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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 — 7:0055: 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 aclosed 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 
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3 mﬁada) " (ii) (1 + 3'2) X (3 — j4) = ‘? Give the answer in rectangular form. =3«$4+5é+? 5‘ “+3.2. : ? Give the answer in polar form. ... 1111461
(111) .83 1112.492 x m3 eJ = wife—~— {A {9” as)
M W‘ l 3 (iv) = ? Give the answer in polar form.
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1 0 =5 3 (1510.)é a All =
Algae [A150 ‘ 23$.
“ 3.25: i I J? = (elm)? ‘ at 3 h Ilb. (8points) Given that + ,1 1V, 1:in :: {kgfzx
ix 1V
— :> aim14v determine V3] in the following opamp 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 AB. + 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
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r 0 V0
2 I"
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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)(»$n'n(t)) 1* 991160 :) MDCt)$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”): Ae, 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
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QC“"§ 12:: iv:
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This note was uploaded on 08/08/2009 for the course ECE 210 taught by Professor Whoever during the Fall '07 term at University of Illinois at Urbana–Champaign.
 Fall '07
 whoever
 Signal Processing

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