Editing Reflection coefficient (section)

== Electrical networks ==
A transmission line is an example of a [[Two-port network|2-port]] [[electrical network]], but reflection coefficents are useful in the analysis of any electrical networks. A reflection coefficent for each port in the same way as for the boundary of a transmission line. It will, however, also depend on the porperties of connections at other ports and so is not a property intrinsic to the network itself. For a 2-port network with the 2x2 [[Scattering parameters|scattering matrix]] ''S'', and with a source and load connected to its input and output, where the reflections off the source back into the input are <math>\Gamma_S</math> and the reflections off the load back into the output are <math>\Gamma_L</math>, then the relfection coefficients at the input and output are given by:<ref>Pozar, David M. (2012); p. 197.</ref>

:<math>|\Gamma_\mathrm{in}| = \left|S_{11} + \frac{S_{12}S_{21}\Gamma_L}{1-S_{22}\Gamma_L}\right|</math> and <math>|\Gamma_\mathrm{out}| = \left|S_{22} + 
\frac{S_{12}S_{21}\Gamma_S}{1-S_{11}\Gamma_S} \right|</math>