Velocity factor

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
95–99	Open-wire "Ladder" Line
80	Belden 9085 twin-lead
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.

See also

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

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. 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.
5. Kaiser, Kenneth L. (2005). Transmission Lines, Matching, and Crosstalk. CRC Press. p. 2-24. ISBN 9780849363627.