# Velocity factor

(Redirected from Wave propagation speed)

The velocity factor (VF), also called wave propagation speed or velocity of propagation (VoP or $v_{\mathrm {P} }$ ), 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 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, 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 for network cables
VF (%) Cable Ethernet physical layer
74–79 Cat-7 twisted pair
77 RG-8/U Minimum for 10BASE5
67 Optical fiber (silica glass) Minimum for 10BASE-FL, 100BASE-FX, ...
67 Plastic optical fiber (PMMA) 1000BASE-RHx
63 Plastic optical fiber (polystyrene)
65 RG-58A/U Minimum for 10BASE2
65 Cat-6A twisted pair 10GBASE-T
64 Cat-5e twisted pair 100BASE-TX, 1000BASE-T
58.5 Cat-3 twisted pair Minimum for 10BASE-T

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

VF (%) Transmission line
93 HJ8-50B 3 inch Heliax coaxial cable (air dielectric)
86 RG-8 Belden 7810A coaxial cable (gas-injected foam high-density polyethylene)
83 RG-6 Belden 1189A coaxial cable, RG-11 Belden 1523A coaxial cable
82 RG-8X Belden 9258 coaxial cable (foamed polyethylene dielectric)
77 RG-8/U generic (foamed polyethylene)
66 Belden 8723 twin shielded twisted pair stranded (polypropylene insulator)
66 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), $\kappa$ or $\epsilon _{\mathrm {r} }$ , of the material through which the signal passes:

$\mathrm {VF} ={\frac {1}{\sqrt {\kappa }}}\$ in the usual case where the relative permeability, $\mu _{\mathrm {r} }$ , is 1. In the most general case:

$\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:

$\mathrm {VF} ={\frac {1}{c_{\mathrm {0} }{\sqrt {L'C'}}}}\$ where $L'$ is the distributed inductance (in henries per unit length), $C'$ is the capacitance between the two conductors (in farads per unit length), and $c_{\mathrm {0} }$ is the speed of light in vacuum.

### Optical wave

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

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