Editing Two-port network (section)

== Application ==
The two-port network model is used in mathematical [[circuit analysis]] techniques to isolate portions of larger circuits.  A two-port network is regarded as a "[[black box]]" with its properties specified by a [[matrix (mathematics)|matrix]] of numbers.  This allows the response of the network to signals applied to the ports to be calculated easily, without solving for all the internal voltages and currents in the network.  It also allows similar circuits or devices to be compared easily.  For example, transistors are often regarded as two-ports, characterized by their {{mvar|h}}-parameters (see below) which are listed by the manufacturer.   Any [[linear circuit]] with four terminals can be regarded as a two-port network provided that it does not contain an independent source and satisfies the port conditions.

Examples of circuits analyzed as two-ports are [[filter (signal processing)|filter]]s, [[matching network]]s, [[transmission line]]s, [[transformer]]s, and [[small-signal model]]s for transistors (such as the [[hybrid-pi model]]). The analysis of passive two-port networks is an outgrowth of [[Reciprocity (electromagnetism)#Reciprocity for electrical networks|reciprocity theorems]] first derived by Lorentz.<ref>{{cite web |url=http://www.emcs.org/acstrial/newsletters/summer03/jasper.pdf |title=Reciprocity and EMC measurements |author=Jasper J. Goedbloed |publisher=EMCS |access-date=28 April 2014 }}</ref>

In two-port mathematical models, the network is described by a 2 by 2 square matrix of [[complex number]]s.  The common models that are used are referred to as {{mvar|z}}-''parameters'', {{mvar|y}}-''parameters'', {{mvar|h}}-''parameters'', {{mvar|g}}-''parameters'', and {{mvar|ABCD}}-''parameters'', each described individually below.  These are all limited to linear networks since an underlying assumption of their derivation is that any given circuit condition is a linear superposition of various short-circuit and open circuit conditions.  They are usually expressed in matrix notation, and they establish relations between the variables
:{{math|''V''{{sub|1}}}}, voltage across port 1
:{{math|''I''{{sub|1}}}}, current into port 1
:{{math|''V''{{sub|2}}}}, voltage across port 2
:{{math|''I''{{sub|2}}}}, current into port 2

which are shown in figure&nbsp;1.  The difference between the various models lies in which of these variables are regarded as the [[independent variable]]s.  These [[electric current|current]] and [[voltage]] variables are most useful at low-to-moderate frequencies. At high frequencies (e.g., microwave frequencies), the use of [[Power (physics)|power]] and [[energy]] variables is more appropriate, and the two-port current&ndash;voltage approach is replaced by an approach based upon [[scattering parameters]].