# Coax Cable Velocity Factor

### The velocity factor of a coax cable is important in applications where phasing of signals is important – phased antennas, matching stubs and many other applications need a knowledge of the velocity factor.

The coax cable velocity factor is a parameter that is always mention in the datasheets for the different types of coaxial feeder.

The velocity factor is an important specification in some instances, although ordinary applications of simply feeding an antenna it may not be of importance.

The coax cable velocity factor reflects the fact that the speed at which a signal travels within a coax cable is not the same as an electromagnetic wave travelling in free space: it is reduced by a factor equal to the velocity factor.

## Coax velocity factor basics

The speed at which the signal travels in a medium is normally given the designation Vp or Vg. This is the speed at which the signal travels in comparison to that of a signal travelling in free space. Thus Vp for a signal travelling at the speed of light would be 1.0, and for one travelling at half the speed of light it would be 0.5.

It can be shown that the velocity factor of the cable is the reciprocal of the square root of the dielectric constant:

${V}_{p}=\frac{1}{\sqrt{\varepsilon }}$

## Coax cable electrical length

One important factor of a coax cable in some applications is the wavelength of the signals travelling in it. In the same way that the wavelength of a signal is the speed of light divided by the frequency for free space, the same is also true in any other medium. As the speed of the wave has been reduced, so too the wavelength is reduced by the same factor. Travelling at a slower speed the signal cannot travel as far in the same time.

Thus if the velocity factor of the coax cable is 0.66, then the wavelength is 0.66 times the wavelength in free space.

In some instances lengths of coax cable are cut to a specific length to act as an impedance transformer or a resonant circuit, then this needs to be taken into consideration when determining the required length of coax cable.

The advantage of using a coax cable with a low velocity factor is that the length of coax cable required for the resonant length is shorter than if it had a figure approaching 1. This can reduce the space required for items like resonant stubs. It can also reduce the cost as less coax is needed!

## Dielectric materials used in coax

There is a variety of materials that can be successfully used as dielectrics in coax cables. Each has its own dielectric constant, and as a result, coax cables that use different dielectric materials will exhibit different velocity factors.

Dielectric constants & velocity factors
of commonly used coax cable dielectric materials
Coax cable dielectric material Dielectric
constant
Velocity
factor
Polyethylene (PE) 2.3 0.659
Foam polyethylene 1.3 - 1.6 0.88 - 0.79
Air spaced polythene 0.84 – 0.88
Foam polystyrene 0.910
Solid PTFE 2.07 0.695
Air spaced PTFE 0.85 – 0.90

The velocity factor is determined by the dielectric of the coaxial cable. As the dielectric constant will not vary too much from the standard values, it is often sufficient to take the datasheet figures and then cut the cable accordingly. It is obviously best to cut it slightly long at first and then trim back a bit once in situ. In this way any stray effects from cable ends and the like can be accommodated.