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## Chapter 5

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**Chapter 5**Operational Amplifier**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**Terminal Voltage and Currents**Vd=V2-V1 (differencial input) Vo=AVd=A(V2-V1) A: gain (open-loop voltage gain)**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**i1**i2 Ideal op amp model Ideal op amp • i1=0 , i2=0 ; • V1=V2**Applications**Inverting Amplifier**Applications**Noninverting amplifier If Rf=0; R1=, then=>**+**+ First stage Second stage Vi Vo The voltage follower - - Applications**Applications**Summing amplifier**2**a 3 b 3 1 1 2 4 Difference Amplifier Note: be careful while using nodal analysis, do not set nodal equation at the output terminal.**Example:**Find out Vo**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