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202_HW_set2 - page 1 Spring 09 EE202 HOMEWORK PROBLEMS(SET...

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page 1 Spring 09 1 EE202 H OMEWORK P ROBLEMS (S ET 2) S PRING 09 TO THE STUDENT: ALWAYS CHECK THE ERRATA on the web. Quotes for your Parent's Parties: 1. It requires a very unusual mind to undertake the analysis of the obvious. –Alfred North Whitehead. 2. No race can prosper until it learns that there is as much dignity in tilling a field as in writing a poem. –Booker T. Washington 3. No task, rightly done, is truly private. It is part of the world's work. –Woodrow Wilson 4. All stories are true; some actually happened. --Megan McKenna 5. The problem is not solved, but the paper work is complete.– M.F. Chang 6. It is much easier to recognize error than to find truth; for error lies on the surface and may be overcome; but truth lies in the depths … -- Goethe 7. The secret of patience is finding something to do in the meantime. -- Bits and Pieces, November 1982 D UE M ONDAY W EEK 4 (F EB 2) Suggestion: Do what you can by hand, but ALWAYS check in MATLAB, or use MATLAB and then do by hand to practice for Exam I. 13. Consider the circuit below. Suppose L = 1 H, R 1 = 15 Ω , C = 0.01 F, and R 2 = 5 Ω . Suppose v C ( t ) is the desired output. (a) Find the input admittance Y in ( s ) = 1 Ls + R 1 + ?? ?? in terms of literals and then substitue numbers. Combine terms to form a rational function.
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page 2 Spring 09 2 (b) Find the input impedance Z in ( s ) = ?? s 2 + R eq L s + 1 LC in which case V s ( s ) = ???? (write down the formula). (c) Use voltage division to express V C ( s ) in terms of V s ( s ) and then in terms of Z in ( s ) and I s ( s ) . Thus determine the transfer function H ( s ) . The leading coefficient of the denominator polynomial is to be 1. (d) Given the “correct” answer to part, (i) compute the impulse response of the circuit, and (ii) compute the step response of the circuit. (e) Suppose the input is i s ( t ) = 2 e ! 5 t u ( t ) A. Find the partial fraction expansion of V C ( s ) and then compute v C ( t ) assuming zero initial conditions on L and C . PLOT the resulting time function in MATLAB for 0 t 1 s.
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