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Problem 2 400(s2+2s+25) G(s) = s(s+10)2(s+100)

Problem 2 400(s2+2s+25) G(s) = s(s+10)2(s+100)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Problem 2 400(s2+2s+25) G(s) = s(s+10)2(s+100)
Transcribed Image Text:Problem 2 400(s2+2s+25) G(s) = s(s+10)2(s+100)
For problems 1-3, given a transfer function G(s) sketch the magnitude and phase characteristics in the logarithmic scale (i.e. Bode-plots) of the system using the following rules-of-thumb: i. "Normalize" the G(s) by extracting poles/zeros, substituting s=jw and writing the TF using DC-gain KO and time-constants ii. Arrange break-points (poles , zeros or wn for complex-conjugate poles) in ascending order ii. Based on the term Ko(jw)+k, determine: a. initial slope of the magnitude-response asymptote for low frequencies as + k 20 dB/dec (e.g. flat for k=0, -20 dB/Dec for one pole at s=0 etc.) b. "anchor" point through which the magnitude-response asymptote passes for w=1 (i. e.20 log10 Ko) initial value of the phase-response asymptote for low frequencies as Fk 90° C. iv. Start going from w=0 towards o v. For each break-point that corresponds to a real pole/zero you encounter, adjust: a. magnitude-response asymptote slope by – m 20 dB/Dec for a pole and + m20 dB/Dec for a zero (m= multiplicity/order of pole/zero at the breakpoint) b. phase-response asymptote by - m90° for a single pole and + m 90° for a single zero (m= multiplicity/order of pole/zero at the breakpoint) vi. For each break-point wn that corresponds to a complex-conjugate set of poles/zeros, adjust: a. magnitude-response asymptote slope by -m40 dB/Dec for a set of cc poles and +m40 dB/Dec for a set of cc zeros (m= multiplicity/order of cc poles/zeros at the breakpoint) b. phase-response asymptote by – m180° for a set of cc poles and + m180° for a set of cc zeros (m= multiplicity/order of cc poles/zeros at the breakpoint) c. For { < v2/2 (or 0.7) be aware of a resonant "bump" or a "dip" of approximately - 1 M, = 25 vii. Draw the approximate magnitude and phase responses by fitting a curve along the asymptotes For all problems, apply and clearly indicate the bode-plot rules. For each graph, find/indicate the approximate frequency for which the magnitude response crosses the value 0 dB. Find/indicate the approximate frequency for which the phase response crosses the value -180° (for some graphs, this will be for w->
Transcribed Image Text:For problems 1-3, given a transfer function G(s) sketch the magnitude and phase characteristics in the logarithmic scale (i.e. Bode-plots) of the system using the following rules-of-thumb: i. "Normalize" the G(s) by extracting poles/zeros, substituting s=jw and writing the TF using DC-gain KO and time-constants ii. Arrange break-points (poles , zeros or wn for complex-conjugate poles) in ascending order ii. Based on the term Ko(jw)+k, determine: a. initial slope of the magnitude-response asymptote for low frequencies as + k 20 dB/dec (e.g. flat for k=0, -20 dB/Dec for one pole at s=0 etc.) b. "anchor" point through which the magnitude-response asymptote passes for w=1 (i. e.20 log10 Ko) initial value of the phase-response asymptote for low frequencies as Fk 90° C. iv. Start going from w=0 towards o v. For each break-point that corresponds to a real pole/zero you encounter, adjust: a. magnitude-response asymptote slope by – m 20 dB/Dec for a pole and + m20 dB/Dec for a zero (m= multiplicity/order of pole/zero at the breakpoint) b. phase-response asymptote by - m90° for a single pole and + m 90° for a single zero (m= multiplicity/order of pole/zero at the breakpoint) vi. For each break-point wn that corresponds to a complex-conjugate set of poles/zeros, adjust: a. magnitude-response asymptote slope by -m40 dB/Dec for a set of cc poles and +m40 dB/Dec for a set of cc zeros (m= multiplicity/order of cc poles/zeros at the breakpoint) b. phase-response asymptote by – m180° for a set of cc poles and + m180° for a set of cc zeros (m= multiplicity/order of cc poles/zeros at the breakpoint) c. For { < v2/2 (or 0.7) be aware of a resonant "bump" or a "dip" of approximately - 1 M, = 25 vii. Draw the approximate magnitude and phase responses by fitting a curve along the asymptotes For all problems, apply and clearly indicate the bode-plot rules. For each graph, find/indicate the approximate frequency for which the magnitude response crosses the value 0 dB. Find/indicate the approximate frequency for which the phase response crosses the value -180° (for some graphs, this will be for w->
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