entc 3320 op amp review operational amplifiers (op-amps) circuit symbol of an op-amp widely used...
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ENTC 3320
Op Amp Review
Operational amplifiers (op-amps)
Circuit symbol of an op-amp
Widely usedOften requires 2 power supplies + VResponds to difference between two signals
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)
Model of an ideal op-amp
•Usually used with feedback•Open-loop configuration not used much
V+
V
Vout = A(V+ -V)+-
+
-
I
I+
Summary of op-amp behavior
Vout = A(V+ - V)
Vout/A = V+ - V
Let A infinity
then,
V+ - V 0
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
To analyze an op-amp circuit
•Write node equations at + and - terminals (I+ = I = 0)
•Set V+ = V
•Solve for Vout
Inverting configuration
Very popular circuit
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/ Vi = -R2/R1
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 weighted summer
Vo = - Rf(V1 / R1 + V2 / R2 + V3 / R3)
To analyze an op-amp circuit
•Write node equations at + and - terminals (I+ = I = 0)
•Set V+ = V
•Solve for Vout
IntegratorI1 = (Vi - V)/R1
I2 =
set I1 = I2,
(Vi - V)/R1 =
but V- = V+ = 0
Vi/R1 =
Solve for VoOutput is the integral of input signal. CR1 is the time constant
I1
I2
dt
VVdC o
dt
VVdC o
dt
dVC o
dtvCR
v io1
1
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
I
Vo = Vi(1+R2/R1)
Buffer amplifier
Vi = V+ = V = Vo
Isolates input from output
Vo = Vi
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
Difference amplifier
Use superposition,
• set V1 = 0, solve for Vo
• (noninverting amp)
• set V2 = 0, solve for Vo
• (inverting amp)
V02 = (1 + R2/R1) [R4/(R3+R4)] V2V2 R4/(R3+R4)
Difference amplifier
V01 = -(R2/R1)V1
Difference amplifier
Add the two results
• V0 = V01 + V02
If R1 = R2 = R3 = R4
1
21
43
4
1
22 1
R
RV
RR
R
R
RVVo
1212 12
111 VVVVVo
Design of difference amplifiersFor 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)] = 3Set R3 = 0