Matakuliah
Tahun
Versi
: H0042/Teori Rangkaian Listrik
: 2005
: <<versi/01
Pertemuan 12
Complex Frequency and the
Laplace Transform
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Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Menguraikan teori dasar transformasi
Laplace
2
Outline Materi
• Materi 1 : mengenal fungsi domain
waktu pada rangkaian RLC.
• Materi 2 : mengenal persamaan
transformasi
• Materi 3 : mengenal operasi transformasi
Laplace
3
Chapter 14 Complex Frequency and
the Laplace Transform
Fig. 14.1 A series RLC circuit to which a damped sinusoidal ...
Fig. 14.2 The unit-impulse function d (t – t0).
Fig. 14.3 A circuit that is analyzed by transforming the …
Fig. 14.5 Circuit for Example 14.5.
Fig. 14.6 Circuit for Example 14.6.
Fig. 14.8 Graph for Example 14.7.
Table 14.1 Laplace transform pairs.
Table 14.2 Laplace transform operations.
Table 14.2 (continued.)
Engineering Circuit Analysis Sixth Edition
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin
Copyright © 2002 McGraw-Hill, Inc. All Rights Reserved.
4
A series RLC circuit to which a damped sinusoidal
forcing function is applied. A frequency-domain
solution for i(t) is desired.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
5
The unit-impulse function d(t – t0). This function is
often used to approximate a signal pulse whose
duration is very short compared to circuit time
constants.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
6
A circuit that is analyzed by transforming the
differential equation 2di/dt + 4i = 3u(t) into
s[sI(s) – i(0-)] + 4I(s) = 3/s.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
7
Determine i(t) for t > 0 in the series RC
circuit shown below.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
8
Find v(t) for the circuit shown below.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
9
Determine the transform of the
rectangular pulse v(t) = u(t-2) – u(t-5),
shown below.
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
10
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
11
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
12
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
13
• Problem 5. If a complex time-varying voltage is
given as vs(t) =(20 -j 30) e (-2 +j50)t V, find (a)
vs(0.1) in polar form; (b)Re {vs(t)};(c)Re [v(0.1
];(d) s;(e)s*
• Problem 7. (a) Let vs =10e-2t cos(10t +30)V in
the circuit of Fig. 14.10, and work in the
frequency domain to find Ix .(b) Find ix(t).
14
RESUME
• Pengenalan transformasi Laplace dan
fungsi dari rangkaian listrik beban RLC.
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