1. 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

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

3. 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

4. Chapter 14 Complex Frequency and the Laplace Transform
Fig A series RLC circuit to which a damped sinusoidal ...
Fig The unit-impulse function d (t – t0).
Fig A circuit that is analyzed by transforming the …
Fig Circuit for Example 14.5.
Fig Circuit for Example 14.6.
Fig Graph for Example 14.7.
Table Laplace transform pairs.
Table Laplace transform operations.
Table (continued.)
Engineering Circuit Analysis Sixth Edition
W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin
Copyright © McGraw-Hill, Inc. All Rights Reserved.

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

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

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

8. 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.

9. 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.

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

11. 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.

12. 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.

13. 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.

14. 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 , and work in the frequency domain to find Ix .(b) Find ix(t).

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