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Unformatted text preview: 1 7 Summary of Lecture #14 9/24/2010 Zeros and poles of Z(s), Y(s) and H(s) Finite zeros and poles First order or simple poles and zeros Repeated zeros and poles, (double, triple etc) Zero and pole at infinity Gain constant Pole-zero plots Poles Zeros Gain constant Bounded and unbounded signals Stable, unstable and metastable systems Examples Classification of responses Complete response = ZIR+ZSR = TSR + SS = NTR + FCR See me before 10/01 if your Test#1 score is less than 30. 8 Zeros and poles of Z(s), Y(s ) and H(s) Pole-zero plots Finite zeros and poles, z 1 , z 2 , p 1 , p 2 etc. First order or simple zeros and poles Repeated zeros and poles (double , triple zeros and poles etc.) Zero and pole at infinity Gain constant K ) p s )( p s ( ) z s )( z s ( K b s b s b s a s a s a s a ) s ( H 2 1 2 1 1 1 n 1 n n 1 1 m 1 m m m---- = + + + + + + =---- j o o x 9 A signal, f(t) , is bounded if | f(t) | < K 1 < for all time t and for some constant K 1 . A circuit or system is stable if every bounded input signal yields a bounded response. A system or circuit is stable if and only if all poles of H(s) lie in the open left half complex plane. Open left half complex plane : Re(s) = < 0 (excluding = 0 ) Poles in right half plane? Unstable systems or circuits First order poles on j -axis?...
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- Spring '06