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sp2002_exam1soln

# sp2002_exam1soln - ECE 210/211 Analog Signal Processing...

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Unformatted text preview: ECE 210/211 Analog Signal Processing Spring 2002 University of Illinois Hiskens, Kudeki, Ma Exam 1 Thursday, February 14 —- 7:00-55: 15 PM Name: S 01 Q Ho A Section: 8 AM 9 AM 1 PM (circle one) Please clearly print your name and circle your section in the boxes above. This is a-closed book and closed notes exam. Calculators are not allowed. Please show all of your work. Backs of pages may be used for scratch work if necessary. Good luck! [Problem 1 (25) ‘ Problem 2 {25) Problem 3 (25) Problem 4 {25) I Total Score (100) la. (8 points) . m 1 (“0‘ a+jb‘ Determine |C| and AC in terms of a and b. t 1 - L. ‘ -“ ff 3 mﬁada) " (ii) (1 + 3'2) X (3 — j4) = ‘? Give the answer in rectangular form. =3«\$4+5é+? 5‘ “+3.2. : ? Give the answer in polar form. ... 1111461 (111) .83 1112.492 x m3 eJ = wife—~— {A {9” as) M W‘ l 3 (iv) = ? Give the answer in polar form. 3 «so ' J 3 J‘- a 1" 1 0 =5 3 (1510.)é a All = Algae| [A150 ‘ 23\$. “ 3.25: i I J? = (elm)? ‘ at 3 h Ilb. (8points) Given that + ,1 1V, 1:in :: {kgfzx ix 1V — :> aim-14v determine V3] in the following op-amp circuit: \15 J? 1c. (9 points) Given that dy _ —2t 3? + 5y(t) — 36 and y(0+) = 3; determine y(t), t > o. 23. (I2 pomrs) 0.5 82 2A Determine the Thevenin equivalent seen from terminals A-B. + ARIN-[er CUf‘V Ln in HAM}, =5 UA3.\/+Lrlul t2, UOH R“. = (“saw 2:: ‘ 33- ﬂ. 5:— A 2. I3 182 2b. (13 points) Write the nodal equations describing the voltages V1, V2, V3 in the following circuit. Do not solve. VI. I E1 + 'L\ + "L5 “L O V" VII—“J; _ I —"'"' ‘30 a '5. ‘ + R‘ 4 V‘ -\J‘ V .— 3 V3 1’ ’ R ‘ * A ‘ o 3 A. Nix—V" 3. xv: Alﬁrhﬂ+:4c V' \J' -V V| I 1. 'EE’ * :——-—"—"3“' ‘I C) Vrvx 1:" '* s a. Rx \J ..\I \J‘ \f‘ 3 - is *' L; .t ,1 IO a‘ a“ 3. f 25 points) 33”H —w,<» m r 0 V0 2 I" *1” 0 Vs“) d. (a) In the circuit above find a pair of expressions for ix(t) and é’i that depend on v50) and v00). 4g .= QﬁﬂVw—ﬁ) e3) Mg; _e_ .. ’K/l— Mazaah ,5 ' yum 0 ) dt j) 3%? :3 a? (b) Using the expressions from part (3) determine v0(t) if vs(t) = 1 cos(t) V. Veto : cc» (4c) 3) Mfr): 2% :(2)(»\$n'n(t)) 1* 99-1160 :) MDCt)\$ﬁ3 F :2: '5, ,_ r“ I 42% sari-(e (tagger (c) In the systems description of the circuit above, what is y(t) in terms of f(t) for an arbitrary {(t)? (HINT: Determine the differential equation relating input and output.) fm=wm ymzmm=? system If (f) 49w“ “it”: wafer—Bahkwga-‘ga from ////L”/ 7t 2?? 4161 J] "5 we) . =.— d2 " Wt) €769 _ f 4. (25 points) t=0860 t=23ec The circuit above is in the DC state until t = 0 sec when switch 81 is opened". At t: 2 sec, 82 is closed. ' (3) Find v(t), t < 0. “1 um um: (9V ' (:0: W (b) Find V(t), 0 < t < 2 sec. my UP). %TVL#):O ‘ v31“ 95—:0 7 gut-“l1 in} UH”): A-e, 3' um): 3V =9?ﬁ3 8 (c) Determine v(2). A1 _ V621): 36,1 1 33* ((1) Determine v(oo). «m m. an (e) Determine the RC—time constant for t > 2 see. (Laﬁtte/NIL: m 5A .A v 1 QC“"§ 12:: iv: ’3. "U‘E ...
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