 EM Wave Lab
  33. 33. Electronic Circuits8. Integrator Miller integrator Integrator Frequency : w int = 1/RC Infinite DC gain : weak at DC imperfection 33 EM Wave Lab
  34. 34. Electronic Circuits8. Integrator DC imperfection 34 EM Wave Lab
  35. 35. Electronic Circuits8. Integrator Differentiator HPF with infinite corner frequency. Noise magnifier at High Frequency 35 EM Wave Lab

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