final_s99

final_s99 - FINAL EXAM EE 350 7 May 1999 Name(Print ID...

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Unformatted text preview: FINAL EXAM EE 350 7 May 1999' Name (Print): ID#: Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO EXAM FORM A Instructions: 1. You have 2 hours (120 minutes total) to complete this exam. 2. This test consists of six problems. The exam score is calculated by adding the five largest problem scores. 3. This is a closed book exam. However, as told earlier, you are allowed 2 sheets of 8V2” x 11” paper for notes, formulas, etc... 4. Solve each part only in the space following each question. Be sure to place your answers in the boxes (as appropriate) provided. If you need more space, continue on the reverse side and write the question number; for example, Question 4.2) continued..; NO credit will be given to a solution that does not meet this requirement. 5. 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) Question 1.1 (10 points) Below are the responses, y:(t) and y2(t), of the same system to two different inputs, f. (t) and f2(t). Based only upon the infonnation presented, determine if the system is (circle your answer) a) Linear YES NO 1)) Time Invariant YES N0 0) Causal YES NO I d) Instantaneous YES NO 6) Stable YES NO Response of the system to fit) = um. Response of the system to f(t) = u(t—5). Outputs in volts. 9 7‘ c in - or Response of the system to f(t) -= 2u(t) - 2u(t-5). 0 1 2 3 4 5 6 7 8 9 10 Time in seconds. Figure l - Some responses of a system. Question 1.2 (10 points) Determine if f(t) is an energy signal, power signal, or neither. 1 If it is an energy or power signal, compute its measure. f (t) = 3e%'u(- t)-— 3e_J’~'u(t) Problem 2: (10 points) With respect to the circuit in Figure 2, the input is the voltage f(t) and the output is the voltage, y(t). 100 Figure 2 - Circuit for Problem 2, all parts. The ordinary differential equation system model which relates the input f(t) to the output y(t) was found to be flaw) = 0.81 d: dt i Question 2.1 (5 points) Find the transfer function, \ 1"(s) H(s) = NS). Place your answer in the box provided. H(s) = Question 2.2 (5 points) Find the zeroes, poles, characteristic roots, natural frequencies, and corner frequencies of the system given in Figure 2. Be sure to include appropriate units where applicable. Place your answers in the appropriate boxes below. Characteristic Roots = Natural Frequencies = Corner Frequencies 2 Question 2.3 (5 points) Using Laplace transform analysis, find the zero-state response, y,,,(t) when f(t) = 20e'2‘u(t). Place your answer in the box provided. mt) = Question 2.4 (5 points) Using Laplace transform analysis, find the zero-input response, yzi(t), when the initial current through the inductor, iL(0’), is 3 A. Place your answer in the box provided. Problem 3: (20 points) Consider the feedback control system shown in Figure 3. R(s) Y8) Figure 3 — The system for Problem 3. Question 3.1 (10 points) Assume that Gc(s)=10 4 Gp(s)h 5+4 1 R(s) Find the wansfer function R( ) . Express your answer as the ratio of two S polynomials in s. Place your answer in the box provided. £9). _ R(s) _ Question 3.2 (10 points) Now consider the new set of transfer functions: 06(5) = K GAS) = H(S) =1 5 5+5. Determine the value of K that gives the closed loop system a rise time that is half that of the plant, Gp(s). Place your answer in the box provided. Problem 4: (20 points) Question 4.1 (20 points) Using the semilog graphs on the following page, for ja) How) rah—KO if: 191 103 +1)(105 +1) sketch the Bode magnitude plot on the upper graph and the Bode phase plot on the lower graph. For each sketch, apply the following rules: I DO NOT simply regurgitate what your calculator displays. Bode plots are straight-line approximations. Using curved lines will result in 0 points for Problem 4. Each sub-factor must be shown with a dashed line and clearly identified. The total Bode plot must be a solid line with the slopes of the straight—line segments clearly labeled. Correction factors do not need to be used. Be sure to label the vertical and horizontal axes of each sketch appropriately. The semilog graphs on page 11 are for your scratch work and will not be graded. 10 THIS PAGE IS FOR SCRATCH WORK AND WILL NOT BE GRADED. 1 1 Problem 5: (20 points) Consider the amplitude modulation system shown in Figure 4. The spectrum of the input signal f(t), F00), is shown in Figure 5. 2005(200t + 90°) Figure 4 — Amplitude modulation system. F(co) Figure 5 — Spectrum of the input signal. Question 5.1 (8 points) In the space below, sketch the spectrum of z(t). 12 Consider the system shown in Figure 6 where H003) describes a 2nd order system. Here, the input, f(t), and the output, y(t), are voltages. f(t) Ham) Y(t) Figure 6 Use the magnitude response and phase response functions of H603) shown on the next page to answer the following questions. Question 5.2 (4 points) Find the system’s DC. gain in terms of Voltage/Voltage. Place your answer in the box provided. D.C. Gain (V/V) = Question 5.3 (4 points) What type of responsc will the system exhibit to a unit step input? Briefly explain your reasoning. Question 5.4 (4 points) Find the sinusoidal steady-state response, y(t), when the input is fit) = 255in(1000t — 25 a). Place your answer in the box provided. ya) = I3 -150 -200 Magnitude Response Phase Response Problem 6: (20 points) Question 6.1 (10 points) Consider the system shown in Figure 7. f(t) 1f(t) 5T0) Figure 7 - The system for Question 6.1 Assume that Mt) is given by 5T(t) : fish —{).Oln). nah-OD Determine the maximum bandwidth (in Hz) of the signal, fit), that will allow perfect recovery ofthe signal from its samples. Place your answer in the box provided. Maximum Bandwidth (Hz) of f(t) = 15 rm, Question 6.2 (10 points) Consider the system shown in Figure 8. Figure 8 - The system for Question 6.2. w A Assume that T = 1 second. If fit) = Z sin[—§—n]§(t — n), sketch the output, f(t) . fl'—'-fl) 16 ...
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final_s99 - FINAL EXAM EE 350 7 May 1999 Name(Print ID...

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