Norton's theorem for linear electrical networks, known in Europe as the Mayer–Norton theorem, states that any collection of voltage sources, current sources, and resistors with two terminals is electrically equivalent to an ideal current source, I, in parallel with a single resistor, R. For single-frequency AC systems the theorem can also be applied to general impedances, not just resistors. The Norton equivalent is used to represent any network of linear sources and impedances, at a given frequency. The circuit consists of an ideal current source in parallel with an ideal impedance (or resistor for non-reactive circuits).
Norton's theorem is an extension of Thévenin's theorem and was introduced in 1926 separately by two people: Siemens & Halske researcher Hans Ferdinand Mayer (1895–1980) and Bell Labs engineer Edward Lawry Norton (1898–1983). The Norton equivalent circuit is a current source with current INo in parallel with a resistance RNo. To find the equivalent,
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In the example, the total current Itotal is given by:
The current through the load is then, using the current divider rule:
And the equivalent resistance looking back into the circuit is:
So the equivalent circuit is a 3.75 mA current source in parallel with a 2 kΩ resistor.
A Norton equivalent circuit is related to the Thévenin equivalent by the following equations:
The term "Norton equivalent" is also used in queueing theory for a similar concept. In a reversible queueing system, it is often possible to replace an uninteresting subset of queues by a single (FCFS or PS) queue with an appropriately chosen service rate.[1]