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ee541F11HW07

# ee541F11HW07 - EE 541 USC Viterbi School of Engineering J...

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EE 541 USC Viterbi School of Engineering J. Choma Homework #07 99 Fall Semester, 2011 U niversity of S outhern C alifornia USC Viterbi School of Engineering Ming Hsieh Department of Electrical Engineering EE 541: Homework Assignment #07 Fall, 2011 Due: 11/01/2011 Choma Problem #37: When terminated at its output port in a resistance, R , the passive network ab- stracted in Figure (P37a) is to produce the voltage transfer function,  2 o 2 s ss 1 V 1 aQ a H(s) , V2 a1s s 11 a a 1 aQ a         where parameters “a” and “Q” are positive constants and the transfer function is written in terms of a normalized impedance of 1 ohm and a normalized frequency of 1 radian per second . In general, a normalized one-ohm impedance corresponds to an actual R-ohm impedance, while 1 radian per second reflects an actual frequency of o radians -per-second . V o V s V s Passive RLC Network R R R Z(s ) a Z(s) b RR R V o (a). (b). Figure (P37) (a). If the network is realized as the constant resistance tee structure offered in Figure (P37b), give normalized mathematical expressions for the requisite impedances, Z a (s) and Z b (s) . (b). Determine the relationship between parameters “Q” and “a,” such that Z a (s) is realizable as an interconnection of a minimal number of branch elements.

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ee541F11HW07 - EE 541 USC Viterbi School of Engineering J...

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