HW 3 ans - [email protected] icl.syr.edu ELE232 Electrical...

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[email protected] - icl.syr.edu ELE232 - Electrical Fundamentals II – 1FEB2008 Homework 3 - Due : Friday, 8FEB2008 Problem 1 : (a) Find an expression for the system function H(s) = V 0 (s) V IN (s) for this circuit . Write it in canonical form; coefficient of the highest power of ‘s’ equal to ‘1’ in both numerator and denominator. (Put in the numbers as the last step.) (b) Draw the pole-zero diagram for H(s) . (c) Write an expression for the frequency response function H(j ! ) = V 0 (j ! ) V IN (j ! ) . Write it in canonical form; real part of complex expressions equal to ‘1’. (a) First find the impedance of the parallel combination of R 1 and C . Z || = R 1 sC R 1 + 1 sC = R 1 R 1 Cs + 1 . Notice that this expression has unit of ohms since each term in the denominator is dimension-less . (b) Next use the voltage divider rule to obtain an expression for V 0 (s) in terms of V IN (s) . V 0 (s) = R 2 R 2 + R 1 R 1 Cs + 1 V IN (s) = R 2 R 1 Cs + 1 ( ) R 2 R 1 Cs + R 2 + R 1 V IN (s) = R 2 R 2 R 1 C R 1 Cs + 1 ( ) s + R 2 + R 1 R 2 R 1 C V IN (s) H(s) = s + 1 R 1 C !
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