C = 1µF. %3D L i(t) R v(t) C v.lt) Figure Q2 a) Show that the transfer function Yc(sc is given by V(s)/ V.(s) = G(s) V(s) 1/LC R 1 s2 + s-+ LC Using appropriate calculations or otherwise, is the circuit overdamped, critically damped, underdamped or undamped? b) By substituting the values of R, L and C in the transfer function G(s). Derive the frequency response expression G(ja) and hence evaluate the gain |G(ja)| and phase p(w). c) Sketch the Bode diagram (Gain and phase) of the transfer function G(s) clearly indicating all the key information including the -3db point, system gain and all the relevant calculations.

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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Q2) Consider the following RLC circuit outlined in Figure Q2, where R = 2502, L = 10mH and
C = 1µF.
i(t)
R
v(t)
v.lt)
Figure Q2
Show that the transfer function Ve(S7e is given by
V.(s)
V(s)
a)
V.(s)
G(s)
V (s)
1/LC
R
1
s2 + s=+.
LC
Using appropriate calculations or otherwise, is the circuit overdamped, critically
damped, underdamped or undamped?
b)
By substituting the values of R, L and C in the transfer function G (s). Derive the
frequency response expression G(jw) and hence evaluate the gain |G(jw)| and
phase o(w).
c)
Sketch the Bode diagram (Gain and phase) of the transfer function G(s) clearly
indicating all the key information including the -3db point, system gain and all the
relevant calculations.
Transcribed Image Text:Q2) Consider the following RLC circuit outlined in Figure Q2, where R = 2502, L = 10mH and C = 1µF. i(t) R v(t) v.lt) Figure Q2 Show that the transfer function Ve(S7e is given by V.(s) V(s) a) V.(s) G(s) V (s) 1/LC R 1 s2 + s=+. LC Using appropriate calculations or otherwise, is the circuit overdamped, critically damped, underdamped or undamped? b) By substituting the values of R, L and C in the transfer function G (s). Derive the frequency response expression G(jw) and hence evaluate the gain |G(jw)| and phase o(w). c) Sketch the Bode diagram (Gain and phase) of the transfer function G(s) clearly indicating all the key information including the -3db point, system gain and all the relevant calculations.
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