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810 ⏐⏐⏐ NETWORK THEOREMS (ac)
IN
Z N
FIG. 18.59
The Norton equivalent circuit for ac networks.
I
R 1
+
k1V2 –
k 2 I
R 2
Z Th
FIG. 18.58
Determining Z Th using the procedure Z Th � E g/ I g.
Applying Kirchhoff’s current law, we have
Ig � k2I � �k2�� � �
Eg k1Eg Eg � � �
R2 R1 R2
� Eg� � 1 k1k2 � �
R2 R1 �
Ig R1 � k1k2R2 and � ���
Eg R1R2 Eg R1R2 or ZTh ����� Ig R1 � k1k2R2 as obtained above.
I g
+
Eg –
The last two methods presented in this section were applied only to
networks in which the magnitudes of the controlled sources were
dependent on a variable within the network for which the Thévenin
equivalent circuit was to be obtained. Understand that both of these
methods can also be applied to any dc or sinusoidal ac network containing
only independent sources or dependent sources of the other
kind.
18.4 NORTON’S THEOREM
The three methods described for Thévenin’s theorem will each be
altered to permit their use with Norton’s theorem. Since the Thévenin
and Norton impedances are the same for a particular network, certain
portions of the discussion will be quite similar to those encountered in
the previous section. We will first consider independent sources and the
approach developed in Chapter 9, followed by dependent sources and
the new techniques developed for Thévenin’s theorem.
You will recall from Chapter 9 that Norton’s theorem allows us to
replace any two-terminal linear bilateral ac network with an equivalent
circuit consisting of a current source and an impedance, as in
Fig. 18.59.
The Norton equivalent circuit, like the Thévenin equivalent circuit, is
applicable at only one frequency since the reactances are frequency
dependent.
Th