Tutorial on Wavelength – and Dielectric Constant or Velocity Factor

Dielectric Constant
For any capacitor, and that includes the structure of coaxial cable, the capacitance (the ability to store charge) is a function of the material that separates the “plates” of the capacitor. The material that separates the plates is described as the “dielectric” and can range from a vacuum to air and on to more dense dielectrics like polyethylene or PTFE (Teflon). Not just the capacitance is affected. The dielectric material also affects the breakdown voltage. In general, changing the dielectric from vacuum or air to some other dielectric increases the capacitance. The ratio of the capacitance of a particular structure with any given dielectric other than air – to the capacitance of the same structure with an air dielectric – is called the Dielectric Coefficient, or e for that material. Or….. expressed as a formula:

The speed that a signal travels within a coax cable is not the same as an electromagnetic wave travelling in free space. Instead, it is affected by the dielectric that is used within the coax cable. This has the effect of slowing the wave, or signal, down. This can be of great importance in some applications (usually where line is being used to perform an impedance transformation), although for many purposes it does not need to be known.

Velocity factor

The velocity factor is the fraction of the speed at which the signal travels when compared to a signal travelling in free space. Thus the velocity factor, or relative speed, 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.

The velocity factor of the cable is found to be the reciprocal of the square root of the dielectric constant:

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

If resonant lengths of RF coax cable are to be used, then it is necessary to know the velocity factor of the coax cable. It is often possible to determine this to a sufficient degree of accuracy from just knowing the type of the dielectric material.

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 in free space is the speed of light divided by the frequency, the same is also true in any other dielectric. Since the speed of the wave is reduced, so is the wavelength reduced by the same factor. Thus if the velocity factor of the coax cable is 0.66, then the wavelength is 0.66 times the wavelength in free space.  Or,

In some instances, lengths of coax cable are cut to a specific length to act as an impedance transform element, or a resonant circuit. In such applications, this velocity effect 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 velocity factor closer to unity. Not only does this save on cost, but it can also be significantly more convenient to use and house.

There is a flip side to using cable with a low velocity factor. Given coaxial cables with the same center and shield diameters, cables with lower propagation velocity will have a higher capacitance per foot, and this must be factored into the selection process when the cable is being used for some applications. These applications usually involve shorter lengths of cable employed for shielded runs in equipment where the source, or termination, impedance does not match the cable impedance (ZO).

For more reading on these, and related, subjects: