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Voltage standing wave ratio (VSWR) (pronounced "vizwar" [1] [2]) is the ratio of maximum to minimum voltage on a transmission line . For example, a VSWR of 1.2 means a peak voltage 1.2 times the minimum voltage along that line, if the line is at least one half wavelength long.
In telecommunications and transmission line theory, the reflection coefficient is the ratio of the complex amplitude of the reflected wave to that of the incident wave. The voltage and current at any point along a transmission line can always be resolved into forward and reflected traveling waves given a specified reference impedance Z 0.
In radio frequency (RF) practice this is often measured in a dimensionless ratio known as voltage standing wave ratio (VSWR) with a VSWR bridge. The ratio of energy bounced back depends on the impedance mismatch. Mathematically, it is defined using the reflection coefficient. [2]
A time-domain reflectometer; an instrument used to locate the position of faults on lines from the time taken for a reflected wave to return from the discontinuity.. A signal travelling along an electrical transmission line will be partly, or wholly, reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impedance of the line, or if ...
where is the magnitude of the reflection coefficient. Note that as the reflection coefficient approaches zero, power to the load is maximized. If the reflection coefficient is known, mismatch can be calculated by = In terms of the voltage standing wave ratio :
The reflection coefficient can be calculated using: = +, where (Gamma) is the reflection coefficient (0 denotes full transmission, 1 full reflection, and 0.5 is a reflection of half the incoming voltage), and are the impedance of the first component (from which the wave enters) and the second component, respectively.
This is correct for reflection coefficients with a magnitude no greater than unity, which is usually the case. A reflection coefficient with a magnitude greater than unity, such as in a tunnel diode amplifier, will result in a negative value for this expression. VSWR, however, from its definition, is always positive.
Log area ratios (LAR) can be used to represent reflection coefficients (another form for linear prediction coefficients) for transmission over a channel. While not as efficient as line spectral pairs (LSPs), log area ratios are much simpler to compute. Let be the kth reflection coefficient of a filter, the kth LAR is: