Norton’s Theorem

Norton’s Theorem statement

Statement for DC

Norton’s theorem states that any two terminal linear network having number of voltage sources, current sources and resistances can be replaced by a simple equivalent circuit consisting of a single current source, I_N in parallel with a resistance R_N. Whereas the value of the current source, I_N is the short circuit
current through terminals of the network when the terminals are shorted and the Norton’s resistance, R_N is the equivalent resistance measured between the terminals when all independent sources are turned off; i.e the independent ideal voltage source is replaced by a short circuit and ideal current source with open circuit.

Statement for AC

Norton’s theorem states that any two terminal linear network having number of voltage sources, current sources and impedances can be replaced by a simple equivalent circuit consisting of a single current source, I_N in parallel with an impedance Z_N. Whereas the value of the current source, I_N is the short circuit current through the terminals of the network and the Norton’s impedance, Z_N is the equivalent impedance measured between the terminals of the networks when all independent sources are turned off.

Norton’s Equivalent

The below figures show the Norton’s equivalent circuit.

Norton's equivalent for AC

Norton's equivalent circuit for DC

Procedure for Finding the Norton’s equivalent

The following circuit is considered for finding the Norton’s equivalent.

Main Circuit for analysis

For finding the Norton’s current, replace the load with a short circuit as in the below figure and find the current through the short circuited path. This givens the Norton’s current I_N.

Circuit for finding Norton's current, I_N

For finding the Norton’s resistance remove the load and turn off all the independent sources. The given circuit has two sources namely one current source and one voltage source. Replacing the current source with open circuit and voltage source with a short circuit leads to the following circuit. Find the equivalent resistance between the terminals from the obtained circuit. This gives the Norton’s resistance R_N.

Circuit for finding Norton's resistance 

Form the Norton’s equivalent from the above obtained values of I_N and R_N.

Norton's equivalent