1. Operational Amplifier
Chapter 5
Operational Amplifier

2. Introduction
An op amp is an active circuit element designed to perform mathematical operation of addition, subtraction, multiplication, division, differentiation, and integration.
A typical op amp: a) pin configuration, b) circuit symbol

3. Terminal Voltage and Currents
Vd=V2-V1 (differencial input)
Vo=AVd=A(V2-V1)
A: gain (open-loop voltage gain)

4. i1 i2
Actual op amp: Ri(very large); Ro(very small); A(very large)
Idealization: Ri=> ; Ro=>0 ; A=> 
As Vo is limited, we can get from Vo=A(V2-V1) that: V2=V1
As Ri=> , we can get i1=0, i2=0

5. Ideal op amp
Ideal op amp model i1 i2
i1=0 , i2=0 ;
V1=V2

6. Applications
Inverting Amplifier

7. Applications
Noninverting amplifier
If Rf=0; R1=, then=>

8. Applications Vi Vo + -
First stage
Second stage
The voltage follower

9. Applications
Summing amplifier

10. Difference Amplifier 2 1 3 4 a b
Note: be careful while using nodal analysis, do not set nodal equation at the output terminal.

11. Example:
Find out Vo

12. P.P.5.10 As a voltage follower,
va = v1 = 2V
where va is the voltage at the right end of the 20 k resistor.
As an inverter, vb =
Where vb is the voltage at the right end of the 50k resistor. As a summer
v0 =
= [6 - 15] = 9V