examII_s98 - EE 350 EXAM II 19 MAR 1998 Name Soiu‘ili on...

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Unformatted text preview: EE 350 EXAM II 19 MAR 1998 Name: Soiu‘ili on; ID#: Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO Test Form A This test consists of four problems. Answer each problem on the exam itself; if you use additional paper, repeat the identifying information above, and staple it to the rest of your exam when you hand it in. (.2 Problem 1: (25 points) 1. (9 points) A LTI system with input f(t) and output y(t) is described by the ODE 1340+ 3W) + 2W) = f + 31'“)- Find the frequency response function Hm) = where 17 and 13' are the phasor representations of y(t) and f(t) respectively. (94- 594-21; = -F+3-F 9w32V+39w3ir+ 2 i? =- New? + 39» +23 = P {WVHJ If. F ((flwjlg 1" 316V 2. (14 points) Now consider another LTI system described by the frequency response function 10731.9 Hm) : (1w +100)(Jw +1000)‘ Construct the Bode magnitude and phase plots using the semilog grids provided in Figure 1. In order to receive credit: 0 In both your magnitude and phase plots, indicate each term separately using dashed lines. 0 Indicate the slope of the straight—line segments and corner frequencies of the final magnitude and phase plots. 0 Do not show the 3 dB corrections in the magnitude plot. a DO NOT COPY THE DISPLAY FROM YOUR CALCULATOR !! no" __€1_vy_____..___ ‘____.__—-l “(don =- [01:03 (dwlloo + L) [dug/[99° 1- 1) ll '00 W I (dew/(00 +l)(iW/l°°° +0 C Phase deg 45 | 4:: 01 1o2 103 Frequency (rad/sec) Figure l: Problem 2: (25 points) 1. (6 points) Write the current-voltage phasor relationships for each of the circuit elements shown below. Use I and V for the current and voltage, respectively. Indicate the current direction and voltage polarity in the diagram below. A» M N + I I +11: M 1<1+ Figure 3: (a) (3 points) What is the DC gain '1’ (b) (3 points) What is the high frequency gain (in dB) '? (c) (3 points) Classify the filter type (for example, lowpass, bandpass, etc.). (d) (10 points) Find the frequency response function H(Jw) = 17/13 in terms of R1, R2, and C. Express your ansWer in a form that is suitable for constructing a Bode magnitude and phase plot (DO NOT SKETCH THE BODE PLOT). (“-3 94: DC ’5th Col-P cu l‘g-Cvr‘ i5 GM <7an C "NW4: (Z! 2 00% QA‘Q .53 DC. adufl - ail-T. “i=0 at, Problem 3: (25 points) 1. (10 points) Find the impulse response function h(t) of the system described by the ODE 9+4y(t) =f(t). __LH: & set at) -_- was) «mil. 15ml. gm = 5b, l-s) ed}, 1+.) 1 ce. + . - —-- J—- a 7:0 0. 5.:Ln‘5‘c105 E» + ‘15-‘- I a? 4i =47? J choose. C— ‘1 I a“? . ‘H: .— -\1t 39.), Iflhéwwm. ktt)=%é= e. no +Jqll-e )5“) -m :0 2. (10 points) The output ofa system (different from the one in part 1) when the input is fl!) = 4u(t) is y(t) = 643"]:1105). Determine the impulse response h(t) of this system. --t {‘69 :- u.(t) —% ace): Egge'uLt/LI-E) :. [6-2 AZMJTU bet): (if; = -32e't/?-u.ce) + lee-t/Z—5'('tl “a = - 322"E/(5;,+ 165051 3. (5 points) The block diagram below is composed of three LTI systems whose impulse response functions are h1(t), [12(1), and h3(t). This system can also be represented by a single impulse response function hltl W) = f“) * Mt)- Express h(t} in terms of hl(t), hg(t), and MO). f(t) Figure 4: Owe : 16st: + l:* “WM : 5k ‘l" “(Elkl‘laefifl 8 10 Problem 4: (25 points) A LTI system with input f(t) and output y(t) is described by the impulse response function h(t) :u(t+ 1) —u(t— 1). 2 points) Sketch Mt). 3 points) Is the signal h(t) causal or noncausal ? In order to receive partial credit, justify your answer. 1 ( 2 ( 3. (5 points) Is the LTI system BIBO stable '? Justify your answer. 4 ( 12 points) The input f0) = W) - u(t - 1) is applied to the system. Find and neatly sketch the zero-state response y(t) using the convolution method. 5. (3 points) Is the system described by 110‘.) causal or noncausal ? In order to receive partial credit, justify your answer. l bet) 2. TR?- SFanaQ hf-h) is nonCcLuSuQ . ' becwse, 5H7) #0 Fur—Kt <0- e "l H as The 5 Ls [5/30 3. Littmhflt :2 Lcu 2 2_ 4 0O =9 [a ‘4 Wt) Eli l a": m (-1) 4= s h 04:.) r hf-b—t) 12 13 ...
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