1. ECE 2006 Chapter 5: Operational Amplifiers

2. Differential Amplifier Not Practical Prior to IC Fabrication 2 Inputs, Output is A v *(V 1 - V 2 )

3. Common Mode Rejection Differential Amps won’t Amplify Signals that are Common to both Inputs

4. Operational Amplifier Three Stages: –Differential Amplifier (Input Stage) –Voltage Amplifier (High Gain) –Output Stage (low output impedance)

5. Op Amp Characteristics High Input Impedance ( 1 M-Ohm) Low Output Impedance (100 Ohms) High Voltage Gain (100,000) 2 Differential Inputs –Inverting Input (V-) –Non-Inverting Input (V+)

6. Equivalent Circuit Model Differential Input Voltage determines Output Voltage

7. Ideal Op Amp Input Impedance is Infinite (No input Current) Voltage Gain is Infinite Inverting and Non-inverting inputs at equal potential

8. Feedback Open Loop Voltage Gain is so High that External Feedback is always used Output Signal is Fed Back to an Input Terminal

9. Analysis of Ideal Op Amp Circuits Set V- = V+ and I- = I+ = 0 Write Nodal Equation(s)

10. Basic Op Amp Circuits Voltage Follower: Impedance Matching or Isolation Unity Gain: V out = V in

11. Inverting Amplifier V out = -(R 2 /R 1 )*V in

12. Non-Inverting Amplifier V out = V in *(R 1 +R 2 )/R 1

13. Summing Amplifier V out = -(V 1 *R f /R 1 + V 2 *R f /R 2 + V 3 *Rf/R 3 )

14. Difference Amplifier V out = (V 2 -V 1 )*R 2 /R 1

15. Analysis of the Voltage Follower Provides “Current Isolation” – No Power Drawn from Input Circuit

16. References Heathkit, Electronic Circuits, EB-6104A, 2002 Alexander, Fundamentals of Circuit Analysis – 2 nd Edition, McGraw-Hill, 2004