fa2004_exam1soln

fa2004_exam1soln - l / * ‘- Fall 2004 ECE 210/211 Analog...

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Unformatted text preview: l / * ‘- Fall 2004 ECE 210/211 Analog Signal Processing University of Illinois Basar, Hasegawa-Johnson, Mitofsky t Exam 1 Thursday, September 30, 2004 —— 7:00-8:15 PM rk if necessary. All answers should include work. Backs of pages may be used for scratch wo units wherever appropriate. I Good luck! Probleml ProblemZ Problem 3 Problem4 Problem 1 (8 points each) a) Place dots in the complex plane corresponding to the following complex numbers. 1. 2e]? J Im Im / Ar/xz‘dfio 19 l’Vq’ (VT’fl'E’v /\' '4 ('1, 1V sréfir’HD‘ 0.59 ( 3 )V1+( ’l )V2=( l' ) (/1 >v1+< Ll>v2=( \ > _ c) Write, but do not solve, two loop equations’that could be solved in order to find numerical values for the currents i1 and i2. 2 ;I , 3+4). +3(;,‘.1>t7=0 “3:. +‘4iy/7t3(L"-):O m, ’3 '1'” ’“l '"(0" P7;1-; 7 3 V 3i1 (H )il+(-3 )iz=(w" > (cwil+(7 )i2=(7 ) Problem 2 (25 points) a) In the circuit shown, find the node voltage v1 and the current i1. , 5r, maize ’r (I " 4 ‘* ‘ ‘ "1 i‘i‘n’ «mine and {$131 fit} ' »; .LI/‘MV’a-VZ)” “‘0 r, 20,131; Hog: /\r “Fag-Pic) Z ‘5 7 O /"' -\' )ro ’V: :0 V: l v: = ‘i no :‘6 ,V/ +HW—VWZO ‘ 9 L V’» 5“— P : K7: (10,8) ‘3’ 25" R "f 2 H x ’ L P29: W ’?V? p ,v‘,(/0*83,'i y '4 xv: Hwy/:20 55» 7x" ’ 5 3 Pm=—s—_/ W Problem 3 (26 points) a) Find the Thevenin equivalent circuit to the left of a and b. b) The inductor shown below carries a current i(t) of 3 A at t = 0. Determine and plot i(t) versus t for t > 0 if the inductor voltage v(t) for t > 0 is shown. v(t) L=2H —) i(t) _!Y\N'\_ + «0' £0 153/? a” 7’ O rot +3 t/sec ifiii’o ’ ((r) 4-} I<L<L 15bq9W+i03 '1— ’ .- LE’WfH Problem 4 (25 points) The switch is open t < O; at the time t = 0 the switch is closed and remains closed thereafter. T13: , I 2 \C H 2— ‘4 = capacitor is initially uncharged. q ’1'; + ,’\C* Efifio V; ‘1 " ‘4 ‘ ' v: + X :0 a) What is i(O‘)? Show your work. , v’ , V1,) : - __ q ‘L aw — r “7f” 'f V: ' .ii‘ "L b b) What is i(O“)? Show your work. gawk/h ddsas at 670+ Ll,V-; 7 + 7/ . f 1’. W \l’o/hje O'CGJS‘J Cé‘flacrb( '1 V’V, V, 60,-“ cheay, :AsW bf/ VT’ZC’ fl: 0/”"'1." if \ r at “0’ W MW“; e, ; 5v: 3cm ;,§ “‘6 (Jacket-Ya) 5° at {’50 1”, 55 ) 7’ r70 0 \ c) What is i(oo)= lim i(t)? A -®H r v '0de t—->o° /" A ’ e70 Carib/war) «55¢» flaw; + i; ‘_ dyad, '1 ll n’LQ’VzV‘p’Naso 1’ a; if": 3"— K/VZWLN‘Vw 32°70 V_ 6 r ab (“ind/O U" ‘3 5 C :9? u E~® G ’ ._ -‘f K: s We, . mew»:ch Law: M; a» b"? _ m(1,5+23k*'l-l~’°&10 d) What is the time constant tau (1:) for the systeIHt > 0? q '06 To l‘ a, v a ’f I, /“ I ‘10 6 ' V; JC “4!; I II ' ’50 , . h"; A e I 5 Ih+\f ‘ (I trib / , .: amok” 1 2 e) Express i(t) fort>0. u (o); g) ...
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fa2004_exam1soln - l / * ‘- Fall 2004 ECE 210/211 Analog...

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