11Fall_Exam2 - ECE 210/211 Analog Signal Processing Fall...

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Unformatted text preview: ECE 210/211 Analog Signal Processing Fall 2011 University of Illinois Basar, Franke, Peck, Trick Exam 2 Thursday, Oct. 20, 201 l - 7:00-8:15 PM Name: . SW0“: 9 AM 10 AM 1 PM 2 PM (c1rcle one) . C'aSS‘ ECE 210 ECE 211 (Circle one) Please clearly PRINT your name 1N 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 ifnecessary. All answers should include units wherever appropriate. Problem I (25 points) Problem 2 (25 points) Problem 3 (25 points) Problem 4 (25 points) Total (100 points) Problem 1 (a) Find the cosine function f(t) with frequency (1) =10 rad/sec corresponding the following phasors. (i) F= (1+j)3 f(t)= (ii) F= 9% +e'j%(1+ Ji 5%) f(t): (b) An LT] circuit has the following steady-state response functions: Input f(t) = 2 Cos 2t output y(t) = -4 sin (2t — 45") Input f(t) = Sin (5t - 30") output y(t) = 2 Cos 5t Input f(t) = 5 output y(t) = 2 Find the values ofthe frequency responses in polar form (Lei—1(0)) = |H((o)| 4H(m)) H(0) = H(2) = H(5) : (c) In the following circuit, what impedance ZL will absorb the maximum average power. What is the maximum average power absorbed by ZL. 29 29 ’\/\/\x /\/\/\/ N r H 3Cost 2H ZL max P = 8V Problem 2 (3) Consider the circuit below a + 5 cos t 0 2H V0“) 0 b _ (i) Find the V”, and Zth ofthe circuit (in phasor form) between a and b. Vlh : Zlh = (b) Now, consider the following circuit. i(t) icGt) + 2 cos (0t 0 V0“) 12F _ (i) What is the resonant frequency ofthis circuit? (00 = (ii) What is the current i(t) at this frequency? i(t) = (iii) What is the voltage v0(t) at this frequency? V00) : (iv) Find icsS (t) at a) = :11— rad/sec. Problem 3 (Each parts a—c ofthis problem utilizes different circuits) (a) For the circuit shown, the frequency response function is defined as: V (m) 1H + H(m)= 152(0) is(t) IQ 4o v0(t) (i) Draw the frequency—domain circuit. Determine and correctly label all impedances as well as the voltage and current that define the frequency response function. (ii) Solve for the frequency response function identiﬁed above. H((n) I (iii) Find v0(t) at a) = 0 if is(t) = 2 Cos (0t. V0“): atm=0 (b) In the following circuit, v0(t) = 0 at a) = rad/sec. 19 w + 3H 2 COM v0(t) 3F (c) The magnitude and phase sketches of the frequency response (H((D) = V0(m)M ((0)) of a LTl circuit are provided below. 4H8») )H(m)] 30° 8 to I —— —30° _4 4 ‘9 Write the expression for v0(t) when vi(t) = l0 cos (3t) + 4 cos (6t + 45°) Problem 4 (25 points) m) (a) (2 pts) Find the average 1 value ofthe periodic voltage waveform f(t). _T_7_T_ JAM/8 F0 (b) (4 pts) What is the average power and rms value of f(t)? avg H mlS (c) (2 pts) Given x(t) = 10 f(t), ﬁnd the average power and rms value of x(t). (d) (5 ptS) Given the exponential Fourier coefﬁcients F0 from Part (a) and F]: l F3: 3ﬁn,and 124:0, ﬁndﬂzﬁ, ai and b, for i= 1,2,3 where f(t)= a—Z" + im“ Cos nw0t+ bn sin moot) a_o : n:l 2 3I : a2 : a = (e) (3 pls) What is the average value and the average power ofthe periodic waveform g(t)? (f) (3 pts) Express the periodic waveform g(t) in terms of f(t). g(t) = (g) (6pts) From Part (f) and Part (d) ﬁnd the exponential Fourier coefficients G,, i = I, 2, and 3 for the periodic waveform g(t). Ponder-serials rel. of Hi): _ _ '- {(0. with pgﬁqd r =- Z1; - (‘00 . I‘ -- 4.4 E:='1 an cos(ﬁ§k)ot) +‘bn'siln(nmlot) _' [Cal f(t) _ '- v _ ‘ fName: .' _ ' Condition: _‘ '. Multipliéation- . _ 'ConstantK _ _ ww— mam-Haw , . a . .v m .40) +4. _ z - -.-- t emuan - - AH: . . Even funcfidﬁs" f(t)_= 929:4- 2211 an Cos(nwot)' - — j coefﬁcients .& _2 c '. I I -- : I 7297 211:1 cos(n0)0t + 6n) fi(t)i+g(t),+---I4—§F,;+G‘n+t... HI HE EH ...
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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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11Fall_Exam2 - ECE 210/211 Analog Signal Processing Fall...

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