Voltage standing wave ratio - encyclopedia article about Voltage standing wave ratio.

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.

Relationship to the Reflection Coefficient

The voltage component of a standing wave in a uniform transmission line consists of the forward wave (with amplitude $\text{[math]}$ ) superimposed on the reflected wave (with amplitude $\text{[math]}$ ).

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 $\text{[math]}$ is defined thus:

$\text{[math]}$

$\text{[math]}$ is a complex number that describes both the magnitude and the phase shift of the reflection. The simplest cases, when the imaginary part of $\text{[math]}$ is zero, are:

$\text{[math]}$ : maximum negative reflection, when the line is short-circuited,
$\text{[math]}$ : no reflection, when the line is perfectly matched,
$\text{[math]}$ : maximum positive reflection, when the line is open-circuited.

For the calculation of VSWR, only the magnitude of $\text{[math]}$ , denoted by ρ, is of interest.

At some points along the line the two waves interfere constructively, and the resulting amplitude $\text{[math]}$ is the sum of their amplitudes:

$\text{[math]}$

At other points, the waves interfere destructively, and the resulting amplitude $\text{[math]}$ is the difference between their amplitudes:

$\text{[math]}$

The voltage standing wave ratio is then equal to:

$\text{[math]}$

As ρ, the magnitude of $\text{[math]}$ , always falls in the range [0,1], the VSWR is always ≥ +1.

The SWR can also be defined as the ratio of the maximum amplitude of the electric field strength to its minimum amplitude, i.e. $\text{[math]}$ .

Further analysis

To understand the standing wave ratio in detail, we need to calculate the voltage (or, equivalently, the electrical field strength) at any point along the transmission line at any moment in time. We can begin with the forward wave, whose voltage as a function of time t and of distance x along the transmission line is:

$\text{[math]}$

where A is the amplitude of the forward wave, ω is its angular frequency and k is a constant (equal to ω divided by the speed of the wave). The voltage of the reflected wave is a similar function, but spatially reversed (the sign of x is inverted) and attenuated by the reflection coefficient ρ:

$\text{[math]}$

The total voltage $\text{[math]}$ on the transmission line is given by the principle of superposition, which is just a matter of adding the two waves:

$\text{[math]}$

Using standard trigonometric identities, this equation can be converted to the following form:

$\text{[math]}$

where $\text{[math]}$

This form of the equation shows, if we ignore some of the details, that the maximum voltage over time $\text{[math]}$ at a distance x from the transmitter is the periodic function

$\text{[math]}$

This varies with x from a minimum of $\text{[math]}$ to a maximum of $\text{[math]}$ , as we saw in the earlier, simplified discussion. A graph of $\text{[math]}$ against x, in the case when ρ = 0.5, is shown below. $\text{[math]}$ and $\text{[math]}$ are the values used to calculate the SWR.

Standing wave ratio for ρ = 0.5

It is important to note that this graph does not show the instantaneous voltage profile along the transmission line. It only shows the maximum amplitude of the oscillation at each point. The instantaneous voltage is a function of both time and distance, so could only be shown fully by a three-dimensional or animated graph.

Practical implications of SWR

SWR has a number of implications that are directly applicable to radio use.

SWR is an indicator of reflected waves bouncing back and forth within the transmission line, and as such, an increase in SWR corresponds to an increase in power in the line beyond the actual transmitted power. This increased power will increase RF losses, as increased voltage increases dielectric losses, and increased current increases resistive losses.
Matched impedances give ideal power transfer; mismatched impedances give high SWR and reduced power transfer.
Higher power in the transmission line also leaks back into the radio, which causes it to heat up.
The higher voltages associated with a sufficiently high SWR could damage the transmitter. solid state radios which have a lower tolerance for high voltages may automatically reduce output power to prevent damage. Tube radios may arc. The high voltages may also cause transmission line dielectric to break down and/or burn.
VSWR measurements may be taken to ensure that a waveguide is contiguous and has no leaks or sharp bends. If such bends or holes are present in the waveguide surface, they may diminish the performance of transmitter and receiver equipment strings. Arcing may occur if there is a hole, if transmitting at high power, usually 200 watts or more (Need reference for the power statement). Waveguide plumbinghttp://www.fnrf.science.cmu.ac.th/theory/waveguide/Waveguide%20theory%2012.html is crucial for proper waveguide performance. Reflected power may occur and damage equipment as well. Another cause of bad VSWR in a waveguide is moisture build-up, which can typically be prevented with silica gel or pressurization of the waveguide with dry gas.
A very long run of coaxial cable especially at a frequency where the cable itself is lossy can appear to a radio as a matched load. The power coming back is, in these cases, partially or almost completely lost in the cable run.

References

Federal Standard 1037C and from MIL-STD-188
The ARRL Handbook chapter 19: "Transmission lines"
http://www.temcom.com/pages/dBCalc_manual.html
http://www.haefely.com/literature/pdf/emc/Cond_RF_Application_Note_01.pdf (obsolete link)
Understanding the Fundamental Principles of Vector Network Analysis, Hewlett Packard Application note 1287-1, 1997 (Online PDF copy here)
An online conversion tool between VSWR, return loss and reflection coefficient.

External links

Online VSWR Calculator

Telecommunication is the transmission of signals over a distance for the purpose of communication. In modern times, this process typically involves the sending of electromagnetic waves by electronic transmitters, but in earlier times telecommunication may have involved the use of
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amplitude is a nonnegative scalar measure of a wave's magnitude of oscillation, that is, the magnitude of the maximum disturbance in the medium during one wave cycle.

Sometimes this distance is called the peak amplitude
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standing wave, also known as a stationary wave, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves
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node is a point along a standing wave where the wave has minimal amplitude. This has implications in several fields. For instance, in a guitar string, the ends of the string are nodes.
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A transmission line is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission.
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Voltage (sometimes also called electric potential difference or electrical tension) is the potential similarity of electrical potential between two points of an electrical or electronic circuit, expressed in volts.
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Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second.

Definition

The amount of electric current (measured in amperes) through some surface, e.g.
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characteristic impedance or surge impedance of a uniform transmission line, usually written , is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections.
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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.
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In mathematics, a complex number is a number of the form

where a and b are real numbers, and i is the imaginary unit, with the property i ² = −1.
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For other senses of this word, see magnitude.

The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which
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Interference is the addition (superposition) of two or more waves that results in a new wave pattern.

As most commonly used, the term interference usually refers to the interaction of waves which are correlated or coherent with each other, either because they
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electric field. This electric field exerts a force on other electrically charged objects. The concept of electric field was introduced by Michael Faraday.

The electric field is a vector field with SI units of newtons per coulomb (N C⁻¹
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angular frequency ω (also referred to by the terms angular speed, radial frequency, and radian frequency) is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity.
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The principle of superposition can refer to several different scientific concepts:

Superposition principle in linear algebra, which describes how certain physical quantities behave when occurring at the same place and time.

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Trigonometry (from Greek trigōnon "triangle" + metron "measure"^[1]), informally called trig, is a branch of mathematics that deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right angled
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The term solid state was introduced in the 1960s to describe electronic devices whose circuits contained neither vacuum tubes nor mechanical devices such as relays, as transistors replaced vacuum tubes in most consumer electronics.
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A dielectric is a physical model commonly used to describe how an electric field behaves inside a material. It is characterised by how an electric field interacts with an atom. It is possible to approach dielectrics from either a classical interpretation or a quantum one.
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waveguide may refer to any linear structure that guides electromagnetic waves. However, the original and most common meaning is a hollow metal pipe used for this purpose.

A dielectric waveguide employs a solid dielectric rod rather than a hollow pipe.
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Silica gel is a granular, porous form of silica made synthetically from sodium silicate. Despite the name, silica gel is a solid.

Silica gel is most commonly encountered in everyday life as beads packed in a semi-permeable plastic.
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In telecommunication, return loss is the ratio, at the junction of a transmission line and a terminating impedance or other discontinuity, of the amplitude of the reflected wave to the amplitude of the incident wave.
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A time-domain reflectometer (TDR) is an electronic instrument used to characterize and locate faults in metallic cables (for example, twisted wire pairs, coaxial cables) and, in the OTDR domain: optical fibers.
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The SWR meter or VSWR (voltage standing wave ratio) meter measures the standing wave ratio in a transmission line. This is an item of radio equipment used to check the quality of the match between the antenna and the transmission line.
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Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current (AC). Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative magnitudes of the voltage and current, but also the
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Federal Standard 1037C, entitled Telecommunications: Glossary of Telecommunication Terms is a United States Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended.
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MIL-STD-188 is a series of U.S. military standards relating to telecommunications.

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Key people Bill Hewlett, Co-founder
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Standing wave ratio
(redirected from Voltage standing wave ratio)

Relationship to the Reflection Coefficient

Further analysis

Practical implications of SWR

See also

References

External links

Definition

Purpose

Standing wave ratio (redirected from Voltage standing wave ratio)

Relationship to the Reflection Coefficient

Further analysis

Practical implications of SWR

See also

References

External links

Definition

Purpose

Standing wave ratio
(redirected from Voltage standing wave ratio)