1. ENTC 3320
Op Amp Review

2. Operational amplifiers (op-amps)
Circuit symbol of an op-amp
Widely used
Often requires 2 power supplies + V
Responds to difference between two signals

3. Ideal op-amp Characteristics of an ideal op-amp Rin = infinity
Rout = 0
Avo = infinity (Avo is the open-loop gain, sometimes A or Av of the op-amp)
Bandwidth = infinity (amplifies all frequencies equally)

4. Model of an ideal op-ampV+ V
Vout = A(V+ -V) + - I I+
Usually used with feedback
Open-loop configuration not used much

5. Summary of op-amp behavior
Vout = A(V+ - V)
Vout/A = V+ - V
Let A infinity
then,
V+ - V

6. Summary of op-amp behavior
V+ = V
I+ = I  = 0
Seems strange, but the input terminals to an
op-amp act as a short and open at the same time

7. To analyze an op-amp circuit
Write node equations at + and - terminals (I+ = I = 0)
Set V+ = V
Solve for Vout

8. Inverting configuration
Very popular circuit

9. Analysis of inverting configuration
I1 = (Vi - V)/R1
I2 = (V - Vo)/R2
set I1 = I2,
(Vi - V )/R1 = (V - Vo)/R2
but V = V+ = 0
Vi /R1 = -Vo/R2
Solve for Vo I2 I1
Gain of circuit determined by external components
Vo/ Vi = -R2/R1

10. Summing Amplifier Current in R1, R2, and R3 add to current in Rf
(V1-V)/ R1 + (V2-V)/ R2 + (V3-V)/R3 = (V - Vo)/ Rf
Set V  = V+ = 0, V1/ R1 + V2/ R2 + V3/ R3 = Vo / Rf
solve for Vo,
Vo = - Rf(V1 / R1 + V2 / R2 + V3 / R3) V1 V2 V3 R1 R2 R3 Rf
This circuit is called a weighted summer

11. To analyze an op-amp circuit
Write node equations at + and - terminals (I+ = I = 0)
Set V+ = V
Solve for Vout

12. Integrator
I1 = (Vi - V)/R1
I2 =
set I1 = I2,
(Vi - V)/R1 =
but V- = V+ = 0
Vi/R1 =
Solve for Vo I2 I1
Output is the integral of input signal. CR1 is the time constant

13. Noninverting configuration
(0 - V)/R1 = (V - Vo)/R2
But, Vi = V+ = V ,
(- Vi)/ R1 = (Vi - Vo)/R2
Solve for Vo,
(- Vi)/R1 - (-Vi)/R2 = (-Vo)/R2
Vi (1/R1+ 1/R2) = (Vo)/R2
Vo = Vi (R2/R1+ R2/R Vi I
Vo = Vi(1+R2/R1)

14. Buffer amplifier
Isolates input from output
Vi = V+ = V = Vo
Vo = Vi

15. Analyzing op-amp circuits
Write node equations using:
V+ = V
I + = I = 0
Solve for Vout
Usually easier, can solve most problems this way.
Write node equations using:
op amp model.
Let A infinity
Solve for Vout
Works for every op-amp circuit. OR

16. Difference amplifier Use superposition, set V1 = 0, solve for Vo
(noninverting amp)
set V2 = 0, solve for Vo
(inverting amp)

17. Difference amplifier
V2 R4/(R3+R4)
V02 = (1 + R2/R1) [R4/(R3+R4)] V2

18. Difference amplifier
V01 = -(R2/R1)V1

19. Add the two results
V0 = V01 + V02
If R1 = R2 = R3 = R4

20. Design of difference amplifiers
For Vo = V2 - V1
Set R2 = R1 = R, and set R3 = R4 = R
For Vo = 3V2 - 2V1
Set R1 = R, R2 = 2R, then 3[R4/(R3+R4)] = 3
Set R3 = 0