IEEE Solid-States Circuits Magazine - Summer 2018 - 8

circuit; they are only equivalent in the
sense that they have the same i - v
characteristics and that they have the
same flow of power in and out of the
linear circuit from the viewpoint of
the two terminals!

Misconception 2
This misconception relates to the question of preference for either Thévenin
or Norton equivalent circuits. We state
this question as follows: For a given
linear circuit, is there a preferred
equivalent circuit, i.e., Thévenin or
Norton? If yes, what determines the
choice and why?
At the first glance, it appears that
since the two circuits are equivalent,
there should be no preference as to
which one to use. In fact, as far as the
equations are concerned, both equivalent circuits yield the exact same results. However, we would like to make
two observations and one conclusion here:
■ An ideal voltage source does not
have a Norton equivalent circuit,
and an ideal current source does
not have a Thévenin equivalent
circuit. Recall that an ideal voltage
source has zero resistance in series with it. If we were to represent
this voltage source with a Norton
equivalent circuit, the equivalent
resistance would be zero, but then
we need an infinite current to produce a nonzero voltage across a
zero resistor. Similarly, an ideal
current source, i.e., one with infinite resistance across it, cannot be

■

represented by a Thévenin equivalent circuit because the equivalent resistance would be infinite,
and this would necessitate the
Thévenin voltage source to be infinite to produce a nonzero output
current. So, in these cases, there
is a clear preference for the use of
Thévenin or Norton equivalent circuits, simply because only one of
them exists.
A nonideal voltage source is also
closer in concept to a Thévenin
equivalent circuit than to a Norton
equivalent circuit. Similarly, a nonideal current source is closer to a
Norton equivalent circuit than to
a Thévenin equivalent circuit. For
example, consider a 10-V battery,
which has an internal resistance of
1 W, driving a resistive load in the
100-1,000-W range as shown in Figure 3(a). Under these conditions, the
battery indeed appears to be very
close to an ideal voltage source. In
fact, the voltage that appears across
the load will be somewhere between
9.990 and 9.999 V, very close to
10 V indeed. However, if we decide
to represent this battery with a Norton equivalent circuit, as shown in
Figure 3(b), we will end up with a
10-A current source and a 1-W parallel resistor. In this case, the current
delivered to the load in the two extremes will be 99 mA and 9.9 mA, a
factor of ten difference in the load
current. Clearly, we can judge that
the battery in this case is much closer to an ideal voltage source, in the

+
-

1Ω

+
VL
-

9.90 V

9.99 V

+
10 A

VL
-

1Ω

100 - 1,000 Ω

10 V

IL
100-1,000 Ω

99 mA

9.99 mA
100

1,000

RL (Ω)

100

(a)

1,000

RL (Ω)

(b)

Figure 3: A 10-V battery with a 1X resistor driving a resistive load in the 100-1,000- X
range is closer in behavior to an ideal voltage source than to an ideal current source and,
hence, should be modeled with its thévenin (rather than its norton) equivalent circuit.

su m m e r 2 0 18

IEEE SOLID-STATE CIRCUITS MAGAZINE

sense that it maintains a relatively
constant voltage across the load as
the load varies from 100 to 1,000 W,
than to an ideal current source, in
the sense that the battery cannot
maintain a relatively constant current in the load as we vary the load.
For this reason, it makes sense to
represent the battery circuit with
its Thévenin equivalent circuit
rather than by its Norton equivalent circuit.
How can we decide in advance if
we should use the Thévenin or Norton
equivalent circuit? It depends on the
equivalent resistance and its relation
to the load resistance. If the equivalent resistance is much smaller than
the load resistance, then we know that
the voltage across the load will not
depend much on the load, and hence
a Thévenin equivalent circuit (i.e., a
nonideal voltage source) is more suitable. If the equivalent resistance is
much larger than the load resistance,
then the current through the load will
not vary much with the load; in this
case, we prefer a Norton equivalent
circuit, that is, a nonideal current
source. Finally, if the equivalent resistance and the load resistance are in
the same range, then there is no preference over the two; in this case, both
the current through the load and the
voltage across the load change significantly with the load.
Figure 4 shows an example of an
NMOS transistor used as a source follower with a load resistance R L (dc
biasing not shown). We wish to represent the circuit looking into the source
with its equivalent circuit (Thévenin
or Norton) [1]. Knowing that the resistance looking into the source should be
much smaller than the load resistance,
we think a Thévenin equivalent circuit
would better represent the behavior of
a source follower. However, to arrive
at this Thévenin equivalent circuit, it
turns out that it is easier to find the
Norton equivalent circuit first and
then convert it to the Thévenin equivalent circuit. For the Norton equivalent circuit, we short the output node
to ground and measure the current
(continued on p. 108)

IEEE Solid-States Circuits Magazine - Summer 2018

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