1. Operational Amplifier

2. Ideal OP Amp
Circuit model
Two golden rules to perform calculations on op amps with negative feedback:
iin=0, no current flow into op amp.
V+=V-
Typically one end of op amp is connected to ground, therefore, V+=V-= 0V, virtual ground. Often V+ is connected to ground to avoid stability problem.

3. Applications: building block for analog systems
Amplifiers
Adders and Substractors
Integrators & Differentiators
Clock generators
Filters
Digital-to-analog converters

4. Using op-amps
No flexibility

5. Let’s build a circuit……noninverting amplifier

6. When A is very large Suppose A=106, R1=9R, R2=R Gain:
determined by resistance ratio
insensitive to A, temperature, fab variation

7. Why did this happen? Negative feedback
e.g. vIN=5V
Suppose I perturb the circuit (e.g. force v0 momentarily to 12V somehow
Stable point is when v+v-
Key: negative feedback  portion of output fed to –ve input.
e.g. Car antilock brakes  small corrections

8. How to control a high-strung device
Antilock brakes

9. More op amp insights: Observe, under negative feedback, We also know
 Yield an easier analysis method (under negative feedback)

10. Insightful analysis method: under negative feedback

11. Voltage follower Why is this circuit useful?
has minimum effects on previous and next circuit.

12. Inverting Amplifier
Feedback resistor, always to negative input

13. Summing Amplifier: Add Circuit
If RS1=RS2=…=RSN=RS

14. Non-innverting Amplifier
Feedback resistor, always to negative input

15. Differential Amplifier: Substractor
Very useful if both signals are corrupted with noise: Electrocardiogram (EKG)