Editing Two-port network (section)

==Scattering parameters (S-parameters)==
{{main|Scattering parameters}}
[[File:two-port S-parameters.svg|thumb|right|'''Fig. 17.''' Terminology of waves used in {{mvar|S}}-parameter definition.]]
The previous parameters are all defined in terms of voltages and currents at ports.  {{mvar|S}}-parameters are different, and are defined in terms of incident and [[Signal reflection|reflected waves]] at ports.  {{mvar|S}}-parameters are used primarily at [[UHF]] and [[microwave]] frequencies where it becomes difficult to measure voltages and currents directly.  On the other hand, incident and reflected power are easy to measure using [[directional coupler]]s.  The definition is,<ref name=Vas137>Vasileska & Goodnick, p. 137</ref>

:<math> \begin{bmatrix} b_1 \\ b_2 \end{bmatrix} = \begin{bmatrix} S_{11} & S_{12} \\ S_{21} & S_{22} \end{bmatrix} \begin{bmatrix} a_1 \\ a_2 \end{bmatrix} </math>

where the {{mvar|a{{sub|k}}}} are the incident waves and the {{mvar|b{{sub|k}}}} are the reflected waves at port {{mvar|k}}.  It is conventional to define the {{mvar|a{{sub|k}}}} and {{mvar|b{{sub|k}}}} in terms of the square root of power.  Consequently, there is a relationship with the wave voltages (see main article for details).<ref>Egan, pp. 11–12</ref>

For reciprocal networks {{math|1=''S''{{sub|12}} = ''S''{{sub|21}}}}.  For symmetrical networks {{math|1=''S''{{sub|11}} = ''S''{{sub|22}}}}.  For antimetrical networks {{math|1=''S''{{sub|11}} = –''S''{{sub|22}}}}.<ref>Carlin, p. 304</ref>  For lossless reciprocal networks <math>|S_{11}| = |S_{22}|</math> and <math> |S_{11}|^2 + |S_{12}|^2 = 1.</math><ref>Matthaei et al, p. 44.</ref>