Chap 2. Operational amplifiers (op-amps)

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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
I
V

Vout A(V - V-)
I-
V-
-

• 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- 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
I2
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
I1
Gain of circuit determined by external components
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2.4 Applications of the inverting configuration
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(1R2/R1)
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Input resistance of noninverting amplifier
Rin Vin / I, from definition Rin Vin /
0 Rin infinity
V-
I
Vout A(V -V-)
V
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Input resistance of inverting amplifier
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
(1A) As A approaches infinity, Rin 0
I
V-
V
Vout A(V - V-)
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Summary of op-amp behavior
Inverting configuration
Noninverting configuration
Vi
Rin 0 at this point
Vo/Vi 1R2/R1 Rin infinity
Vo /Vi - R2/R1 Rin R1