# Problem Set 3 Due Friday (5pm), February 24, 2012

```University of California, Berkeley
EE 42/100
Spring 2012
Problem Set 3
Due Friday (5pm), February 24, 2012
1. Solve for the power delivered to the 8-Ω resistance and for the node voltages in the
following circuit.
8Ω
v2
+
v1
5i x
10 Ω
5A
20 Ω
3A
ix
2. Set up a matrix of equations in the form Ax = b using nodal analysis. The vector is
of the form x = (v1 v2 &middot; &middot; &middot;)T (use the node numbers given in the schematic).
is
r2
7
r4
1
r3
+
+
Vs
−
r8
3
+
Vx
−
r5
2
i1
r1
r7
r6
4
r9
5i 1
+
6
10Vx
5
3. Find the Thévenin and Norton equivalents for the following circuit.
5Ω
Ix
V1
+
19 V
10 Ω
20 Ω
V2
4Ω
2Ω
V3
2I x
8Ω
a
+
Voc
−
b
4. Use superposition to find the Thévenin and Norton equivalents for the following
circuit. You may find the Norton/Thévening resistance by zeroing sources.
10Ω
20Ω
7A
30Ω
10 V +
40Ω
5A
5V
+
50Ω
5. For the following circuit, choose the value of RL such that the power dissipated is
maximized.
2 kΩ
4 kΩ
2 mA
RL
6 kΩ
8 kΩ
6. Assuming an ideal op amp, develop an expression for the current gain Gi =
is
Rs
iL
.
iS
R1
RL
iL
7. Assuming an ideal op amp, develop an expression for the voltage gain Gv =
2
vo
.
vS
vo
+
RL
vS
8. If vin (t) = 5 + 3 cos(1000t), determine the value of R2 such that the DC component of
the output voltage vo (t) is 0. What is the resulting output voltage?
R2
10 kΩ
+
+
vo(t)
−
vin (t)
+
1V
9. (a) For the following schematic, determine a constraint on R1 , R2 , R3 and R4 such
that the circuit behaves as a difference amplifier, i.e. vo = K(v2 − v1 ). (b) Suppose
that the resistors values chosen for part (a) are real resistors with 1% precision.
What is the common-mode gain? In other words, if the inputs contain a
common-mode signal
v1 = Vc + vd /2
v2 = Vc − vd /2
how much of Vc appears at the output?
R1
R2
R3
v1
v2
3
R4
vo
```