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. 8-24. 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:
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:
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.