Download Component - Electrical Engineering and Computer Sciences - Exam and more Exams Computer Science in PDF only on Docsity!
University of California, Berkeley Spring 2010 EE 42/100 Prof. A. Niknejad
Midterm Exam (closed book/notes)
Tuesday, February 23, 2010
Guidelines: Closed book. You may use a calculator. Do not unstaple the exam. In order to maximize your score, write clearly and indicate each step of your calculations. We cannot give you partial credit if we do not understand your reasoning. Feel free to use scratch paper.
Electron charge q = 1. 60217646 × 10 −^19 C.
KCL: Kirchhoff’s Current Law states that the net current flow into a node (or super-node or any closed surface) is zero. (^) ∑
Ik = 0
KVL: Kirchhoff’s Voltage Law states that the net voltage drop around any loop is zero. ∑ Vk = 0
Power flow into a component: (positive means power is absorbed or dissipated.
P = I · V
Ohm’s Law: V = I · R
or I = G · V
where G = R−^1. Power dissipated in a resistor: P = I^2 R = V 2 G
Resistors in series add: R = R 1 + R 2 + · · ·
Conductances in parallel add: G = G 1 + G 2 + · · ·
For two resistors in parallel, this implies
R|| =
1 R 1 +^
1 R 2
When a chain of resistors are in series and connected to a voltage source, the voltage across the kth resistor is given by the voltage divider forma
Vk =
Rk R 1 + R 2 + · · ·
When a chain of conductors are in parallel and connected to a current source, the current through the kth conductor is given by the current divider formula
Vk =
Gk G 1 + G 2 + · · ·
Any black box can be modeled using Thevenin or Norton’s Equivalent networks: Voltage source Vth in series with Rth or a current source IN in parallel with RN. You can find the values using open-circuit voltages and short-circuit currents
Vth = Voc
IN = Isc
Rth = RN =
Voc Isc
If there are no sources in the black box, then there is only Rth in the model. You can calculate Rth by calculating the resistance of the black box: Connect a current (or voltage) source and monitor the resulting voltage (or current).
When an ideal op-amp is operated with negative feedback, the following “Golden Rules” apply: V +^ = V − I+^ = I−^ = 0
vs
(c) (4 points) Calculate the voltage at the output driving the load speakers. Each speaker alone has an effective resistance of RL = 9Ω. The amplifier has an open-circuit voltage gain of 40dB (Av = 100) and an input resistance of 10Ω and an output impedance of 3Ω. Assume the source has a voltage of 1V.
R 1
R 2
R 3
R 4
R 5
R 6 R^7
(d) (4 points) Find the equivalent resistance seen by looking into the terminals shown. Do not do any math but simply state the answer using the “||” and “+” operators. Use parenthesis to clarify your answer.
- (17 points) For the following circuit, write nodal equations and put them into standard format, Ax = b. Assume the reference voltage is chosen as shown by the ground symbol.
R 1
R 2
R 3
R 4
I 1
V 1
GxVx + Vx −
- (16 points) Use superposition to find Vx in the following circuit. A = 10, R 1 = 1 kΩ, R 2 = 3 kΩ, and R 3 = 500 Ω.
Vx −
R 1
R 2 AV^1 R 3
V 1
1 A
10 V
- (17 points) Calculate the output voltage vo as a function of v 1 and v 2. (Hint: Partition the circuit into stages.)
R 1
R 2 R^3
R 4
R 5
R 6 R 7
RL
v 1
v 2
vo −
