Transcript Chapter Nine The RLC Circuit

Chapter 9
The RLC Circuit
Fig. 9.1
The source-free parallel RLC circuit.
Fig. 9.3
Circuit from Example 9.1.
User Note:
Fig. 9.5
An example overdamped response.
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Fig. 9.6
An example critically damped circuit.
Fig. 9.8
(and Fig. 9.9) Underdamped response examples.
Fig. 9.10
Simulated overdamped, critically damped, and …
Fig. 9.11
Circuit from Example 9.2.
Fig. 9.15
(a) The series RLC circuit which is the dual …
Fig. 9.18
An RLC circuit that is used to illustrate several …
Engineering Circuit Analysis Sixth Edition
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin
Copyright © 2002 McGraw-Hill, Inc. All Rights Reserved.
t
v 1
dv
  vdt  - i (t0 )  C
 0
R L t0
dt
i(0+) = I0
v(0+) = V0
The source-free parallel RLC circuit.
d 2v
1 dv
1
C 2 

 0
dt
R dt
L
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
Find vC(t) for the circuit of (a).
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
The response v(t) = 84(e-t – e-6t) of the parallel network shown.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
The critically damped response v(t) = 420e-2.45t of the network shown.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
The underdamped response of
the network shown.
The response of the network
for three different resistance
values, showing an increase
in the magnitude of
oscillation.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
Simulated overdamped, critically damped, and underdamped
voltage response for a parallel RLC network with L = 7 H and
C = 1/42 F.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
Determine iL(t) for the circuit shown in (a).
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
(a) The series RLC circuit
which is the dual of (b) a
parallel RLC circuit. The
element values are, of
course, not identical in the
two circuits.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
An RLC circuit that is used to illustrate several procedures by
which the initial conditions may be obtained. The desired
response is nominally taken to be vC(t).
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.