Pertemuan 12 Complex Frequency and the Laplace Transform Matakuliah : H0042/Teori Rangkaian Listrik Tahun : 2005 Versi : <<versi/01 Pertemuan 12 Complex Frequency and the Laplace Transform

Menguraikan teori dasar transformasi Laplace Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Menguraikan teori dasar transformasi Laplace

Materi 1 : mengenal fungsi domain waktu pada rangkaian RLC. Outline Materi Materi 1 : mengenal fungsi domain waktu pada rangkaian RLC. Materi 2 : mengenal persamaan transformasi Materi 3 : mengenal operasi transformasi Laplace

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.

Copyright ©2002 McGraw-Hill. All rights reserved. Fig. 14.1 A series RLC circuit to which a damped sinusoidal forcing function is applied. A frequency-domain solution for I(t) is desired. 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.

Copyright ©2002 McGraw-Hill. All rights reserved. Fig. 14.2 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. 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.

Copyright ©2002 McGraw-Hill. All rights reserved. Fig. 14.3 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. 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.

Fig. 14.5 Circuit for Example 14.5. 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.

Fig. 14.6 Circuit for Example 14.6. 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.

Copyright ©2002 McGraw-Hill. All rights reserved. Fig. 14.8 Graph for Example 14.7. 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.

Table 14.1 Laplace transform pairs. W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved.

Table 14.2 Laplace transform operations. W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved.

Copyright ©2002 McGraw-Hill. All rights reserved. Table 14.2, continued. W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved.

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).

RESUME Pengenalan transformasi Laplace dan fungsi dari rangkaian listrik beban RLC.