Velocity factor

(Redirected from Wave propagation speed)

The velocity factor (VF),[1] also called wave propagation speed or velocity of propagation (VoP or $v_\mathrm{P}$),[2] of a transmission medium is the ratio of the speed at which a wavefront (of an acoustic signal, for example, or an electromagnetic signal, a radio signal, a light pulse in a fibre channel 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.

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).

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) 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 to travel one meter.

Some typical velocity factors for radio communications cables provided in handbooks and texts are:[4][5]

VF% Transmission line
82 RG-8X Belden 9258 coaxial cable (foamed polyethylene dielectric)
66 RG-213 CXP213 coaxial cable (solid polyethylene dielectric)

Calculating velocity factor

VF equals the reciprocal of the square root of the dielectric constant (relative permittivity), $\kappa$, of the material through which the signal passes:

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

The VF of a lossless transmission line is given by:

$\mathrm{VF} = { \frac{1}{c\sqrt{LC}} } \$

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 is the speed of light in vacuum.