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 either the amplitude or the intensity of a reflected wave relative to an incident wave. The reflection coefficient is closely related to the transmission coefficient.

A wave experiences partial transmittance and partial reflectance when the medium through which it travels suddenly changes.

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 (<math>E^-</math>) to that of the incident wave (<math>E^+</math>). This is typically represented with a <math>\Gamma</math> (capital gamma) and can be written as:

<math>\Gamma = \frac{E^-}{E^+} </math>

The reflection coefficient may also be established using other field or circuit quantities. The reflection coefficient can be given by the equations below, where <math>Z_S</math> is the impedance toward the source, <math>Z_L</math> is the impedance toward the load:

Simple circuit configuration showing measurement location of reflection coefficient.

<math>\Gamma = {Z_L - Z_S \over Z_L + Z_S}</math>

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

<math>| \Gamma | = {SWR - 1 \over SWR + 1}</math>

The reflection coefficient is displayed graphically using a Smith chart. Source: from Federal Standard 1037C in support of MIL-STD-188

Seismology

See: reflection seismology

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

Optics

Main article: Fresnel equations

In optics, both intensity and amplitude reflection coefficients are used. Typically, the former are represented by a capital R, while the latter are 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.

References

Books

• Bogatin, Eric (2004). Signal Integrity - Simplified. Upper Saddle River, New Jersey: Pearson Education, Inc.. ISBN 0-13-066946-6.  Figure 8-2 and Eqn. 8-1 Pg. 279