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Th
E 1
12 V
6 �
4 V
E 2
4 �
(a) (b)
a
b
10 �
+
8 V
–
FIG. 9.25
The effect of applying Thévenin’s theorem.
For the network of Fig. 9.25(a), the Thévenin equivalent circuit can
be found quite directly by simply combining the series batteries and
resistors. Note the exact similarity of the network of Fig. 9.25(b) to the
Thévenin configuration of Fig. 9.24. The method described below will
allow us to extend the procedure just applied to more complex configurations
and still end up with the relatively simple network of Fig. 9.24.
In most cases, other elements will be connected to the right of terminals
a and b in Fig. 9.25. To apply the theorem, however, the network
to be reduced to the Thévenin equivalent form must be isolated as
shown in Fig. 9.25, and the two “holding” terminals identified. Once
the proper Thévenin equivalent circuit has been determined, the voltage,
current, or resistance readings between the two “holding” terminals will
be the same whether the original or the Thévenin equivalent circuit is
connected to the left of terminals a and b in Fig. 9.25. Any load connected
to the right of terminals a and b of Fig. 9.25 will receive the
same voltage or current with either network.
This theorem achieves two important objectives. First, as was true
for all the methods previously described, it allows us to find any particular
voltage or current in a linear network with one, two, or any
other number of sources. Second, we can concentrate on a specific
portion of a network by replacing the remaining network with an
equivalent circuit. In Fig. 9.26, for example, by finding the Thévenin
equivalent circuit for the network in the shaded area, we can quickly
calculate the change in current through or voltage across the variable
resistor R L for the various values that it may assume. This is demonstrated
in Example 9.6.
+
E
–
R 1
R 2
R 3
(a) (b)
a
b
a
I L
b
R L
French (Meaux,
Paris)
(1857–1927)
Telegraph Engineer,
Commandant and
Educator
École Polytechnique
and École
Supérieure de
Télégraphie
FIG. 9.26
Substituting the Thévenin equivalent circuit for a complex network.
+
–
E Th
THÉVENIN’S THEOREM ⏐⏐⏐ 329
R Th
Courtesy of the Bibliothèque
École Polytechnique, Paris, France
Although active in the study and design of telegraphic
systems (including underground transmission),
cylindrical condensers (capacitors), and electromagnetism,
he is best known for a theorem first
presented in the French Journal of Physics—Theory
and Applications in 1883. It appeared under the
heading of “Sur un nouveau théorème d’électricité
dynamique” (“On a new theorem of dynamic electricity”)
and was originally referred to as the equivalent
generator theorem. There is some evidence
that a similar theorem was introduced by Hermann
von Helmholtz in 1853. However, Professor
Helmholtz applied the theorem to animal physiology
and not to communication or generator systems,
and therefore he has not received the credit in this
field that he might deserve. In the early 1920s
AT&T did some pioneering work using the equivalent
circuit and may have initiated the reference to
the theorem as simply Thévenin’s theorem. In fact,
Edward L. Norton, an engineer at AT&T at the time,
introduced a current source equivalent of the
Thévenin equivalent currently referred to as the
Norton equivalent circuit. As an aside, Commandant
Thévenin was an avid skier and in fact was commissioner
of an international ski competition in Chamonix,
France, in 1912.
LEON-CHARLES THÉVENIN
a
IL R L
b