Wtransfunc

Wtransfunc - ECE 301 Detailed Solutions Set 5 Transfer...

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Unformatted text preview: ECE 301 Detailed Solutions - Set 5: Transfer Functions 1 5-1. A system has impulse response h t = 10 ; 000 e 5000 t u t , an input x t , and output y t . (a) Compute the transfer function H s . (b) Using Laplace transforms and partial fraction expansion, compute and plot the system output if the input x t is the unit step u t . (c) Using Laplace transforms and partial fraction expansion, compute and plot the system output if the input is x t = e 2000 t u t . DETAILED SOLUTION : (a) Compute the transfer function H s . To work this problem you can use the Laplace transform pair for the exponential: h t = K e a t u t H s = K s a a From the h t given in the problem statement, we see that K = 10 ; 000 ; a = 5000 b Substituting b into a then gives H s = 10 ; 000 s 5000 c (b) Compute and plot the system output if the input x t is the unit step u t . We know that the Laplace transform Y s of the output is given by Y s = H s X s d where H s is the transfer function and X s is the Laplace transform of the input. If x t = u t , the unit step, then X s = 1 = s . Using this result and c in equation d then gives Y s = 10 ; 000 s s 5000 e Now use partial fraction expansion on equation e to obtain Y s = 2 s 2 s 5000 f Taking the inverse Laplace transform of equation f and simplifying then gives the desired result : y t = 2 h 1 e 5000 t i u t g ECE 301 Detailed Solutions - Set 5: Transfer Functions 2 5-1. (cont.) (c) Compute and plot the system output if the input is x t = e 2000 t u t . If x t = e 2000 t u t then using equation a provides X s = 1 s 2000 . With H s given in the problem statement then equation d shows that Y s is given by Y s = H s X s = 10 ; 000 s 2000 s 5000 h Simplifying h using partial fraction expansion then gives Y s = 3 : 33 s 2000 3 : 33 s 5000...
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This note was uploaded on 01/25/2010 for the course ECE 301 taught by Professor Hoozturk during the Spring '08 term at N.C. State.

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Wtransfunc - ECE 301 Detailed Solutions Set 5 Transfer...

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