# Standing wave ratio

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In telecommunications, standing wave ratio (SWR) is the ratio of the amplitude of a partial standing wave at an antinode (maximum) to the amplitude at an adjacent node (minimum), in an electrical transmission line.

The SWR is usually defined as a voltage ratio called the VSWR, for voltage standing wave ratio. For example, the VSWR value 1.2:1 denotes a maximum standing wave amplitude that is 1.2 times greater than the minimum standing wave value. It is also possible to define the SWR in terms of current, resulting in the ISWR, which has the same numerical value. The power standing wave ratio (PSWR) is defined as the square of the VSWR.

SWR is used as a efficiency measure for transmission lines, electrical cables that conduct radio frequency signals, used for purposes such as connecting radio transmitters and receivers with their antennas, and distributing cable television signals. A problem with transmission lines is that impedance mismatches in the cable tend to reflect the radio waves back toward the source end of the cable, preventing all the power from reaching the destination end. SWR measures the relative size of these reflections. An ideal transmission line would have an SWR of 1:1, with all the power reaching the destination and no reflected power. An infinite SWR represents complete reflection, with all the power reflected back down the cable. The SWR of a transmission line is measured with an instrument called an SWR meter, and checking the SWR is a standard part of installing and maintaining transmission lines.

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### Relationship to the reflection coefficient

The voltage component of a standing wave in a uniform transmission line consists of the forward wave (with amplitude Vf) superimposed on the reflected wave (with amplitude Vr).

Reflections occur as a result of discontinuities, such as an imperfection in an otherwise uniform transmission line, or when a transmission line is terminated with other than its characteristic impedance. The reflection coefficient Γ is defined thus:

Γ is a complex number that describes both the magnitude and the phase shift of the reflection. The simplest cases, when the imaginary part of Γ is zero, are:

• Γ = − 1: maximum negative reflection, when the line is short-circuited,
• Γ = 0: no reflection, when the line is perfectly matched,
• Γ = + 1: maximum positive reflection, when the line is open-circuited.