ECE108EXAM%233sol_06

# ECE108EXAM%233sol_06 - ECE108 EXAM#3 1 Given the circuit...

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ECE108 EXAM#3 4/21/06 1. Given the circuit shown below (35pts) (a) Draw the transform domain representation of this circuit (b) If is the input and is the output, determine the transfer function of the system ( ) i vt ( ) o () () () () 0 2 52 2 2 25 ii i s Zs ss s s s Vs Vs HsVs s sZs s s s s + =+= + + == = = + ++ + + Then ( ) 2 o i s Hs Vs s s + (c) Give its pole-zero plot and show the ROC. Factoring the denominator polynomial, ( ) 2s+5 = f o r 1 s+1+2j 1 2 sj σ >− +−

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2 (d) Determine the impulse response of this system. You do not need to simplify your solution. () ( ) 12 2s+5 s+1+2j 1 2 s+1+2j s+1-2j AA Hs sj == + +− where ( ) ( ) 1 21 5 34 1 1 11 4 j j AH ss j jj j −− + =+ + = = =− − −− +− * 4 j j + Then 1 1 41 4 1 js j j s j −+ + + Because the ROC is to the right of all of the poles, both terms in the above expression will result in right-sided signals, i.e., 44 ht e e ut −−    2. Given the following Pole-Zero Diagram of the transfer function of a causal LTI system (35pts) (a) If H (0) = 1, determine the transfer function.
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## This note was uploaded on 10/24/2009 for the course ECE 108 taught by Professor Li during the Spring '08 term at Lehigh University .

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ECE108EXAM%233sol_06 - ECE108 EXAM#3 1 Given the circuit...

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