ECE 342 Solid-State Devices & Circuits 18. Operational Amplifiers

1. ECE 342 Solid-State Devices & Circuits 18. Operational Amplifiers Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jschutt@emlab.uiuc.edu

2. Operational Amplifiers • Universal importance (e.g. amplification from microphone to loudspeakers) General terminal configuration with bias

3. Operational Amplifiers Gain=A Common configuration with bias implied but not shown • Signaling • Differential input stage • Difference between input is amplified

4. Operational Amplifiers • Ideal Op Amp • 1. Infinite input impedance • 2. Zero output impedance • 3. Infinite open-loop gain Ainf • 4. Infinite CMRR or zero common-mode gain • 5. Infinite bandwidth Also, op amps are dc (or direct coupled) amplifiers since they are expected to amplify signals with frequency as low as DC.

5. Differential & Common-Mode Signals • Differential input signal vID=v2-v1 • Common-mode input signal vICm=0.5(v1+v2)

6. Operational Amplifiers Ideally, vICM should be zero to achieve high CMRR. • Amplifier will amplify the difference between the two input signals

7. Practical Considerations The output voltage swing of an op amp is limited by the DC power supply. Since op amp can exhibit high gain, power supply voltage fluctuations must be minimized  use decoupling capacitors from power supply

8. Inverting Configuration Terminal 2 is tied to ground We introduce RF (or R2) to reduce gain (from inf) • When RF is connected to terminal 1, we talk about negative feedback. If RFis tied to terminal 2, we have positive feedback

9. Inverting Configuration Need to evaluate vo/vI Assume ideal Op-Amp Since gain is infinite: Note: A is open-loop gain v1 is virtual ground

10. Inverting Configuration Since input impedance of OP amp is infinite, current through RFis i1

11. Inverting Configuration Closed-Loop gain Observe that the closed-loop gain is the ratio of external components  we can make the closed-loop as accurate as we want. Gain is smaller but more accurate.

12. Inverting Configuration We assumed that the OP-amp was ideal. If we assume that the gain A is finite = A

13. Inverting Configuration Still assume infinite input impedance Closed-loop gain for inverting configuration

14. Inverting Configuration The reflected impedance of RF is given by since  small

15. Inverting Configuration Since the reflected impedance is so small, v1 is thus very small and the inverting terminal is said to be a virtual ground in this configuration We see that Note: To minimize the closed-loop gain (G) on the value of the open-loop gain (A), make 1+RF/R1 << A

16. Input and Output Impedances Inverting Configuration • - If high gain is required, input impedance will be low • - Output impedance is zero

17. Example Find closed-loop gain for A=103, A=104 and A=105 assuming R1=1 kW and RF=100 kW. Assuming vI=0.1 V, find v1. Using formulas A |G| v1 10390.83 -9.08 mV 10499.00 -0.99 mV 10599.90 -0.1 mV Note: Since output of inverting configuration is at terminal of VCVS, output impedance of closed-loop amp is zero.

18. Assume gain is Non-Inverting Configuration

19. Non-Inverting Configuration Infinite input impedance

20. Non-Inverting Configuration Virtual short

21. The Buffer Stage Although voltage gain is low, current gain can be quite high. Buffer stage can be used to interface between processors and switches.

22. The Voltage Follower • - Unity gain amplifier • - 100% negative feedback

23. Frequency Response – Non-Inverting No feedback with feedback description A(f) Ani(f) Gain AMBOaAMBniMidband gain f2oa f2ni 3 dB freqpt GBWoaGBWni Gain-BW prod

24. Frequency Response – Non-Inverting

25. Frequency Response – Non-Inverting

26. Frequency Response – Non-Inverting Gain-Bandwidth product is constant

27. Frequency Response – Non-Inverting Midband voltage gain is reduced from AMBoa to AMBni The upper 3-dB frequency will be greater than that of the op amp by the same factor of gain reduction. If the low-frequency gain of the op amp is AMBoa= 200,000 and with resistors AMBni= 40, the gain is reduced by a factor of 5,000. If the basic 3-db frequency is 5 Hz, the noninverting 3dB frequency will be 25 kHz.

28. Frequency Response – Inverting OP Amp

29. Frequency Response – Inverting OP Amp

30. Frequency Response – Inverting OP Amp

31. Frequency Response – Inverting OP Amp if RF >> R1

32. Frequency Response – Inverting OP Amp if RF >> R1 gain-bandwidth is constant if RF ~ R1 ,

33. Frequency Response – Inverting OP Amp

34. Example Design an amplifier to couple a microphone to a resistive load. The microphone generates a peak output of 50 mV for a typical voice input level and has a 10-kW output impedance. The output voltage across the 2-kW load is to have a peak value of 10 V. the bandwidth of the voltage gain should be at least 40 kHz. If the GBW of the op amp used is 3106 Hz, calculate the bandwidth of the final design The midband voltage gain is: For a single noninverting stage with this gain, the upper corner frequency is:

35. Example (cont’) This value of BW will not work need 2 stages Pick first stage gain 10; second stage gain 20. We must then have: and

36. Example (cont’) Choose R21 and R22arbitrarily and use above equations to extract RF1 and RF2; we get: RF1= 18 kW, RF2 = 38 kW Next, find 3-dB bandwidth of each stage by dividing respective gains into GBWoa or GBWni

37. Example (cont’) The overall gain is: At 3dB point, magnitude squared of denominator must be 2 From which