# Reflection coefficient

The reflection coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered. A reflection coefficient describes the amplitude of a reflected wave relative to that of the incident wave. The reflection coefficient is closely related to the transmission coefficient. The reflectance of a system is also sometimes called a "reflection coefficient".

A wave experiences partial transmittance and partial reflectance when the medium through which it travels suddenly changes. The reflection coefficient determines the ratio of the reflected wave amplitude to the incident wave amplitude.

Different specialties have different applications for the term.

## Telecommunications

In telecommunications, the reflection coefficient is the ratio of the amplitude of the reflected wave to the amplitude of the incident wave. In particular, at a discontinuity in a transmission line, it is the complex ratio of the electric field strength of the reflected wave ($E^-$) to that of the incident wave ($E^+$). This is typically represented with a $\Gamma$ (capital gamma) and can be written as:

$\Gamma = \frac{E^-}{E^+}$

The reflection coefficient may also be established using other field or circuit quantities.

The reflection coefficient can be given by the equations below, where $Z_S$ is the impedance toward the source, $Z_L$ is the impedance toward the load:

Simple circuit configuration showing measurement location of reflection coefficient.

$\Gamma = {Z_L - Z_S\over Z_L + Z_S}$

Notice that a negative reflection coefficient means that the reflected wave receives a 180°, or $\pi$, phase shift.

The absolute magnitude (designated by vertical bars) of the reflection coefficient can be calculated from the standing wave ratio, $SWR$:

$| \Gamma | = {SWR-1 \over SWR+1}$

The reflection coefficient is displayed graphically using a Smith chart.

## Seismology

Reflection coefficient is used in feeder testing for reliability of medium.

## Optics and microwaves

In optics, "reflection coefficient" can refer to either the amplitude reflection coefficient described here, or the reflectance, depending on context. Typically, the reflectance is represented by a capital R, while the amplitude reflection coefficient is represented by a lower-case r.

## Semipermeable membranes

The reflection coefficient in semipermeable membranes relates to how such a membrane can reflect solute particles from passing through. A value of zero results in all particles passing through. A value of one is such that no particle can pass. It is used in the Starling equation.