practice final

# practice final - EE213 Final Closed Book Justify all work...

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Unformatted text preview: EE213 Final May 12, 2008 Closed Book, Justify all work unless otherwise instructed. Good Luck NAME _______________________ Last four digits of SSN _______________ 1) (20) The natural response of a circuit is given by —-1, if: < 2 nat(t) = {— exp(—2(t — 2)), ift Z 2. If possible ﬁnd the step response, the impulse response, and the transfer function. 2) (22) Consider the circuit below. The output is the voltage across the rightmost resistor. a) Given input in(t) = u(t) ﬁnd the zero state response. b) Given initial conditions of 1V across capacitor and no current through inductor ﬁnd zero input response. + W— 0.5H 0.5F In 152 out(t) 3) (24) Consider the circuit below. The output is the voltage across the resistor with value R5. 3.) Write rnatlab code to determine the transfer function H (s) = 0U T(s) / I N (3). Do not solve for the transfer function. b) Write matlab code to ﬁnd the zero state response. c) Determine the value of the transfer function H(s) at very high and very low frequencies from physical arguments. 4) (24) Consider the circuit in problem 3). a) Write the state space equations in standard form. b) Write a matlab script to ﬁnd the zero input response of this circuit assuming initial conditions, v(0)c,«1 = 1V and U(0)02 = 2V. Positive polarity is from left to right and from up to down. 5) (22) a) Show matlab commands for ﬁnding the transfer function of a ﬁlter that has equipripples in the passband and is monotonically attenuating in the stopband with the following speciﬁcations; a maximum 2dB attenuation in passband from _ lKHz to 3KHz and at least 30dB attenuation for frequencies less than 500Hz and greater than 4KHz. List matlab commands for plotting the step response and listing all poles and zeros. b) Discuss how you could implement this ﬁlter using biquads and opamp circuits. c) If the input to the ﬁlter is \$03) = sin(500t) + arr/4) — cos(2000t - 1r/3) + cos(4000t) ﬁnd the output of the ﬁlter y(t). 6 (22) A circuit has the following frequency reSponse. _ jw + 2 HM _ ijw + 1) Find the zero state response if the input is a) \$(t) = 10 cos(47rt). b) Repeat a) when :L'(t) z exp(2t)u(—t). 7) (16) Consider the following step responses labeled in the ﬁgure below; Likelike, Manoa, Nuuanu, and Palolo. Match them up to the pole/ zero plots labeled in the bottom ﬁgure below; Ahi, Moi, Onaga, and Ulua. walla Manon 1.5 ‘l 1 0.! I18 0.5 0.4 0 0.2 -D.5 I) 2 4 e a DD 2 e s I Nuuaru PM 1 I 1.4 1.2 12 1 1 0.3 0.8 0.0 0.6 0 4 04 0.2 02 o D 2 4 a a no 2 4 8 8 Um 0mm -2.s -: -u —l 41.: a u .25 .2 4.5 -1 .05 0 0,5 mm Bum ...
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