Editing Norton's theorem (section)

{{About|the theorem in electrical circuits|Norton's theorem for queueing networks|flow-equivalent server method}}
{{Short description|DC circuit analysis technique}}
{{Use dmy dates|date=August 2019|cs1-dates=y}}
[[File:NortonEquivalentCircuits.png|thumb|upright=1.6|alt=text|Any [[Black box (systems)|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.]]
[[File:Edward Lawry Norton.jpg|200px|thumb| [[Edward Lawry Norton]]]]
In [[Direct current|direct-current]] [[circuit theory]], '''Norton's theorem''', also called the '''Mayer–Norton theorem''', is a simplification that can be applied to [[Electrical network|networks]] made of [[Linear time-invariant system|linear time-invariant]] [[Resistor|resistances]], [[Voltage source|voltage sources]], and [[Current source|current sources]]. 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 power|reactive]] [[Electrical impedance|impedances]] as well as resistances. The '''Norton equivalent''' circuit is used to represent any network of linear sources and impedances at a given [[frequency]].

Norton's theorem and its dual, [[Thévenin's theorem]], are widely used for circuit analysis simplification and to study circuit's [[Initial condition|initial-condition]] and [[Steady state (electronics)|steady-state]] response.

Norton's theorem was independently derived in 1926 by [[Siemens|Siemens & Halske]] researcher [[Hans Ferdinand Mayer]] (1895–1980) and [[Bell Labs]] engineer [[Edward Lawry Norton]] (1898–1983).<ref name="Mayer_1926"/><ref name="Norton_1926"/><ref name="Johnson_2003a"/><ref name="Johnson_2003b"/><ref name="Brittain_1990"/><ref name="Dorf_2010"/>

To find the Norton equivalent of a linear time-invariant circuit, the Norton current ''I''<sub>no</sub> is calculated as the current flowing at the two terminals ''A'' and ''B'' of the original circuit that is now [[Short circuit|short]] (zero impedance between the terminals). The Norton resistance ''R''<sub>no</sub> is found by calculating the output voltage ''V<sub>o</sub>'' produced at ''A'' and ''B'' with no resistance or load connected to, then ''R''<sub>no</sub> = ''V<sub>o</sub>'' / ''I<sub>no</sub>''; equivalently, this is the resistance between the terminals with all (independent) voltage sources short-circuited and independent current sources [[Open-circuit voltage|open-circuited]] (i.e., each independent source is set to produce zero energy). 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 1 ampere test current at the terminals. This voltage divided by the 1&nbsp;A current is the Norton impedance ''R''<sub>no</sub> (in ohms). 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.