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Operational Amplifier

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Presentation on theme: "Operational Amplifier"— Presentation transcript:

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

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