Norton's theorem

At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel.

For alternating current (AC) systems the theorem can be applied to reactive impedances as well as resistances.

The Norton equivalent circuit is used to represent any network of linear sources and impedances at a given frequency.

[1][2][3][4][5][6] To find the Norton equivalent of a linear time-invariant circuit, the Norton current Ino is calculated as the current flowing at the two terminals A and B of the original circuit that is now short (zero impedance between the terminals).

The Norton resistance Rno is found by calculating the output voltage Vo produced at A and B with no resistance or load connected to, then Rno = Vo / Ino; equivalently, this is the resistance between the terminals with all (independent) voltage sources short-circuited and independent current sources open-circuited (i.e., each independent source is set to produce zero energy).

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Any black box containing resistances only and voltage and current sources can be replaced by an equivalent circuit consisting of an equivalent current source in parallel connection with an equivalent resistance.
Edward Lawry Norton
  1. The original circuit
  2. Calculating the equivalent output current
  3. Calculating the equivalent resistance
  4. Design the Norton equivalent circuit
To a Thévenin equivalent