# Equivalent circuit

Equivalent circuit

An equivalent circuit refers to the simplest form of a circuit that retains all of the electrical characteristics of the original (and more complex) circuit. In its most common form, an equivalent circuit is made up of linear, passive elements. However, more complex equivalent circuits are used that approximate the nonlinear behavior of the original circuit as well. These more complex circuits often are called macromodels of the original circuit. An example of a macromodel is the Boyle circuit for the 741 operational amplifier.cite book
author=Richard C. Dorf
title=The Electrical Engineering Handbook
year= 1997
publisher=CRC Press
location=New York
isbn=0072320842
pages=Fig. 27.4, p. 711
]

There are two very renowned two-terminal equivalent circuits:
*Thévenin equivalent - reduces a two-terminal circuit to a single voltage source and a series Thévenin impedance
*Norton equivalent - reduces a two terminal circuit to a current source and a parallel Norton impedance

For a restricted set of linear four-terminal circuits, equivalent two-port networks can be set up. The restriction upon a two-port representation is that of a port: the current entering each port must be the same as the current leaving that port.cite book
author=P.R. Gray, P.J. Hurst, S.H. Lewis, and R.G. Meyer
year= 2001
edition=Fourth Edition
publisher=Wiley
location=New York
isbn=0471321680
pages=§3.2, p. 172
url=http://worldcat.org/isbn/0471321680
] By linearizing a nonlinear circuit about its operating point, such a two-port representation can be made for transistors: see hybrid pi and h-parameter circuits.

Equivalent circuits also can describe and model the electrical properties of materials or biological systems like the cell membrane. The latter is modelled as a capacitor (i.e. the lipid bilayer) in parallel with resistance-battery combinations (i.e. ion channels powered by an ion gradient across the membrane).

References

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