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ENTC 3320 Op Amp Review

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**Operational amplifiers (op-amps)**

Circuit symbol of an op-amp Widely used Often requires 2 power supplies + V Responds to difference between two signals

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**Ideal op-amp Characteristics of an ideal op-amp Rin = infinity**

Rout = 0 Avo = infinity (Avo is the open-loop gain, sometimes A or Av of the op-amp) Bandwidth = infinity (amplifies all frequencies equally)

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**Model of an ideal op-amp**

V+ V Vout = A(V+ -V) + - I I+ Usually used with feedback Open-loop configuration not used much

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**Summary of op-amp behavior**

Vout = A(V+ - V) Vout/A = V+ - V Let A infinity then, V+ - V

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**Summary of op-amp behavior**

V+ = V I+ = I = 0 Seems strange, but the input terminals to an op-amp act as a short and open at the same time

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**To analyze an op-amp circuit**

Write node equations at + and - terminals (I+ = I = 0) Set V+ = V Solve for Vout

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**Inverting configuration**

Very popular circuit

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**Analysis of inverting configuration**

I1 = (Vi - V)/R1 I2 = (V - Vo)/R2 set I1 = I2, (Vi - V )/R1 = (V - Vo)/R2 but V = V+ = 0 Vi /R1 = -Vo/R2 Solve for Vo I2 I1 Gain of circuit determined by external components Vo/ Vi = -R2/R1

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**Summing Amplifier Current in R1, R2, and R3 add to current in Rf**

(V1-V)/ R1 + (V2-V)/ R2 + (V3-V)/R3 = (V - Vo)/ Rf Set V = V+ = 0, V1/ R1 + V2/ R2 + V3/ R3 = Vo / Rf solve for Vo, Vo = - Rf(V1 / R1 + V2 / R2 + V3 / R3) V1 V2 V3 R1 R2 R3 Rf This circuit is called a weighted summer

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**To analyze an op-amp circuit**

Write node equations at + and - terminals (I+ = I = 0) Set V+ = V Solve for Vout

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Integrator I1 = (Vi - V)/R1 I2 = set I1 = I2, (Vi - V)/R1 = but V- = V+ = 0 Vi/R1 = Solve for Vo I2 I1 Output is the integral of input signal. CR1 is the time constant

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**Noninverting configuration**

(0 - V)/R1 = (V - Vo)/R2 But, Vi = V+ = V , (- Vi)/ R1 = (Vi - Vo)/R2 Solve for Vo, (- Vi)/R1 - (-Vi)/R2 = (-Vo)/R2 Vi (1/R1+ 1/R2) = (Vo)/R2 Vo = Vi (R2/R1+ R2/R Vi I Vo = Vi(1+R2/R1)

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Buffer amplifier Isolates input from output Vi = V+ = V = Vo Vo = Vi

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**Analyzing op-amp circuits**

Write node equations using: V+ = V I + = I = 0 Solve for Vout Usually easier, can solve most problems this way. Write node equations using: op amp model. Let A infinity Solve for Vout Works for every op-amp circuit. OR

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**Difference amplifier Use superposition, set V1 = 0, solve for Vo**

(noninverting amp) set V2 = 0, solve for Vo (inverting amp)

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Difference amplifier V2 R4/(R3+R4) V02 = (1 + R2/R1) [R4/(R3+R4)] V2

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Difference amplifier V01 = -(R2/R1)V1

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Add the two results V0 = V01 + V02 If R1 = R2 = R3 = R4

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**Design of difference amplifiers**

For Vo = V2 - V1 Set R2 = R1 = R, and set R3 = R4 = R For Vo = 3V2 - 2V1 Set R1 = R, R2 = 2R, then 3[R4/(R3+R4)] = 3 Set R3 = 0

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