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Encyclopedia > 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). Copy of the original phone of Graham Bell at the MusÃ©e des Arts et MÃ©tiers in Paris Telecommunication is the transmission of signals over a distance for the purpose of communication. ... A ratio is a dimensionless, or unitless, quantity denoting an amount or magnitude of one quantity relative to another. ... Amplitude is a nonnegative scalar measure of a waves magnitude of oscillation, that is, magnitude of the maximum disturbance in the medium during one wave cycle. ... A standing wave, also known as a stationary wave, is a wave that remains in a constant position. ... A standing wave. ...

The SWR is usually defined as a voltage ratio called the VSWR, for voltage standing wave ratio. 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 SWR. International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... In electricity, current refers to electric current, which is the flow of electric charge. ...

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). 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. ...

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: The characteristic impedance of a uniform transmission line is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. ... The term reflection coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered. ...

$Gamma = {V_r over V_f}.$

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: 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 = âˆ’1. ...

• 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.

For the calculation of VSWR, only the magnitude of Γ, denoted by ρ, is of interest. 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 it belongs. ...

At some points along the line the two waves interfere constructively, and the resulting amplitude Vmax is the sum of their amplitudes: Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...

$V_max = V_f + V_r = V_f + rho V_f = V_f (1 + rho).,$

At other points, the waves interfere destructively, and the resulting amplitude Vmin is the difference between their amplitudes:

$V_min = V_f - V_r = V_f - rho V_f = V_f ( 1 - rho).,$

The voltage standing wave ratio is then equal to:

$VSWR = {V_max over V_min} = {{1 + rho} over {1 - rho}}.$

As ρ, the magnitude of Γ, 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. Emax / Emin. In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ...

## Contents

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:

$V_f(x,t) = A sin (omega t - kx),,$

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: It has been suggested that this article or section be merged into Angular velocity. ...

$V_r(x,t) = rho A sin (omega t + kx).,$

The total voltage Vt on the transmission line is given by the principle of superposition, which is just a matter of adding the two waves: In physics, the principle of superposition states that the net displacement at a given place and time caused by two or more waves traversing the same space is the vector sum of the displacements which would have been produced by the individual waves separately. ...

$V_t(x,t) = A sin (omega t - kx) + rho A sin (omega t + kx).,$

Using standard trigonometric identities, this equation can be converted to the following form: Wikibooks has a book on the topic of Trigonometry Trigonometry (from the Greek trigonon = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right triangles). ...

$V_t(x,t) = A sqrt {4rhocos^2 kx+(1-rho)^2} cos(omega t + phi),,$

where ${tan phi}={{(1+rho)}over{(1-rho)}}cot(kx).$

This form of the equation shows, if we ignore some of the details, that the maximum voltage over time Vmot at a distance x from the transmitter is the periodic function

$V_mathrm{mot} = A sqrt {4rhocos^2 kx+(1-rho)^2}.$

This varies with x from a minimum of A(1 − ρ) to a maximum of A(1 + ρ), as we saw in the earlier, simplified discussion. A graph of Vmot against x, in the case when ρ = 0.5, is shown below. Vmin and Vmax 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. Image File history File links Swr. ...

## Practical implications of SWR

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

1. 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.
2. Matched impedances give ideal power transfer; mismatched impedances give high SWR and reduced power transfer.
3. Higher power in the transmission line also leaks back into the radio, which causes it to heat up.
4. 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.
5. 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 both TX and RX 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 plumbing[1] 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.
6. 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.

In electronics, solid state circuits are those that do not contain vacuum tubes. ... A dielectric, or electrical insulator, is a substance that is highly resistant to electric current. ... It has been suggested that this article or section be merged with Waveguide (optics). ... Beads of silica gel Silica gel is a granular, porous form of silica made synthetically from sodium silicate. ...

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. ... In telecommunication, a time-domain reflectometer (TDR) is an electronic instrument used to characterize and locate faults in metallic cables ( twisted pair, coax). ... The SWR meter or SWR metre when is commonly a VSWR meter which measures the standing wave ratio in a transmission line. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ...

## References

• Federal Standard 1037C and from MIL-STD-188
• The ARRL Handbook chapter 19: "Transmission lines"
• http://www.temcom.com/pages/dBCalc_manual.html
• 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.

Results from FactBites:

 Standing wave ratio - Wikipedia, the free encyclopedia (893 words) 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). The SWR is usually defined as a voltage ratio called the VSWR, for voltage standing wave ratio. 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.
 Standing Waves (530 words) In each case we represent the wave amplitude by a complex phasor whose length is proportional to the size of the wave and whose phase angle tells us the relative phase with respect to the origin or zero of the time variable. In the case of positive travelling waves, the phase decreases as (-j beta x) with increasing distance x from the generator; whereas for negative travelling waves the phase advances as (+ j beta x) with increasing distance x from the generator. In the case of a complex reflection coefficient gamma, the phase angle of gamma determines where along the line the first standing wave minimum lies, in terms of the wavelength and the position of the load.
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