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DC circuit analysis technique
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
In direct-current circuit theory, Norton's theorem (aka Mayer-Norton theorem) is a simplification that can be applied to networks made of linear time-invariant resistances, voltage sources, and current sources. At a pair of terminals of the network, it can be replaced by a current source and a single resistor in parallel.
To find the equivalent, the Norton current Ino is calculated as the current flowing at the terminals into a short circuit (zero resistance between A and B). This is Ino. The Norton resistance Rno is found by calculating the output voltage produced with no resistance connected at the terminals; equivalently, this is the resistance between the terminals with all (independent) voltage sources short-circuited and independent current sources open-circuited. This is equivalent to calculating the Thevenin resistance.
When there are dependent sources, the more general method must be used. The voltage at the terminals is calculated for an injection of a 1Amp test current at the terminals. This voltage divided by the 1 A current is the Norton impedance Rno. This method must be used if the circuit contains dependent sources, but it can be used in all cases even when there are no dependent sources.
Example of a Norton equivalent circuit
The original circuit
Calculating the equivalent output current
Calculating the equivalent resistance
Design the Norton equivalent circuit
In the example, the total current Itotal is given by: