1 Pertemuan 5 Useful Circuit Analysis Techniques Matakuliah: H0042/Teori Rangkaian Listrik Tahun: 2005 Versi: <<versi/01

2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Merangkum rangkaian listrik dengan teorema thevenin norton Menghitung tahanan dan sumber thevenin-norton.

3 Outline Materi Materi 1: analisa rangkaian menurut teorema Norton. Materi 2 :aplikasi teorema Norton Materi 3 : analisa rangkaian menurut teorema Thevenin Materi 4 : aplikasi teorema Thevenin

4 Chapter 5 Useful Circuit Analysis Techniques Engineering Circuit Analysis Sixth Edition W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin Copyright © 2002 McGraw-Hill, Inc. All Rights Reserved. Fig Figs. from Example 5.6 (Thévenin/ Norton Equivalents). Fig Circuit from Example 5.10.

5 Fig (a) A complex network including a load resistor R L. (b) A Thévenin equivalent network connected to R L. (c) A Norton equivalent network connected to R L. W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved. (a) A complex network including a load resistor R L. (b) A Thévenin equivalent network connected to R L. (c) A Norton equivalent network connected to R L.

6 In the phasor domain, a two-terminal circuit containing linear elements and sources can be replaced by the Thevenin or Norton equivalent circuits shown in Fig The general concept of Thevenin's and Norton's theorems and their restrictions are the same as in the resistive circuit studied in Chapter 3. The important difference here is that the signals VT, IN, V, and I are phasors, and VT=1/YN and ZL are complex numbers representing the source and load impedances. Finding the Thevenin or Norton equivalent of a phasor circuit involves the same process as for resistance circuits, except that now we must manipulate complex numbers. The thevenin and Norton circuits are equivalent to each other, so their circuit parameters are related as follows:

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8 Fig Figures from Example 5.6 (Thévenin/ Norton Equivalents). W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved. Determine the Thévenin and Norton Equivalents of Network A in (a).

9 Fig Circuit from Example W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved. Find the Thévenin equivalent of the circuit shown in (a). Fig Circuit from Example 5.10.

10 EXAMPLE Both sources in Fig. 8-25(a) operate at a frequency of =5000 rad/s. Find the steady-state voltage vR(t) using source transformations. SOLUTION: In this example we use source transformations. We observe that the voltage sources are connected in series with an impedance and can be converted into the following equivalent current sources:

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12 shows the circuit after these two source transformations. The two current sources are connected in parallel and can be replaced by a single equivalent current source:

13 The four passive elements are connected in parallel and can be replaced by an equivalent impedance: The voltage across this equivalent impedance equals VR,since one of the parallel elements is the resistor R. Therefore, the unknown phasor voltage is

14 The value of VR is the same as found using superposition. The corresponding time-domain function is

15 RESUME Rangkaian listrik dapat dengan sumber dan beban majemuk dapat dianalogikan sebagai sumber dan tahanan tunggal dengan metode penyederhanaan rangkaian menurut teorema thevenin- norton.