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The Norton equivalent circuit appears in Fig. 18.73(a). In Fig.
18.73(b), we find that
I N
and in Fig. 18.73(c) that
Or, rearranging, we have
(a)
Z N
I N
I = 0
(b)
Z N
FIG. 18.73
Defining an alternative approach for determining Z N.
I sc � I N
E oc � I NZ N
Z N �
E oc
� IN
I sc
IN
(18.9)
and ZN � � (18.10)
Eoc
�
Isc The Norton impedance can also be determined by applying a source
of voltage E g to the terminals of interest and finding the resulting I g,as
shown in Fig. 18.74. All independent sources and dependent sources not
controlled by a variable in the network of interest are set to zero, and
ZN � � Eg
�
Ig (18.11)
For this latter approach, the Norton current is still determined by the
short-circuit current.
EXAMPLE 18.17 Using each method described for dependent sources,
find the Norton equivalent circuit for the network of Fig. 18.75.
Solution:
I N For each method, I N is determined in the same manner. From Fig.
18.76, using Kirchhoff’s current law, we have
0 � I � hI � I sc
or I sc ��(1 � h)I
Applying Kirchhoff’s voltage law gives us
NORTON’S THEOREM ⏐⏐⏐ 815
(c)
Z N
Network
+
E oc = I N Z N
–
Z N
I g
+
E g
–
FIG. 18.74
Determining the Norton impedance using the
approach Z N � E g / I g.
+
E
–
+
E
–
I
R 1
hI
FIG. 18.75
Example 18.17.
R 2
I + –
V R2
R 1
hI
R 2
Norton
FIG. 18.76
Determining I sc for the network of Fig. 18.75.
I sc
I sc