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Consider a stable system with rational transfer function H(s) whose pole-zero plot is shown in Figure (a) (True or False) The system is causal. Justify your answer. (b) Sketch the normalized power gain G(w) = |H(jw)|2/|H (0)|² versus w ≥ 0, clearly labeling the values at w = 1 and w= 2, and the asymptote as w→∞. Note: This is a linear plot rather than a Bode plot. (c) Assuming that H(0) = 3, find an explicit expression for H(s).

Consider a stable system with rational transfer function H(s) whose pole-zero plot is shown in Figure (a) (True or False) The system is causal. Justify your answer. (b) Sketch the normalized power gain G(w) = |H(jw)|2/|H (0)|² versus w ≥ 0, clearly labeling the values at w = 1 and w= 2, and the asymptote as w→∞. Note: This is a linear plot rather than a Bode plot. (c) Assuming that H(0) = 3, find an explicit expression for H(s).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Consider a stable system with rational transfer function H(s) whose pole-zero plot is shown in Figure (a) (True or False) The system is causal. Justify your answer. (b) Sketch the normalized power gain G(w) = |H(jw)|²/|H(0)|² versus w ≥ 0, clearly labeling the values at w = 1 and w 2, and the asymptote as w →∞. Note: This is a linear plot rather than a Bode plot. (c) Assuming that H(0) = 3, find an explicit expression for H(s). (d) Denoting the input and output of the system as x(t) and y(t), respectively, specify a differ- ential equation relating them.
Transcribed Image Text:Consider a stable system with rational transfer function H(s) whose pole-zero plot is shown in Figure (a) (True or False) The system is causal. Justify your answer. (b) Sketch the normalized power gain G(w) = |H(jw)|²/|H(0)|² versus w ≥ 0, clearly labeling the values at w = 1 and w 2, and the asymptote as w →∞. Note: This is a linear plot rather than a Bode plot. (c) Assuming that H(0) = 3, find an explicit expression for H(s). (d) Denoting the input and output of the system as x(t) and y(t), respectively, specify a differ- ential equation relating them.
X -1 X Figure Im(s) 2 +1 Re(s)
Transcribed Image Text:X -1 X Figure Im(s) 2 +1 Re(s)
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