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 Arrange break-points (poles , zeros or wn for complex-conjugate poles) in ascending order Based on the term Ko(jw)+k, determine: ii. iii. 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 K) initial value of the phase-response asymptote for low frequencies as Fk 90° С. iv. Start going from w=0 towards ∞ 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) For {< v2/2 (or 0.7) be aware of a resonant "bump" or a "dip" of approximately С. 1 M, =
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 Arrange break-points (poles , zeros or wn for complex-conjugate poles) in ascending order Based on the term Ko(jw)+k, determine: ii. iii. 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 K) initial value of the phase-response asymptote for low frequencies as Fk 90° С. iv. Start going from w=0 towards ∞ 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) For {< v2/2 (or 0.7) be aware of a resonant "bump" or a "dip" of approximately С. 1 M, =
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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Transcribed Image Text:Problem 3
1000
G(s)
(s2+16s+100)
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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