boylistad

Th
Method 3: See Fig. 18.49.
Eg Ig ���
(R1 � R2) � j XC Eg and ZTh � � R1 � R2 � j XC � Ig
The following example has a dependent source that will not permit
the use of the method described at the beginning of this section for
independent sources. All three methods will be applied, however, so
that the results can be compared.
EXAMPLE 18.12 For the network of Fig. 18.50 (introduced in Example
18.6), determine the Thévenin equivalent circuit between the indicated
terminals using each method described in this section. Compare
your results.
Solution: First, using Kirchhoff’s voltage law, ETh (which is the
same for each method) is written
ETh � V � mV � (1 � m)V
However, V � IR1 so E Th � (1 � m)IR 1
Z Th
I R 1
+
V
–
�V
– �
Method 1: See Fig. 18.51. Since I � 0, V and mV � 0, and
ZTh � R1 (incorrect)
Method 2: See Fig. 18.52. Kirchhoff’s voltage law around the indicated
loop gives us
V � mV � 0
and V(1 � m) � 0
Since m is a positive constant, the above equation can be satisfied
only when V � 0. Substitution of this result into Fig. 18.52 will yield
the configuration of Fig. 18.53, and
Isc � I
+
FIG. 18.50
Example 18.12.
Thévenin
THÉVENIN’S THEOREM ⏐⏐⏐ 807
hI R 1 R 2
X C
FIG. 18.48
Determining the short-circuit current for the
network of Fig. 18.46.
R 1
R 2
X C
+
Eg –
I sc
I g
Z Th
I sc
FIG. 18.49
Determining the Thévenin impedance using
the approach Z Th � E g / I g.
R 1
+
V = 0
–
�V � = 0
– +
FIG. 18.51
Determining Z Th incorrectly.
I R 1
+
V
–
�V �
–
Z Th
FIG. 18.52
Determining I sc for the network of Fig. 18.50.
+
I sc
I sc