# Velocity factor

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The velocity factor (VF), [1] also called wave propagation speed or velocity of propagation (VoP or ${\displaystyle v_{\mathrm {P} }}$), [2] of a transmission medium is the ratio of the speed at which a wavefront (of an electromagnetic signal, a radio signal, a light pulse in an optical fibre or a change of the electrical voltage on a copper wire) passes through the medium, to the speed of light in a vacuum. For optical signals, the velocity factor is the reciprocal of the refractive index.

A transmission medium is a material substance that can propagate energy waves. For example, the transmission medium for sounds is usually a gas, but solids and liquids may also act as a transmission medium for sound.

In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as

## Contents

The speed of radio signals in a vacuum, for example, is the speed of light, and so the velocity factor of a radio wave in a vacuum is unity, or 100%. In electrical cables, the velocity factor mainly depends on the insulating material (see table below).

Vacuum is space devoid of matter. The word stems from the Latin adjective vacuus for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often discuss ideal test results that would occur in a perfect vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is lower than atmospheric pressure. The Latin term in vacuo is used to describe an object that is surrounded by a vacuum.

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299,792,458 metres per second. It is exact because by international agreement a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299792458 second. According to special relativity, c is the maximum speed at which all conventional matter and hence all known forms of information in the universe can travel. Though this speed is most commonly associated with light, it is in fact the speed at which all massless particles and changes of the associated fields travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. In the special and general theories of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.

The use of the terms velocity of propagation and wave propagation speed to mean a ratio of speeds is confined to the computer networking and cable industries. In a general science and engineering context, these terms would be understood to mean a true speed or velocity in units of distance per time, [3] while velocity factor is used for the ratio.

## Typical velocity factors

Velocity factor is an important characteristic of communication media such as category 5 cables and radio transmission lines. Plenum data cable typically has a VF between 0.42 and 0.72 (42% to 72% of the speed of light in a vacuum) and riser cable around 0.70. A VF of 0.70 corresponds to a speed of approximately 210,000,000 m/s or 4.76 ns per metre.

Category 5 cable, commonly referred to as Cat 5, is a twisted pair cable for computer networks. Since 2001, the variant commonly in use is the Category 5e specification (Cat 5e). The cable standard provides performance of up to 100 MHz and is suitable for most varieties of Ethernet over twisted pair up to 1000BASE-T. Cat 5 is also used to carry other signals such as telephony and video.

In radio-frequency engineering, a transmission line is a specialized cable or other structure designed to conduct alternating current of radio frequency, that is, currents with a frequency high enough that their wave nature must be taken into account. Transmission lines are used for purposes such as connecting radio transmitters and receivers with their antennas, distributing cable television signals, trunklines routing calls between telephone switching centres, computer network connections and high speed computer data buses.

Plenum cable is electrical cable that is laid in the plenum spaces of buildings. In the United States, plastics used in the construction of plenum cable are regulated under the National Fire Protection Association standard NFPA 90A: Standard for the Installation of Air Conditioning and Ventilating Systems. All materials intended for use on wire and cables to be placed in plenum spaces are designed to meet rigorous fire safety test standards in accordance with NFPA 262 and outlined in NFPA 90A.

Minimum velocity factors for network cables
VF (%)Cable Ethernet physical layer
74–79 Cat-7 twisted pair
77RG-8/UMinimum for 10BASE5 [4]
67 Optical fiber Minimum for 10BASE-FL, [5] 100BASE-FX, ...
65RG-58A/UMinimum for 10BASE2 [6]
65 Cat-6A twisted pair 10GBASE-T
64 Cat-5e twisted pair 100BASE-TX, 1000BASE-T
58.5 Cat-3 twisted pairMinimum for 10BASE-T [7]

Some typical velocity factors for radio communications cables provided in handbooks and texts are given in the following table: [8] [9]

VF (%)Transmission line
93HJ8-50B 3 inch Heliax coaxial cable (air dielectric) [10]
86RG-8 Belden 7810A coaxial cable (gas-injected foam high-density polyethylene) [11]
83RG-6 Belden 1189A coaxial cable, RG-11 Belden 1523A coaxial cable
82RG-8X Belden 9258 coaxial cable (foamed polyethylene dielectric)
77RG-8/U generic (foamed polyethylene)
66Belden 8723 twin shielded twisted pair stranded (polypropylene insulator) [12]
66RG-213 CXP213 (solid polyethylene dielectric)

## Calculating velocity factor

### Electric wave

VF equals the reciprocal of the square root of the dielectric constant (relative permittivity), ${\displaystyle \kappa }$ or ${\displaystyle \epsilon _{\mathrm {r} }}$, of the material through which the signal passes:

In mathematics, a square root of a number a is a number y such that y2 = a; in other words, a number y whose square (the result of multiplying the number by itself, or yy) is a. For example, 4 and −4 are square roots of 16 because 42 = (−4)2 = 16. Every nonnegative real number a has a unique nonnegative square root, called the principal square root, which is denoted by a, where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, which is denoted by 9 = 3, because 32 = 3 · 3 = 9 and 3 is nonnegative. The term (or number) whose square root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this example 9.

The relative permittivity of a material is its (absolute) permittivity expressed as a ratio relative to the vacuum permittivity.

${\displaystyle \mathrm {VF} ={\frac {1}{\sqrt {\kappa }}}\ }$

in the usual case where the relative permeability, ${\displaystyle \mu _{\mathrm {r} }}$, is 1. In the most general case:

${\displaystyle \mathrm {VF} ={\frac {1}{\sqrt {\mu _{\mathrm {r} }\epsilon _{\mathrm {r} }}}}\ }$

which includes unusual magnetic conducting materials, such as ferrite.

The velocity factor for a lossless transmission line is given by:

${\displaystyle \mathrm {VF} ={\frac {1}{c_{\mathrm {0} }{\sqrt {L'C'}}}}\ }$

where ${\displaystyle L'}$ is the distributed inductance (in henries per unit length), ${\displaystyle C'}$ is the capacitance between the two conductors (in farads per unit length), and ${\displaystyle c_{\mathrm {0} }}$ is the speed of light in vacuum.

### Optical wave

VF equals the reciprocal of the refractive index ${\displaystyle {n}}$ of the medium, usually optical fiber.

${\displaystyle \mathrm {VF} ={\frac {1}{n}}\ }$

## Related Research Articles

The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.

In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital communication, used in applications such as digital television and audio broadcasting, DSL internet access, wireless networks, power line networks, and 4G mobile communications.

The propagation constant of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it propagates in a given direction. The quantity being measured can be the voltage, the current in a circuit, or a field vector such as electric field strength or flux density. The propagation constant itself measures the change per unit length, but it is otherwise dimensionless. In the context of two-port networks and their cascades, propagation constant measures the change undergone by the source quantity as it propagates from one port to the next.

The total harmonic distortion (THD) is a measurement of the harmonic distortion present in a signal and is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency. Distortion factor, a closely related term, is sometimes used as a synonym.

Coaxial cable, or coax is a type of electrical cable that has an inner conductor surrounded by a tubular insulating layer, surrounded by a tubular conducting shield. Many coaxial cables also have an insulating outer sheath or jacket. The term coaxial comes from the inner conductor and the outer shield sharing a geometric axis. Coaxial cable was invented by English engineer and mathematician Oliver Heaviside, who patented the design in 1880.

Line-of-sight propagation is a characteristic of electromagnetic radiation or acoustic wave propagation which means waves travel in a direct path from the source to the receiver. Electromagnetic transmission includes light emissions traveling in a straight line. The rays or waves may be diffracted, refracted, reflected, or absorbed by the atmosphere and obstructions with material and generally cannot travel over the horizon or behind obstacles.

Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices.

In the physical sciences, the wavenumber is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas temporal frequency can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance.

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.

Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor, and decreases with greater depths in the conductor. The electric current flows mainly at the "skin" of the conductor, between the outer surface and a level called the skin depth. The skin effect causes the effective resistance of the conductor to increase at higher frequencies where the skin depth is smaller, thus reducing the effective cross-section of the conductor. The skin effect is due to opposing eddy currents induced by the changing magnetic field resulting from the alternating current. At 60 Hz in copper, the skin depth is about 8.5 mm. At high frequencies the skin depth becomes much smaller. Increased AC resistance due to the skin effect can be mitigated by using specially woven litz wire. Because the interior of a large conductor carries so little of the current, tubular conductors such as pipe can be used to save weight and cost.

In physics, a wave vector is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave, and its direction is ordinarily the direction of wave propagation.

The Heaviside condition, named for Oliver Heaviside (1850–1925), is the condition an electrical transmission line must meet in order for there to be no distortion of a transmitted signal. Also known as the distortionless condition, it can be used to improve the performance of a transmission line by adding loading to the cable.

Microstrip is a type of electrical transmission line which can be fabricated using printed circuit board technology, and is used to convey microwave-frequency signals. It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. Microwave components such as antennas, couplers, filters, power dividers etc. can be formed from microstrip, with the entire device existing as the pattern of metallization on the substrate. Microstrip is thus much less expensive than traditional waveguide technology, as well as being far lighter and more compact. Microstrip was developed by ITT laboratories as a competitor to stripline.

The signal velocity is the speed at which a wave carries information. It describes how quickly a message can be communicated between two separated parties. No signal velocity can exceed the speed of a light pulse in a vacuum.

The relative velocity is the velocity of an object or observer B in the rest frame of another object or observer A.

The telegrapher's equations are a pair of coupled, linear differential equations that describe the voltage and current on an electrical transmission line with distance and time. The equations come from Oliver Heaviside who in the 1880s developed the transmission line model. The model demonstrates that the electromagnetic waves can be reflected on the wire, and that wave patterns can appear along the line. The theory applies to transmission lines of all frequencies including high-frequency transmission lines, audio frequency, low frequency and direct current.

The word electricity refers generally to the movement of electrons through a conductor in the presence of potential and an electric field. The speed of this flow has multiple meanings. In everyday electrical and electronic devices, the signals or energy travel as electromagnetic waves typically on the order of 50%–99% of the speed of light, while the electrons themselves move (drift) much more slowly.

The primary line constants are parameters that describe the characteristics of conductive transmission lines, such as pairs of copper wires, in terms of the physical electrical properties of the line. The primary line constants are only relevant to transmission lines and are to be contrasted with the secondary line constants, which can be derived from them, and are more generally applicable. The secondary line constants can be used, for instance, to compare the characteristics of a waveguide to a copper line, whereas the primary constants have no meaning for a waveguide.

## References

1. Gottlieb, I.M., Practical RF power design techniques, TAB Books, 1993, ISBN   0-8306-4129-7, p.251 ('velocity factor')
2. Velocity of Propagation , General Cable Australia Pty Ltd, retrieved 2010-02-13
3. "velocity of propagation" in Walker, P.M.B., Chambers Science and Technology Dictionary, Edinburgh, 1991, ISBN   1-85296-150-3
4. IEEE 802.3 Clause 8.4.1.3
5. IEEE 802.3 Clause 15.3.1.3
6. IEEE 802.3 Clause 10.5.1.3
7. IEEE 802.3 Clause 14.4.2.4
8. H. Ward Silver, N0AX, ed. (2011). "Chapter 22: Component Data and References". The ARRL Handbook For Radio Communications (88th ed.). ARRL. p. 22.48. ISBN   978-0-87259-096-0.
9. Kaiser, Kenneth L. (2005). Transmission Lines, Matching, and Crosstalk. CRC Press. pp. 2–24. ISBN   9780849363627.
10. "8723 Multi-Conductor - Shielded Twisted Pair Cable" (PDF). Belden.com. Retrieved 2017-07-06.