1. Operational Amplifiers Op Amps – a useful building block K. El-Ayat 11

2. 2 Figure 2.2 The op amp shown connected to dc power supplies. Op Amp: A DC coupled high Gain differential Amplifier Many useful applications An Op Amp produces an output voltage that is much larger than the difference between its two inputs (very high gain) -ve +ve

3. 3 Figure 2.3 Equivalent circuit of the ideal op amp. An Ideal Op Amp V out = A(v 2 -v 1 ) Differential input stage  amplified Infinite input impedance Zero Output impedance Infinite open-loop gain A Infinite bandwidth Op amps are DC (direct coupled) Usually used with external components R, C, …

4. 4 Figure 2.6 Analysis of the inverting configuration. The circled numbers indicate the order of the analysis steps. Inverting Op Amp - Analysis Terminal 2 (+ve input)  ground R F (or R 2 ) connected to terminal 1 (-ve) Negative feedback Since open loop gain A very high Then v 1 -v 2 = v o / A = 0 v 1 = v 2 = gnd V O = - (R 2 / R 1 ) * V i i 1 = i 2 & Gain G = - R 2 / R 1 G (closed loop) gain

5. 5 Figure E2.6 Op Amp – Class Analysis Example Find all I, v, gain v 1 = i 1 = i 2 = v o = i L = i o =

6. 6 Figure 2.10 A weighted summer. An Op Amp Application; Weighted Summing Circuit vo = - [(R f / R 1 ) * v 1 + (R f / R 2 ) * v 2 +….+ (R f / R n ) * v n ] i n = ? i = ?

7. 7 Figure 2.11 A weighted summer capable of implementing summing coefficients of both signs. 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 ) Two Op Amp comnibation Summing Circuit, with both signs Can calculate in 2 steps

8. 8 Figure 2.12 The noninverting configuration. Non inverting Op Amp Application Use +ve Op Amp input

9. 9 Figure 2.13 Analysis of the non-inverting circuit. The sequence of the steps in the analysis is indicated by the circled numbers. Non-inverting Op Amp: Analysis v o = v i + (v i /R 1 )*R 2 v o = v i (1 + R 2 /R 1 ) G = 1 + R 2 /R 1

10. 10 Figure 2.14 (a) The unity-gain buffer or voltage follower amplifier. (b) Its equivalent circuit model. Unity Gain Op Amp Voltage follower - unity gain; high current gain Buffer stage between processors - switches G = 1 + 0 /R 1; R 2  0

11. 11 Figure E2.9 Op Amp problem – find v o Assume x is voltage at both Amp inputs –ve, & +ve x = 3/5 (v 1 -v 2 ) + v 2 ; resistor divider I = x / 1 = (v o - x) / 9 v o = 10 x v o = 10 *[ 3/5 (v 1 -v 2 ) + v 2 ] = 6 v 1 + 4 v 2 ANS. I

12. 12 Figure E2.13 Another Op Amp problem – Should be able to analyze v o =

13. 13 Figure 2.16 A difference amplifier. Can use as a difference Op Amp

14. 14 Figure 2.23 Frequency response of an amplifier with a nominal gain of +10 V/V. Frequency response of Op Amp Gain = +10

15. 15 Figure 2.22 Open-loop gain of a typical general-purpose internally compensated op amp. Open-loop gain of Op Amp Gain declines rapidly with freq

16. 16 Figure 9.1 The basic two-stage CMOS op-amp configuration. Two-stage CMOS Op Amp - fyi

17. 17 Figure 9.4 Typical frequency response of the two-stage op amp. Frequency Response of CMOS Op Amp fyi

18. 18 Figure 2.37 The inverting configuration with general impedances in the feedback and the feed-in paths. Inverting Op Amp Application to Impedances