# Does Velocity Factor pose a significant cable loss?

We know that a lower Velocity Factor translates to using shorter runs of cable in resonant circuits. That apparently means that there is resistance to the flow of electrons, slowing them down.

So does that resistance mean that we're also seeing a higher energy loss in the form of heat?

Given a choice of these two cables, which one has the most loss? Is the loss significant in choosing a feedline?

1. Cable having a VF of 66%
2. Cable having a VF of 82%
• This here is one of the reasons I don't really like the water pipes analogy used to talk about electricity. No, a lower group velocity doesn't mean something is "hitting the breaks" and resists the current. It means that the material or geometry of the propagation lead to lower speed, but not that there is resistance :) Mar 8 at 8:33

Velocity factor is not the cause of cable loss, but it is related.

Signals in a coaxial cable travel as transverse electromagnetic waves with currents in the copper and electric fields in the dielectric. In the case that the dielectric is air (or vacuum) with a relative permittivity of 1.0 the wave will travel at the speed of light, VF = 1.0.
If the dielectric has a higher permittivity than free space then the wave will travel slower, with the relationship $$\text{VF}=\frac{1}{\sqrt{\epsilon_r}}$$ which by the way is true for all electromagnetic waves in free space too, like light in glass or water.
There are electrons moving in the metal, but their motion and speed is not really related to the speed of the electromagnetic wave, which travels in the space between the conductors see [this video].

The loss in coaxial cables comes from these non-ideal components.

• the copper has some resistance 1
• the dielectric has some loss which can be modelled as though it is slightly conductive 2
• there can also be some leakage if the cable braid is too sparse

The power lost to the first two is dissipated as heat, the third is radiated away.

Now in the design of coaxial cables, there are only two ways to reduce the loss caused by the dielectric:

1. Use a higher-quality dielectric, meaning a lower loss at the frequency of interest, while still meeting the mechanical needs of the cable. Cheap cables use polyethylene which is already extremely low loss. Better cables use PTFE (teflon) which is not much lower loss but is much stronger and more heat resistant.
2. Use less of the dielectric, more air which can be done in several ways: extruding a cellular structure, using a foam, using a helical structure, using thin supporting discs spaced far apart, or using no supports at all (except for the ends). All of these can be seen in practice, and have the effect of reducing the dielectric loss at the expense of some mechanical complexity and reduced ruggedness.

And the key thing is that when the effective quantity of dielectric is reduced, the velocity factor is also increased. So along with the cable diameter, the velocity factor of a cable is in fact a fairly good indication of the cable loss (keeping all other things constant). Cables with 82% VF (foam PE) will have about half the loss per length than cables of the same diameter with 66% VF (solid PE).

The copper loss can be improved by making the cable larger (which also increases its power handling) and slightly improved by using silver plating. The leakage is usually an insignificant cause of loss but cable can be made less expensive by using a very sparse braid over a layer of aluminimum foil or aluminised mylar.

Notes:
1. The resistive loss in the copper is made larger by the skin effect which forces the current to flow in quite a thin layer on the surface,
2. The dielectric loss might arise from other molecular effects - for example the loss tangent of water [PDF] rises with increasing temperature, and frequency, having a first peak at 24 GHz.
• I think you're correct, but I'm also a bit confused- isn't there dispersion in coaxial cable, implying that there's actually also a geometry-induced component in group velocity (which would makes the speed of propagation depend on the ratio of diameter to wavelength)? Mar 8 at 8:40
• As you covered in your answer, there are some factors that could cause higher loss in higher velocity factor cables, but these factors are generally overwhelmed by higher loss factors that correlate to lower velocity factor. It's not a exact correlation. There is no correlation between dielectric constant and dielectric loss -- just most of the materials we use it looks like there is one. Mar 8 at 12:23
• @MarcusMüller yes coax is also (slightly) dispersive because the copper loss R is larger than the dielectric loss G. This can be derived from the basic Heaviside transmission line equations, no need for Maxwell but of course C and L depend on geometry. At audio frequencies dispersion is a big deal, so telephone lines needed compensating inductors at regular intervals. At RF it's a very small effect, I worked it out once, from memory for 10 metres of RG58/RG223 the spread over 1 MHz to 1 GHz was << 1 ns. Mar 8 at 18:03

Velocity factor is not related to ohmic loss. It tells you how fast a wave will propagate in the transmission line you have chosen with respect to propagating in free space. A velocity factor of 70% means that a signal will propagate at 70% of the speed of light - i.e. 197,865,188 meters per second rather than 209,792,458 meters per second.

The speed of light in any medium is given by: $$c = \sqrt{\frac{\mu}{\epsilon}}$$ where $$\mu$$ is the magnetic permeability of the medium and $$\epsilon$$ is the electric permittivity. Permeability is a physical property of a material that describes the degree to which it allows magnetic fields to pass through it and is defined in Henries per m (H/m). Permittivity is a physical property of a material that describes the degree to which it allows electric fields to pass through it and is defined in Farads per meter (F/m).

The permeability of free space is 4$$\pi$$ $$\times$$ $$10^{-7}$$ H/m and is denoted by $$\epsilon_0$$. The permittivity of free space is 8.854 $$\times$$ $$10^{-12}$$ F/m and is denoted by $$\mu_0$$. If you crunch the numbers and reconcile the units you get:

$$c_0 = \sqrt{\frac{4\pi \times 10^{-7} \text{ H/m}}{8.854\times 10^{-12}\text{ F/m}}} = 299,792,458\text{ m/s}$$

The permittivity and permeability of materials is usually given in terms of how they are relative to that of free space. Teflon is a common insulator in coaxial cable. It has a relative permittivity of about 2.0 and a relative permeability very close to 1. So we can calculate the speed of light in such a cable: $$c \approx \sqrt{\frac{\mu_0}{2\epsilon_0}} = \frac{1}{\sqrt{2}}c_0= 0.7071c_0$$ So we see in the example that the cable would have a velocity factor of about 71%.

1. Below UHF, the losses in the dielectric are negligible.

2. Almost all of the loss in coax below UHF is copper loss, the outermost part of the center conductor and the side of the shield facing it (Skin effect loss.)

So far, no one has suggested that we compare the conductor size in solid dielectric vs. foamed dielectric. :-)

I don't have the dimensions handy, but in the lower-loss foam dielectric coax the center conductor is larger and thus the I^R losses are lower.

I'm certain that this has been mentioned here before, likely by the late Phil Frost. For most of the coaxial cable types used by the cable industry, the metallic conductor loss is a more significant contributor to attenuation than the dielectric, although the latter does play a role.