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Material Type: Exam; Class: PERF GLOBAL CONTEXT; Subject: Theater; University: University of California - Santa Barbara; Term: Winter 2009;
Typology: Exams
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Department of Electrical & Computer Engineering ECE 2B University of California, Santa Barbara Summer 2009 Shynk H.O. #
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Summer 2009
Assume there is no energy in the following RLC circuit before the switch closes at t = 0. (a) Find an expression for the s-domain current I(s) through the 3 kΩ resistor. (b) Specify the type of second-order circuit and sketch the poles and zeros on the s-plane. (c) Use the initial- and final- value theorems to find the currents iL(0+) and iL(∞) through the inductor. (c) From a partial fraction expansion of I(s), find an expression for i(t) for t ≥ 0.
1 k Ω 3 kΩ
t = 0
1 mA 1.6 μF i(t)
Solution:
Summer 2009
A parallel RLC circuit has the following transfer function:
H(s) =
(L/R)s LCs^2 + (L/R)s + 1
with R = 500 Ω, L = 4/3 H, and C = 1 μF. (a) Find the center frequency ωo and the cutoff frequencies ωc 1 and ωc 2. (b) Specify the filter bandwidth B and the quality Q for this circuit. (c) Find the poles and zeros of the transfer function and sketch a Bode diagram of the frequency response.
Solution: