1. OPERATIONAL AMPLIFIERS
Operational Amplifiers(Op-Amp)
Ideal characteristics
Practical Op Amp
Inverting
Non inverting
Applications
Adder
Subtractor
summing
difference
Instrumentation amplifiers

2. OPERATIONAL AMPLIFIER
Operational Amplifiers are represented both schematically and realistically below:
Active component!

4. Originally invented in early 1940s using vacuum tube technology
Initial purpose was to execute math operations in analog electronic calculating machines
Shrunk in size with invention of transistor
Most now made on integrated circuit (IC)
Only most demanding applications use discrete components
Huge variety of applications, low cost, and ease of mass production make them extremely popular
Single-ended Amplifier
Differential Amplifier
Amplifies difference between inputs

5. Output gain high
A ~= 106
Tiny difference in the input voltages result in a very large output voltage
Output limited by supply voltages
Comparator
If V+>V-, Vout = HVS
If V+<V-, Vout = LVS
If V+=V-, Vout = 0V

6. 3-stage Op-Amp

7. Why are they useful? Negative feedback leads to stable equilibrium
Sensor signals are often too weak or too noisy
Op Amps ideally increase the signal amplitude without affecting its other properties
Negative feedback leads to stable equilibrium
Voltage follower (direct feedback)
If Vout = V- , then Vout ~ V+
Closed Loop Transfer Function
H(s) = A / (1 + AF)
When AF >> 1…
H(s) = 1 / F
Where: A = Op Amp Open Loop Gain
F = Feedback Loop Gain

8. Attenuates and phases at high frequencies (depends on slew rate)
Ideal Op Amp
Zin is infinite; ; Zout is zero; Amplification (Gain) Vout / Vin = ∞; Unlimited bandwidth; Vout = 0 when Voltage inputs = 0
Ideal Op-Amp
Typical Op-Amp
Input Resistance
infinity
106  (bipolar)
109   (FET)
Input Current
10-12 – 10-8 A
Output Resistance
100 – 1000 
Operational Gain
Common Mode Gain
10-5
Bandwidth
Attenuates and phases at high frequencies (depends on slew rate)
Temperature
independent
Bandwidth and gain

9. Inverting Op-Amp
                                             
                         

10. Non-inverting Op-Amp

11. Summation

12. Difference
If all resistors are equal:

13. Integrating Op-Amp

14. Differentiating Op-Amp
(where Vin and Vout are functions of time)