3.6 Norton's Theorem

This theorem is analogous to Thevenin's theorem and states that we can replace everything, except the load, in a circuit by an equivalent circuit containing only an independent current source which we will denote as i _N in parallel with a resistance which we will denote as R _N, as shown in Figure 3.46.

Figure 3.46: Replacement of a network by its Norton equivalent

The current source i _N has the value of the short circuit current which would flow if a short were connected between the terminals x and y, where the Norton equivalent is inserted, and the resistance R _N is found from the relation

where v _OC is the open circuit voltage which appears across the open terminals x and y.

Like Thevenin's, Norton's theorem is most useful when a series of computations involves changing the load of a network while the rest of the circuit remains unchanged.

Comparing the Thevenin's and Norton's equivalent circuits, we see that one can be derived from the other by replacing the Thevenin voltage and its series resistance with the Norton current source and its parallel resistance. Therefore, there is no need to perform separate computations for each of these equivalents; once we know Thevenin's equivalent we can easily draw the Norton equivalent and vice versa.

Example 3.11

Replace the network shown in Figure 3.47 by its Thevenin and Norton equivalents.

Figure 3.47: Network for Example 3.11

Solution:

We...