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University of California, Berkeley EE 42/100 Spring 2012 Prof. A. Niknejad 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 · · ·)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