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Chap 2. 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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2.2 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-)+

-

+

-

•Usually used with feedback•Open-loop configuration not used much

I-

I+

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Summary of op-amp behavior

Vout = A(V+ - V-)

Vout/A = V+ - V-

Let A infinity

then,

V+ -V- 0

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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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2.3 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

Vo / Vi = -R2 / R1

Gain of circuit determined by external components

I1

I2

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2.4 Applications of the inverting configuration

V1

V2

V3

R1

R2

R3

Rf

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)

This circuit is called a weighted summer

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2.5 Noninverting configuration

(0 - V-)/R1 = (V- - Vo)/R2

But, Vi = V+ = V-,

( - Vi)/R1 = (Vi - Vo)/R2

Solve for Vo,

Vo = Vi(1+R2/R1)

Vi

I

I

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Input resistance of noninverting amplifier

Vout = A(V+ -V-)

V-

V+

Rin = Vin / I, from definition

Rin = Vin / 0

Rin = infinity

I

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Input resistance of inverting amplifier

Vout = A(V+ - V-)

V-

V+

Rin = Vin / I, from definition

I = (Vin - Vout)/R

I = [Vin - A (V+ - V-)] / R

But V+ = 0

I = [Vin - A( -Vin)] / R

Rin = VinR / [Vin (1+A)]

As A approaches infinity,

Rin = 0

I

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Summary of op-amp behavior

Vi

Inverting configuration Noninverting configuration

Vo/Vi = 1+R2/R1

Rin = infinity

Vo /Vi = - R2/R1

Rin = R1

Rin = 0 atthis point

Vi