op amp review 2
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ENTC 3320
Op Amp Review
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Operational amplifiers (op-amps)Circuit symbol of an op-amp
Widely usedOften requires 2 power supplies + V
Responds to difference between twosignals
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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
Usually used with feedbackOpen-loop configuration not used much
V+
V
Vout = A(V+ -V)+
-
+
-
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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Inverting configuration
Very popular circuit
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Analysis of inverting
configurationI1 = (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 VoGain of circuit determined by external
components
I1
I2
Vo/ V
i= -R
2/R
1
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Summing Amplifier
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,
This circuit is called a weightedsummer
Vo = - Rf(V1 / R1 + V2 / R2 + V3 / R3)
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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+ = 0Vi/R1 =
Solve for Vo
Output is the integral of input
signal. CR1 is the time constant
I1
I2
( )
dt
VVdC
o
( )
dt
VVdC
o
dt
dV
C
o
= dtvCRv io1
1
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Noninverting configuration(0 - V
)/R1 = (V - Vo)/R2
But, Vi = V+ = V ,
(- Vi)/ R1 = (Vi - Vo)/R2Solve for Vo,
(- Vi)/R1 - (-Vi)/R2 = (-Vo)/R2
Vi (1/R1+ 1/R2) = (Vo)/R2
Vo = Vi (R2/R1+ R2/R
Vi
I
I
Vo = Vi(1+R2/R1)
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Buffer amplifier
Vi = V+ = V= Vo
Isolates input from
output
Vo = Vi
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Analyzing op-amp circuitsWrite 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 (noninvertingamp)
set V2 = 0, solve for
Vo (inverting amp)
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V02 = (1 + R2/R1) [R4/(R3+R4)] V2V2 R4/(R3+R4)
Difference amplifier
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V01 = -(R2/R1)V1
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Add the two results
V0 = V01 +V02
IfR1 =R2 =R3 =R4
+
+=
1
2
1
43
4
1
2
21
R
RV
RR
R
R
RVV
o
( ) ( )1212
12
111 VVVVV
o=
+=
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Design of difference amplifiersFor Vo = V2 - V1SetR2 = R1 = R, and set R3 = R4 = R
For Vo = 3V2 - 2V1Set R1 = R, R2 = 2R, then 3[R4/(R3+R4)] = 3
Set R3 = 0