# Velocity factor

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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 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, relative to the speed of light. 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.

## 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.