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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 • Polezero 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) • Polezero 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 ϖ × × o o x ∞← ∞← ∞← ∞← σ 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) = σ σσ < 0 (excluding σ σσ = 0 ) – Poles in right half plane? Unstable systems or circuits – First order poles on j ϖaxis?...
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This document was uploaded on 01/13/2012.
 Spring '06

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