ECE108EXAM%233sol_06

ECE108EXAM%233sol_06 - ECE108 EXAM#3 4/21/06 1. Given the...

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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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ECE108EXAM%233sol_06 - ECE108 EXAM#3 4/21/06 1. Given the...

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