1. Operational Amplifiers Supplemental lecture Rick Matthews

2. The inverting amplifier R2 provides negative feedback.

3. The inverting amplifier R2 provides negative feedback. This means V- is adjusted to V+.

4. The inverting amplifier R2 provides negative feedback. This means V- is adjusted to V+. V+ is zero, so V- must be zero, too.

5. The inverting amplifier R2 provides negative feedback. This means V- is adjusted to V+. V+ is zero, so V- is zero. I

6. The inverting amplifier R2 provides negative feedback. This means V- is adjusted to V+. V+ is zero, so V- is zero. I

7. The inverting amplifier R2 provides negative feedback. This means V- is adjusted to V+. V+ is zero, so V- is zero. I

8. More generally,…

9. Whatever sits in the place of R 1 serves to create a current I that is a function of V in. I=f(V in )

10. More generally,… Whatever sits in the place of R 1 serves to create a current I that is a function of V in. And whatever sits in place of R 2 serves to create a voltage V out that is a second function of I. I=f(V in ) V out = -g(I)

11. More generally,… Whatever sits in the place of R 1 serves to create a current I that is a function of V in. And whatever sits in place of R 2 serves to create a voltage V out that is a second function of I. I=f(V in ) V out = -g(I)

12. Example

15. Example: Exponentiating amp

20. Example: log amp

27. A Multiplier Log Amp Summing Amp Exponential Amp V in1 V in2 V out log(a) log(b) log(a)+log(b) =log(ab) ab

28. A Divider Log Amp Differential Amp Exponential Amp V in1 V in2 V out log(a) log(b) log(a)-log(b) =log(a/b) a/b

29. Calculus Differentiator

30. Calculus Differentiator Integrator

31. Etc. Can you think of a circuit to take cube roots? We can fashion sophisticated analog computers this way.