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T3 (S)

The document provides solutions for various op amp circuit problems, including finding voltage gains and currents using KCL and ideal op amp assumptions. It covers multiple circuits and calculations, detailing the steps to derive values such as vo, io, and Ceq. Additionally, it addresses energy equivalence in capacitors and inductors under DC conditions.

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14 views9 pages

T3 (S)

The document provides solutions for various op amp circuit problems, including finding voltage gains and currents using KCL and ideal op amp assumptions. It covers multiple circuits and calculations, detailing the steps to derive values such as vo, io, and Ceq. Additionally, it addresses energy equivalence in capacitors and inductors under DC conditions.

Uploaded by

sum
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1. For the op amp circuit in Fig.

1, find the voltage


gain vo / vs
 Solution 1:
 Apply KCL at node 1
vs − v1 v1 − v2 v1 − vo
= +
R1 R2 Rf
 for ideal op amp
v1 = v2 = 0

 The voltage gain is


vo Rf
=−
vs R1
1
1. For the op amp circuit in Fig. 1, find the voltage
gain vo / vs
 Solution 2:
 For ideal op amp
v1 = v2 = 0
 R2 is an open circuit
v1 = v2 = 0
 This is an inverting
 Therefore, the voltage
 gain is

vo Rf
=−
vs R1 2
2. Determine io in the circuit of Fig. 2 .
 This is an inverting
 Apply KCL at node a
1 − va va − v2 va − v1
= +
2 4 4
 for ideal op amp
v1 = v2 = 0  va = 0.5V
 Using the inverting expression
10
vo = − va = −1.25V
4
 Therefore, the current
vo − 0 vo − 0
io = + = −0.375mA
10 5 3
3. For the op amp circuit in Fig. 3, determine the value
of v2 in order to make vo = -16.5V

 Recognize that this is a


summer with three inputs

 Using the summer expression


 50 50 50 
vo = −  × 2 + × v2 + × (−1) 
 10 20 50 

 Hence,
vo = 3V

4
4. Determine vo in the op amp circuit of Fig. 4 (I)
 Notice it is cascaded
op amp circuits

 B is a voltage follower

 According to the
superposition principle,
consider A, B and C separately

5
4. Determine vo in the op amp circuit of Fig. 4 (II)
 For A, ideal op amp
i1 = i2 = 0  v1 = v2 = 0
 Apply KCL at node 1
2 2
i3 = i4 = mA  V7 = 0 − × 20 = −8V
5 5
 For B, recognize that this is a
voltage follower
V3 = 3V
 For ideal op amp
i5 = i6 = 0  v3 = v4 = v5 = 3V 6
4. Determine vo in the op amp circuit of Fig. 4 (III)
 For ideal op amp
v3 = v4 = v5 = 3V
a
 Apply KCL at node a
v5 − 0 v6 − v5
=  v6 = 8V
30 50
 C, for ideal op amp
v8 = v9 = 0 v6 = 8V v7 = −8V

 Apply KCL at node b


vo − 0 v6 − 0 0 − v7
+ =
100 80 40
 v0 = 10V 7
4. Determine Ceq for each circuit in Fig. 4
 Capacitors in A and B are parallel
C A = CB = 2C

 CA and CB are series capacitors

2C × 2C
 CA = =C
2C + 2C

8
5. Calculate the value of R that will make energy
stored in the capacitor and inductor the same
 Under dc condition
Inductor-short circuit
Capacitor-open circuit
 Thus,
2
i1 = 5 V1 = i1 R
R+2
 Then
1 2 1 2
wc = Cv1 = wl = Li1 V1
2 2
 R = 5Ω i1

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