1. 1 Chapter 8 Operational Amplifier as A Black Box  8.1 General Considerations  8.2 Op-Amp-Based Circuits  8.3 Nonlinear Functions  8.4 Op-Amp Nonidealities  8.5 Design Examples

2. CH8 Operational Amplifier as A Black Box2 Chapter Outline

3. CH8 Operational Amplifier as A Black Box3 Basic Op Amp  Op amp is a circuit that has two inputs and one output.  It amplifies the difference between the two inputs.

4. CH8 Operational Amplifier as A Black Box4 Inverting and Non-inverting Op Amp  If the negative input is grounded, the gain is positive.  If the positive input is grounded, the gain is negative.

5. CH8 Operational Amplifier as A Black Box5 Ideal Op Amp  Infinite gain  Infinite input impedance  Zero output impedance  Infinite speed

6. CH8 Operational Amplifier as A Black Box6 Virtual Short  Due to infinite gain of op amp, the circuit forces V in2 to be close to V in1, thus creating a virtual short.

7. CH8 Operational Amplifier as A Black Box7 Unity Gain Amplifier

8. CH8 Operational Amplifier as A Black Box8 Op Amp with Supply Rails  To explicitly show the supply voltages, V CC and V EE are shown.  Ex) VCC=+5V, VEE=-5V; VCC=+5V, VEE=0V (general)

9. CH8 Operational Amplifier as A Black Box9 Noninverting Amplifier (Infinite A 0 )  A noninverting amplifier returns a fraction of output signal thru a resistor divider to the negative input.  With a high A o, V out /V in depends only on ratio of resistors, which is very precise.

10. CH8 Operational Amplifier as A Black Box10 Noninverting Amplifier (Finite A 0 )  The error term indicates the larger the closed-loop gain, the less accurate the circuit becomes. Ex 8.3

11. CH8 Operational Amplifier as A Black Box11 Extreme Cases of R 2 (Infinite A 0 )  If R 2 is zero, the loop is open and V out /V in is equal to the intrinsic gain of the op amp.  If R 2 is infinite, the circuit becomes a unity-gain amplifier and V out /V in becomes equal to one.

12. CH8 Operational Amplifier as A Black Box12 Inverting Amplifier  Infinite A 0 forces the negative input to be a virtual ground. Virtual ground: + 와 –node 의 전압이 같아서 ground(0V) 로 보인다는 말임

13. CH8 Operational Amplifier as A Black Box13 Another View of Inverting Amplifier Inverting Noninverting

14. CH8 Operational Amplifier as A Black Box14 Gain Error Due to Finite A 0  The larger the closed loop gain, the more inaccurate the circuit is.

15. CH8 Operational Amplifier as A Black Box15 Complex Impedances Around the Op Amp  The closed-loop gain is still equal to the ratio of two impedances.

16. CH8 Operational Amplifier as A Black Box16 Integrator

17. CH8 Operational Amplifier as A Black Box17 Integrator with Pulse Input

18. CH8 Operational Amplifier as A Black Box18 Comparison of Integrator and RC Lowpass Filter  The RC low-pass filter is actually a “passive” approximation to an integrator.  With the RC time constant large enough, the RC filter output approaches a ramp.

19. CH8 Operational Amplifier as A Black Box19 Lossy Integrator  When finite op amp gain is considered, the integrator becomes lossy as the pole moves from the origin to - 1/[(1+A 0 )R 1 C 1 ].  It can be approximated as an RC circuit with C boosted by a factor of A 0 +1.

20. CH8 Operational Amplifier as A Black Box20 Differentiator

21. CH8 Operational Amplifier as A Black Box21 Differentiator with Pulse Input

22. CH8 Operational Amplifier as A Black Box22 Comparison of Differentiator and High-Pass Filter  The RC high-pass filter is actually a passive approximation to the differentiator.  When the RC time constant is small enough, the RC filter approximates a differentiator.

23. CH8 Operational Amplifier as A Black Box23 Lossy Differentiator  Finite op amp gain 의 경우, 미분기는 원점 zero 에서 – (A 0 +1)/R 1 C 1 의 pole 을 추가  RC HPF 와 비교하여 R  R/(A 0 +1) 로 근사화 가능.

24. CH8 Operational Amplifier as A Black Box24 Op Amp with General Impedances  This circuit cannot operate as ideal integrator or differentiator.

25. CH8 Operational Amplifier as A Black Box25 Voltage Adder  If A o is infinite, X is pinned at ground, currents proportional to V 1 and V 2 will flow to X and then across R F to produce an output proportional to the sum of two voltages. If R 1 = R 2 =R AoAo

26. CH8 Operational Amplifier as A Black Box26 Precision Rectifier

27. CH8 Operational Amplifier as A Black Box27 Inverting Precision Rectifier (input=V in,output=V x )

28. CH8 Operational Amplifier as A Black Box28 Logarithmic Amplifier  By inserting a bipolar transistor in the loop, an amplifier with logarithmic characteristic can be constructed.  This is because the current to voltage conversion of a bipolar transistor is a natural logarithm.

29. CH8 Operational Amplifier as A Black Box29 Square-Root Amplifier  By replacing the bipolar transistor with a MOSFET, an amplifier with a square-root characteristic can be built.  This is because the current to voltage conversion of a MOSFET is square-root.

30. CH8 Operational Amplifier as A Black Box30 Op Amp Nonidealities: DC Offsets by mismatch Wafer 제작과정에서 생길 수 있는 length, oxide thickness 등등의 차이

31. CH8 Operational Amplifier as A Black Box31 Op Amp Nonidealities: DC Offsets  Offsets in an op amp that arise from input stage mismatch cause the input-output characteristic to shift in either the positive or negative direction (the plot displays positive direction).

32. CH8 Operational Amplifier as A Black Box32 Effects of DC Offsets  As it can be seen, the op amp amplifies the input as well as the offset, thus creating errors.

33. CH8 Operational Amplifier as A Black Box33 Saturation Due to DC Offsets  Since the offset will be amplified just like the input signal, output of the first stage may drive the second stage into saturation.

34. CH8 Operational Amplifier as A Black Box34 Offset in Integrator 시간이 지나면 출력전압이 계속 커져서 전원전압까지 올라감

35. CH8 Operational Amplifier as A Black Box35 Offset in Integrator  A resistor can be placed in parallel with the capacitor to “absorb” the offset. However, this means the closed-loop transfer function no longer has a pole at origin. 출력전압이 계속 커지는 것을 막아줌

36. CH8 Operational Amplifier as A Black Box36 Input Bias Current  The effect of bipolar base currents can be modeled as current sources tied from the input to ground.

37. CH8 Operational Amplifier as A Black Box37 Effects of Input Bias Current on Noninverting Amplifier  It turns out that I B1 has no effect on the output and I B2 affects the output by producing a voltage drop across R 1.

38. CH8 Operational Amplifier as A Black Box38 Input Bias Current Cancellation  We can cancel the effect of input bias current by inserting a correction voltage in series with the positive terminal.  In order to produce a zero output, V corr =-I B2 (R 1 ||R 2 ).

39. CH8 Operational Amplifier as A Black Box39 Correction for  Variation  Since the correction voltage is dependent upon , and  varies with process, we insert a parallel resistor combination in series with the positive input. As long as I B1 = I B2, the correction voltage can track the  variation. Current offset 이 없는 경우에 위와 같이 전류가 흐른는 경우에도 출력으로 DC offset 이 생기게 되는데, OP-AMP 의 +node 에서 바라본 저항과 –node 에서 바라본 저항이 같아지도록 하면 제거된다.

40. CH8 Operational Amplifier as A Black Box40 Effects of Input Bias Currents on Integrator  Input bias current will be integrated by the integrator and eventually saturate the amplifier.

41. CH8 Operational Amplifier as A Black Box41 Integrator’s Input Bias Current Cancellation  By placing a resistor in series with the positive input, integrator input bias current can be cancelled.  However, the output still saturates due to other effects such as input mismatch, etc. 앞과 같은 방법으로 저항 추가

42. CH8 Operational Amplifier as A Black Box42 Speed Limitation  Due to internal capacitances, the gain of op amps begins to roll off. Open loop Gain(feedback 회로를 연결하지 않은 ) 의 주파수 특성

43. 43 Continued : Gain X bandwidth = constant OP-AMP 를 이용해서 만든 회로는 OP- AMP 의 한계를 넘어서는 특성을 절대로 보일 수 없다. Closed loop Gain(feedback 회로를 연결된 ) 의 주파수 특성

44. CH8 Operational Amplifier as A Black Box44 Bandwidth and Gain Tradeoff  Having a loop around the op amp (inverting, noninverting, etc) helps to increase its bandwidth. However, it also decreases the low frequency gain.

45. CH8 Operational Amplifier as A Black Box45 Slew Rate of Op Amp # step 입력에 대해서 출력이 step 출력이 나오지 않게 됨 : OP-AMP 가 가지고 있는 최대 단위 시간당 전압의 변화를 slew rate 라고 함. 1)step 입력에 대해서 M2 가 off 되고, M4 가 공급해 주는 전류에 의해서, Vout 이 High 로 올라 간다. 출력전압은 capacitor 에 공급되는 전류에 의해서 High 로 올라가기 때문에, linear 하게 커지는 출력전압이 나온다. 2)step 입력에 대해서 M1 이 off 되고, M2 가 빼내는 전류에 의해서, Vout 이 Low 로 떨어진다. 출력전압은 capacitor 에서 빼내는 전류에 의해서 Low 로 떨어지기 때문에, linear 하게 떨어지는 출력전압이 나온다. # Slew rate 한계를 가지는 OP-AMP 를 사용한 회로 : 출력이 단위시간당 전압의 변화가 OP- AMP 의 slew rate 를 넘게 되는 경우에 출력 파형이 입력파형과 다르게 나옴. A) 출력 전압의 큰 변화가 생기는 경우, B) 주파수가 높은 경우

46. CH8 Operational Amplifier as A Black Box46 Slew Rate of Op Amp: 전압의 큰 변화  In the linear region, when the input doubles, the output and the output slope also double. However, when the input is large, the op amp slews so the output slope is fixed by a constant current source charging a capacitor.  This further limits the speed of the op amp.

47. CH8 Operational Amplifier as A Black Box47 Comparison of Settling with and without Slew Rate  As it can be seen, the settling speed is faster without slew rate (as determined by the closed-loop time constant).

48. CH8 Operational Amplifier as A Black Box48 Slew Rate Limit on Sinusoidal Signals: 주파수가 높은 경우  As long as the output slope is less than the slew rate, the op amp can avoid slewing.  However, as operating frequency and/or amplitude is increased, the slew rate becomes insufficient and the output becomes distorted.

49. CH8 Operational Amplifier as A Black Box49 Maximum Op Amp Swing  To determine the maximum frequency before op amp slews, first determine the maximum swing the op amp can have and divide the slew rate by it.

50. CH8 Operational Amplifier as A Black Box50 Nonzero Output Resistance  In practical op amps, the output resistance is not zero.  It can be seen from the closed loop gain that the nonzero output resistance increases the gain error.

51. CH8 Operational Amplifier as A Black Box51 Design Examples  Many design problems are presented at the end of the chapter to study the effects of finite loop gain, restrictions on peak to peak swing to avoid slewing, and how to design for a certain gain error.