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Unformatted text preview: FINAL EXAMINATION EE 350 Continuous Time Linear Systems
December 15, 1999 Name (Print): ID. number : Section number : Do not turn this page until you are told to do so Problem Weight 1
4 Total Test form A Instrngtions 1. 2. You have 1 hour and 50 min. (110 min. total) to complete this exam. This test consists of six problems. The exam score is calculated by adding the ﬁve highest
problem scores. . This is a. closed book exam. You are allowed two sheets of 8.5” x 11” of paper for notes as mentioned in the syllabus. . Solve each part of the problem in the space following the question. Place your ﬁnal answer in the box when provided. If you need more space, continue your solution on the reverse side
labeling the page with the question number; for example, “Qution 4.2) Continued”. NO
credit will be given to solution that does not meet this requirement. . DO NOT REMOVE ANY PAGES FROM THIS EXAM. Loose papers will not be accepted and a grade of ZERO will be assigned. Problem 1: (20 Points) Consider the periodic signal f (t) in Figure 1. Figure I: The signal f(t) for Problem 1. Question 1.1 (3 Point) Is the signal odd, even or neither? Question 1.2 (7 Points) Determine if f (t) is an energy signal, power signal or neither. If it is an
energy or power signal, compute its measure. Question 1.3 (10 Points) Determine the trigonometric Fourier series of f (t). Problem 2: (20 Points) Question 2.1 (10 Points) Find the diﬂ'erential equation that models the inputoutput relation
of the circuit shown in Figure 2. ﬁt) 0 3'“) Figure 2: The circuit for Problem 2.1. Question 2.2 (10 Points) A LTI system with input f (t) and output y(t) is described by the differential equation i3? + 10y (t) = f(t). Suppose that y(0) = 6 and f (t) = 8e‘2‘u(t). Calculate the natural response yn(t), the force response y¢(t), the zeroinput response yz_{(t), the zerostate respose yzn,(t), and the total respose y(t) for
t Z 0. Problem 3: (20 Points) Question 3.1 (10 Points) Using Laplace transform techniques, ﬁnd the transfer function Y(s) /F(3)
for the circuit shown in Figure 3, where L = 10 H, C = 10‘3 F, and R = 10 0. Express your answer in the form
Y(s) _ k F(s) _ 32+as+b' Figure 3: The circuit for Problem 3.1. is driven by the input f (t) = (4 + 28—4t)u(t). Find the zerostate response y(t) of the system for
t 2 0. Problem 4: (20 Points) Consider the DSBLC amplitude modulation system in Figure 4. Let
the carrier frequency we = 10051 rad/sec, the message m(t) = «~Qsinc(1rt). Figure 4: Diagram of the DSB—LC amplitude modulation. Question 4.1 (6 Points) What is the minimum value of A so that the message m(t) can be
recovered from the signal y(t) by using envelope detector? Question 4.2 (14 Points) Find the expression for the frequency spectrum Y(w) in terms of A
and we and sketch its amplitude spectrum in the graph provided in Figure 5. Y( (0)1 Figure 5: The graph for sketching the amplitude spectrum Y(w). Problem 5: (20 Points) Question 5.1 (12 Points) Consider the feedback system in Figure 6 where 3
(3+4)(s+9)* 13(3) = 0(3) = 23, K = 1/3. Figure 6: Block diagram of a feedback system for Problem 5. Determine the overall transfer function H (a) of the closedloop feedka system. Write your solution
in a. form suitable for Bode sketching, i.e., 39(8/01 + 1)(8/a2 + 1)   ° (slam + 1) He) =K1 (alﬁl+1)(s/ﬁ2+1)“(8/3n+1) ' 10 (continued) 11 Question 5.2 (8 Points) Consider a. transfer function 0(a) of a. certain system. 3
432+6K3+9' Determine the ranges of K such that the response of the system to a unit step input is underdamped,
overdamped, and critically damped. C(s) = 12 Problem 6: (20 Points) Question 6.1 (12 Points) Construct a straight line approximation of the Bode magnitude and
phase of the frequency response function 20 }
H(jw) = —.—. 1
1030 + 1 To receive credit, you must correctly label the axes and indicate all slopes and corner frequencies. Atﬂankgnun1uwpkaﬁngthlnuunﬂudalelponleofHanokxFﬁobbnteJ. Magnitude h 68. 10 1o 10 1D
quuencyhlldhem Alﬂlnksplphiorpknung EarphonereagentscﬂiiUmotanﬂrlﬂemn8.1 PusanInsure“. 10 10 10 10
ﬁlquunyklnﬁhee 13 2. (10 points) A secondorder linear timeinvariant system has a frequency response func
tion with the magnitude and phase plots shown in Figure 4. The input to the system is
f(t) = 10 + cos(2000 t — 45°). Find the steadystate response y(t) of the system. 13 Question 6.2 (8 Points) A system has the frequency response shown in Figure 7. If the signal f (t) = 28 cos (10423 — 30°) is applied to the system, determine the steadystate response of the
system. 14 1139]”; u! Aouanbaa Phase in Degrees Magnitude in dB Figure 7: The frequency reaponse of the system for Problem 6.2. 15 8&888&8$8 ...
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This note was uploaded on 03/17/2008 for the course EE 350 taught by Professor Schiano,jeffreyldas,arnab during the Fall '07 term at Pennsylvania State University, University Park.
 Fall '07
 SCHIANO,JEFFREYLDAS,ARNAB

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