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Th
obtained by applying a source of voltage to the terminals of interest and
determining the source current as indicated in Fig. 18.39. For this
method, the source voltage of the original network is set to zero. The
Thévenin impedance is then determined by the following equation:
ZTh � � Eg
�
Ig (18.4)
Note that for each technique, E Th � E oc, but the Thévenin impedance is
found in different ways.
EXAMPLE 18.10 Using each of the three techniques described in this
section, determine the Thévenin equivalent circuit for the network of
Fig. 18.40.
Solution: Since for each approach the Thévenin voltage is found in
exactly the same manner, it will be determined first. From Fig. 18.40,
where IXC � 0,
Due to the polarity for V and
defined terminal polarities
R2(mV) mR2V VR1 � ETh � Eoc ��� ���
R1 � R2 R1 � R2 The following three methods for determining the Thévenin impedance
appear in the order in which they were introduced in this section.
Method 1: See Fig. 18.41.
ZTh � R1 � R2 � j XC Method 2: See Fig. 18.42. Converting the voltage source to a current
source (Fig. 18.43), we have (current divider rule)
R1R2
��� R1 � R �� 2
Isc � �
�mR2V
�� R1
� R2
——
� (R1 � R2) � j XC m
�(R V
1 � R2)� �
R � 1
——
(R1 � R2) � j XC mV
�
R1
——
(R1 � R2) � j XC �V �
R1 R 1 R 2 I sc
FIG. 18.43
Converting the voltage source of Fig. 18.42 to a current source.
X C
I sc
�
+
–
�V
THÉVENIN’S THEOREM ⏐⏐⏐ 805
I g
Z Th
+
Network E g
FIG. 18.39
Determining Z Th using the approach
Z Th � E g / I g.
–
�V �
+
R 1
R 1
R 2
X C
FIG. 18.40
Example 18.10.
R 2
R 1
R 2
X C
–
X C
+
–
I sc
Thévenin
Z Th
FIG. 18.41
Determining the Thévenin impedance for the
network of Fig. 18.40.
FIG. 18.42
Determining the short-circuit current for the
network of Fig. 18.40.
I sc