1. Operational Amplifiers (Op-Amps)

2. Operational Amplifier (Op-Amp)
Not a discrete device (resistor, cap, ind, diode, transistor etc.)
IC !
2-input terminals
Inverting and non-inverting
Output terminal
Two supply terminals
Inexpensive – yet very useful in instrumentation applications
We will only consider ideal op-amps !

3. Operational Amplifiers (Op-Amps)

4. Ideal Op-Amps 5 characteristics Infinite open-loop voltage gain
Infinite input impedance
Zero output impedance
Infinite bandwidth
Zero input voltage offset

5. A Simple Model for the Op-Amp
Very High Gain amplifier with a high input and low output resistance !
AOL: “Open-Loop” Gain ( )
RIN: input resistance (Mohms)
ROUT: Output Resistance (10s of ohms)

6. Input Current (IN) is zero !
Ideal Op-Amps
“Golden Rules”
Input currents = 0
Difference in input voltages = 0
Input Current (IN) is zero !
V+=V-

7. Ideal Op-Amps Analysis Procedure Calculate the input voltage
Write node equation at op-amp input to find the output voltage

8. Inverting Amplifier Since Ia = 0, I1 = If Vb = 0 Va = 0
Find the voltage gain Vo/Vi.
Calculate the input voltage
Write node equation at op-amp input to find the output voltage

9. Non-Inverting Amplifier
Since Ia = 0, I1 = If
Vb = Vi
Va = Vi
Find the voltage gain Vo/Vi.
Calculate the input voltage
Write node equation at op-amp input to find the output voltage

10. Integrator
By KVL, Vout = –VC

11. Differentiator

12. Two-Stage Amplifier Gain = Vo1/Vi Gain = Vo2/Vo1
Total Gain = (Vo1/Vi) (Vo2/Vo1) = Vo2/Vi

13. Example

14. Example

15. Work this Example!_________