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**Operational Amplifier**

Chapter 5 Operational Amplifier

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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

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**Terminal Voltage and Currents**

Vd=V2-V1 (differencial input) Vo=AVd=A(V2-V1) A: gain (open-loop voltage gain)

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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

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

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Applications Inverting Amplifier

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

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

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Applications Summing amplifier

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

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Example: Find out Vo

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**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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