1. Ch. 5 – Operational Amplifiers
Ideal Amplifier
Symbol
Circuit Model
vi = input voltage; vo = A vi ; A = amplification or gain
Both voltages are with respect to ground
Input current is zero  input power is zero  power amplification is infinite
vo is “bare voltage” infinite output power

2. Improvements:
Input resistance Ri; input current ii
Output resistance Ro (Thevenin equivalent as seen by load)
Real Amplifier Model
Has 3 parameters:
is the open-circuit amplification

3. If a source (vs and Rs) and a load (RL) are connected, find the real amplifier gain.

4. OPERATIONAL AMPLIFIERS:
An operational amplifier (or op amp) is an electronic unit that behaves like a voltage-controlled voltage source, and can be used to perform mathematical operations such as addition, subtraction, multiplication, division, differentiation and integration.
a) Circuit symbol (ideal)
b) pin configuration

5. The five terminals of the op amp are:
a) The inverting input, vn (pin 2), b) The non-inverting input, vp (pin 3)
c) The output, vo (pin 6), d) The positive power supply, V+, pin 7.
e) The negative power supply, V-, pin 4.
Real op amp – typical values
The differential input voltage vd (or vi) is
vd = vp -vn.
The output voltage is given by
vo = A vd = A (vp – vn)

6. Ideal Op AMP with NEGATIVE FEEDBACK Analysis Technique
Assumptions:
and
Results:
Therefore, the input terminals of an ideal op amp are both a short circuit and an open-circuit.
Example:
a) Use the ideal op amp technique to predict vo.

7. Why does Vp = Vn ?? [The Concept]
Think of a home heating system Vn
A(Vp-Vn) Vp Vp Vn
A(Vp-Vn)
See also – Inverted Pendulum

8. Why does Vp = Vn ?? [The Proof!]
Compare a) with a real op amp with Ri = 105, A = 104, and Ro =0.

9. OP AMP Circuits
1. Voltage Follower - See example above.

10. 2. Basic Inverting Amplifier

11. Ex. 3 Determine vo.
Ans. -12 V

12. 3. Basic Non-inverting Amplifier

13. Example 4.
Answer: 7 V

14. 4. Current-to-voltage converter

15. 5. Voltage-to-current converter

16. 6. Summing Circuit

17. Example 5. Find vo and io.
Ans: -3.8,

18. 7. Difference Amplifier

20. Ex. 6. Design an op-amp circuit with inputs v1 and v2 such that
vo = -5v1 + 3v2
a) Use a difference amplifier

21. b) Use a cascaded op amp circuit

22. 8. Op-amp Integrator

23. 9. Op-amp Differentiator

24. Cascaded op amp Circuits
Cascade connection - head-to-tail arrangement of two or more circuits such that the output of one is the input of the next.
Given: v1=2V; v2=1.5V
Find: vo
Ans: 9V