Velocity factor

Template:Short description The velocity factor (VF),<ref>Gottlieb, I.M., Practical RF power design techniques, TAB Books, 1993, Template:ISBN, p.251 ('velocity factor')</ref> also called wave propagation (relative) speed or (relative) velocity of propagation (VoP or Template:Nobreak<ref>Velocity of Propagation, General Cable Australia Pty Ltd, retrieved 2010-02-13</ref> 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 vacuum. For optical signals, the velocity factor is the reciprocal of the refractive index.

The speed of radio signals in vacuum, for example, is the speed of light, and so the velocity factor of a radio wave in vacuum is 1.0 (unity). In air, the velocity factor is ~0.9997. In electrical cables, the velocity factor mainly depends on the insulating material (see table below).

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,<ref>"velocity of propagation" in Walker, P.M.B., Chambers Science and Technology Dictionary, Edinburgh, 1991, Template:ISBN</ref> 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 vacuum) and riser cable around 0.70 (approximately 210,000,000 m/s or 4.76 ns per metre).

Minimum velocity factors allowed for network cable standards

VF (%)	Cable type	Ethernet physical layer
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	Cat-7 twisted pair
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	RG-8/U	Minimum for 10BASE5<ref>IEEE 802.3 Clause 8.4.1.3 The minimum required velocity of propagation is 0.77 c.</ref>
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	Optical fiber (silica glass)	Minimum for 10BASE-FL,<ref>IEEE 802.3 clause 15.3.1.3 The propagation delay shall be ≤5 μs/km. (This is equivalent to a velocity of propagation of 0.67c.)</ref> 100BASE-FX, ...
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	Plastic optical fiber	1000BASE-RHx PMMA
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	Plastic optical fiber	polystyrene
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	RG-58A/U	Minimum for 10BASE2<ref>IEEE 802.3 Clause 10.5.1.3 The minimum required velocity of propagation is 0.65 c.</ref>
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	Cat-6A twisted pair	10GBASE-T
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	Cat-5e twisted pair	100BASE-TX, 1000BASE-T
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	Cat-3 twisted pair	Minimum for 10BASE-T<ref>IEEE 802.3 Clause 14.4.2.4 The maximum propagation delay of twisted pair shall be 5.7 ns/m (minimum velocity of 0.585 × c).</ref>

Some typical velocity factors for radio communications cables provided in handbooks and texts are given in the following table:<ref>Template:Cite book</ref><ref>Template:Cite book</ref>

VF (%)	Transmission line	Center insulation
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	open-wire line ("ladder line")	air insulated
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	HJ8-50B 3 inch Heliax coaxial cable	citation	CitationClass=web }}</ref>
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	RG-8 Belden 7810A coaxial cable	gas-injected foamed high-density polyethylene<ref>Template:Cite report</ref>
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	RG-6 Belden 1189A coaxial cable, RG-11 Belden 1523A coaxial cable
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	RG-8X Belden 9258 coaxial cable	foamed polyethylene dielectric
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	Belden 9085 twin-lead
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	RG-8/U generic	foamed polyethylene
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	Belden 8723 twin shielded stranded twisted pair	citation	CitationClass=web }}</ref>
check|unknown=|preview=Page using Template:Center with unknown parameter "_VALUE_"|ignoreblank=y| 1 | style }}	RG-213 CXP213	solid polyethylene dielectric

Calculating velocity factor

Electric wave

VF equals the reciprocal of the square root of the dielectric constant (relative permittivity), <math>\kappa</math> or <math>\epsilon_\mathrm{r}</math>, of the material through which the signal passes:

<math>\mathrm{VF} = { \frac{1}{\sqrt{\kappa}} } \ </math>

in the usual case where the relative permeability, <math>\mu_\mathrm{r}</math>, is 1. In the most general case:

<math>\mathrm{VF} = { \frac{1}{\sqrt{\mu_\mathrm{r}\epsilon_\mathrm{r}}} } \ </math>

which includes unusual magnetic conducting materials, such as ferrite.

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

<math>\mathrm{VF} = { \frac{1}{c_\mathrm{0}\sqrt{L'C'}} } \ </math>

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

Optical wave

VF equals the reciprocal of the refractive index <math>{n}</math> of the medium, usually optical fiber.

<math>\mathrm{VF} = { \frac{1}{n} } \ </math>

See also

• Coaxial cable
• Propagation delay
• Signal velocity
• Speed of electricity
• Speed of sound
• Telegrapher's equations