Velocity factor

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The velocity factor (VF), [1] also called wave propagation speed or velocity of propagation (VoP or ), [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.

Transmission medium material substance that can propagate energy waves

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.

Radio technology of using radio waves to carry information

Radio is the technology of signalling or communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmitter connected to an antenna which radiates the waves, and received by a radio receiver connected to another antenna. Radio is very widely used in modern technology, in radio communication, radar, radio navigation, remote control, remote sensing and other applications. In radio communication, used in radio and television broadcasting, cell phones, two-way radios, wireless networking and satellite communication among numerous other uses, radio waves are used to carry information across space from a transmitter to a receiver, by modulating the radio signal in the transmitter. In radar, used to locate and track objects like aircraft, ships, spacecraft and missiles, a beam of radio waves emitted by a radar transmitter reflects off the target object, and the reflected waves reveal the object's location. In radio navigation systems such as GPS and VOR, a mobile receiver receives radio signals from navigational radio beacons whose position is known, and by precisely measuring the arrival time of the radio waves the receiver can calculate its position on Earth. In wireless remote control devices like drones, garage door openers, and keyless entry systems, radio signals transmitted from a controller device control the actions of a remote device.

Refractive index optical characteristic of a material

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


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 Space that is empty of matter

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.

Speed of light speed at which all massless particles and associated fields travel in 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 twisted pair cable for carrying signals

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.

Transmission line specialized cable or other structure designed to carry alternating current of radio frequency

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
95–99 Open-wire "Ladder" 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)
80Belden 9085 twin-lead
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), or , of the material through which the signal passes:

Square root inverse operation of square for finding the original base number

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.

Relative permittivity

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

in the usual case where the relative permeability, , is 1. In the most general case:

which includes unusual magnetic conducting materials, such as ferrite.

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

where is the distributed inductance (in henries per unit length), is the capacitance between the two conductors (in farads per unit length), and is the speed of light in vacuum.

Optical wave

VF equals the reciprocal of the refractive index of the medium, usually optical fiber.

See also

Related Research Articles

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Skin effect

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.

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Primary line constants

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.


  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
  5. IEEE 802.3 Clause
  6. IEEE 802.3 Clause
  7. IEEE 802.3 Clause
  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.
  12. "8723 Multi-Conductor - Shielded Twisted Pair Cable" (PDF). Retrieved 2017-07-06.