11Spring_Exam2 - ECE 210/211 Analog Signal Processing...

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Unformatted text preview: ECE 210/211 Analog Signal Processing Spring 2011 Basar, Eden, Schutt-Aine, Trick University of Illinois Exam 2 Thursday, March 17, 201 1 - 7:00-8:15 PM 1 Name: A . Seem” 9 AM 10 AM 1 PM 2 PM (Clrcle one) r . Class: ECE 210 ECE 211 (Circle one) L 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) (21) 39 + 3H Coscot y(t) 3F What is the frequency co of the input current that will cause y(t) to be zero? (0 : (b) Compute the phasors F of the following signals. _ . F = f[(t) — cos 5t + s1n 5t 1 F2 = (C) i) What impedance ZL will absorb the maximum average power in the circuit shown above? Z: L ii) What is the maximum average power P absorbed by ZL. (d) An LTl system has frequency response H(co) as follows: |H(<o)| Ifthe input f(t) is 3 + 10 Cos % t+ 7 Sin(§ t+ 30°], the output y(t) is 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 (0 = 106 s'1 . At the end of the 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 V0“) 0 1 pH \—V——/b\—V—/ \—\/——/ TRANSMITTER TRANSMITTER ANTENNA LINE (a) Find the total impedance Z 0fthe circuit between a-b, in terms of C. Z: (b) The capacitor C is to be tuned until the current i is in phase with the voltage source v0(t) = v0 Cos wt. Calculate the value of C. Problem 3 (25 points) (a) For the following circuit, find the frequency response function H((o) = Simplify your answer. IQ 1 Q y(t) f(t) 0 2F 4H HUD) = (b) A linear system with input f(t) and output y(t) is described by the frequency response Y ' . . — = ((0) = J0) .Determme the followmg: F 5+jw (i) Amplitude of y(t) when f(t) = J? sin(5t+ Amplitude = (ii) Output y(t) when input is f(t) = 7 + 5 cos (5t)V. Problem 4 (25 points) f(t) In the exponential form the fourier coefficients for l the given pulse are F0 =1, F, =—l—, F, =0, F3 =——l, 2 7r ” 37! (a) (10 pts) For the given square wave express the fourier coefficients G" in terms of the F" coefficients above. Also, compute an and b” for n = 0, l, 2, and 3. (b) (15pm) Repeat part (a) for the given triangular Wave. Compute X0 and express X, in terms I of F” fornzi l, i 2, also compute an and b” for n = 0, l, 2, and 3. f(r). period T = 1’1 MCoefficients ll)” 00 '11“) I Zn=—oo File] 0 F,, = % fr f(r)e‘j"'”"’a'1 Exponential £29 + 220:, a,, cos(nw(,!) + b" sin(na)0!) Trigonometric bn : _ F—n) Cu = 2iFni 0n 2 1F" Compact for real f(!) 52° + Z°° c” cos(nw,,! + 9,.) Ii=l “5'9 5-1 Summary of different representations of periodic signal [(1) having period T = and funda- ( Mma‘ fre<Juency a)". The formula for F,, in the upper right corner will be derived in Section 6.2. Condition: Constant K f(1)<—> F,,,g(1) <-—> Gm... Scaling Kf(() 6 KB, Addition f(,) + gm + H 1:" + G" + 1 Time shift Delay 10 f(, _ ,0) H Fne—jnwnn, Derivative Continuous f(!) $4 H jnwan Hermitian Real f(t) f(—I) = f(!) ft—I) = —f(t) F—n=F‘ I1 'Even function f(!) = 329 + 22:1 an cos(na)(,!) f(1) 2 22:1 b" sin(na),,!) P E % IT mmzdr = $21.00 tFnP J Odd function 'Average power Table 6.3 Properties of Fourier series. ...
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This note was uploaded on 04/04/2012 for the course ECE 210 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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11Spring_Exam2 - ECE 210/211 Analog Signal Processing...

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