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11Spring_Exam2soln - ECE 210/211 Analog Signal Processing...

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Unformatted text preview: ECE 210/211 Analog Signal Processing Spring 2011 University of Illinois Basar, Eden, Schutt-Aine, Trick Exam 2 Thursday, March 17,2011 - 7:00-8:15 PM Section: (circle one) Class: (circle one) ECE210 ECE 211 Please clearly PRINT your name TN CAPITAL LETTERS and circle your section in the boxes above. This is a closed book and closed notes exam. Calculators are not allowed. Please show all your work. Backs of pages may be used for scratch work if necessary. All answers should include units wherever appropriate. Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points) Problem 4 (25 points) Total (100 points) Problem 1 (25 points) (a) 39 ‘ J. : 3H+ Wfko “M deTd‘wc O/ Cosmt Y“) r ' 3F M.w:fi:th~éZ/S What is the frequency co ofthe input current that will cause y(t) to be zero? Yaw/é- (b) Compute the phasors F of the following signals. [at _ .1 4/; 0 f1(t)=0055t+sin5t -. FI— __5——4.—__ /”J‘ 2 «l 1 1-1/6"” 4 (C) i) What impedance ZL will absorb the maximum average power in the circuit shown above? \ ' ... .\ Z = .— 2; " / ' J _ L _—L)_—/ ii) What is the maximum average power P absorbed by ZL. 0 _._le£.‘2 ,LV‘I :/ = ‘5— W [AVCyL— 1 72:62:4'2 }'}2//Q(ZL) gigw P J“— (d) An LTl system has frequency response H(co) as follows: |H(<o)| £0» 0 I flew, We)! = a #(é—Jiw . . 1 . 5 D . 49 6016??? +50?) lfthe1nputf(t)1s 3 +10 Cos 3 t+ 7 Sin —3— t+ 30 , the output y(t) 1s 3 Problem 2 (25 points) The circuit shown below illustrates a radio-frequency (RF) transmitter driving a transmission line and an antenna. The source v0 is a steady state sinusoidal source operating at a frequency (1) = 106 s'l . At the end ofthe transmission is a variable capacitor at the base of an antenna represented by a resistor R = 100 Q in parallel with a 1 pH inductor. Tuning capacitor 1 pH \T—V—/b\—V—_/ \——\/_/ TRANSMITTER TRANSMITTER ANTENNA LINE (3) Find the total impedance Z ofthe circuit between a-b, in terms of C. 2: 4’ + g/ovszl Z‘wL: «Ma flyo!‘ x0001?) 4“” we r WL c: xmfid‘ 000‘!) V “g 4‘ -— D . 10’0 . 2‘: 4/ 1'./0fi “FT, , ‘( “E Q afhfi /9 + /+o ‘ ( /0 __ /2 (. + 2: 75m 4 “3“ ¢ (b) The capacitor C is to be tuned until the current i is in phase with the voltage source v0(t) : vO Cos (0t. Calculate the value of C. 4/ /0 mm JWLXZIZO/ 4’0 /0 1’5, /0‘7+/ —é ‘ </ c" : /0 </: H) : Aflaa/a/l: W C= /.' want/F Problem 3 (25 points) (a) For the following circuit, find the frequency response function H(co) = Simplify your answer. ' a , at E6 W Ye: “ 2” 19 W Q2 +3); L3 TLic »,_ a. y(t) W Va = 3L I c " f(t) 2F . 0 .fl/ ¢®)+RL .g 18/4— (1.32 a ‘. ‘. —-£0 —;:y-:fltj>____4::é._~ T «MW = «A 7. r ‘ )Z \ l __ 2 + ‘ ' " 8 + (1“ Jam { /+J.wL UL¢+I Jan: (1)) A linear system with input f(t) and output y(t) is described by the frequency response X = (w) = J0), .Determine the following: F 5 + Jco (i) Amplitude of y(t) when f(t) = x/E sin(5t+ (fl: IHQQlJfl : 53 adj? .:[ I 1.5:}, /+J Amplitude = L (ii) Output y(t) when input is f(t) = 7 + 5 cos (5t)V. #5: 0‘51 IL?“ :J-flé‘” Problem 4 (25 points) In the exponential form the fourier coefficients for l —l the given pulse are F0 =—, F| 2i, F2 :0, IQ =——, 2 7r 37r (a) (10pts) For the given square wave express the fourier coefficients G” in terms ofthe F coefficients above. Also, compute a” and b" for n : 0, l, 2, and 3. “L60 :AFo-l =0 (“WA . .Z G _ FdanA/_l&€d“ {5% 2n” .4 ‘ - fl EJM/ZI”:I§ f2): ( :“q :r /‘ bl Fll’z c)/ 3 377’ (b) (15 pts) Repeat part (a) for the given triangular Wave. Compute X0 and express X” in terms of F" forn =i l, i 2, also compute an and b” forn=0, 1, 2, and 3. ...
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