# Velocity factor in coax cables

I mainly see the term "velocity factor" used when referring to the velocity of propagation of an electromagnetic wave front in coax cables. This velocity seems strongly dependent on the properties of the cable's dielectric. Would coax cables stripped of their tubular shielding (but not their dielectric) have the same velocity factor as a normal coax line? Or is the velocity affected by electromagnetic coupling between the core and shield?

• When you say "stripped of their tubular shielding," do you mean the non-conducting outermost layer of the cable, or do you mean stripped of the ground sheath with a bare dielectric? – rob Oct 6 '18 at 14:25
• @rob I meant stripped of the conductive ground sheath with the dielectric still intact. Basically just a wire surrounded by the same dielectric. – James Oct 6 '18 at 15:54

Well, in vacuum the velocity of a wave is $$c_0=3\cdot10^8$$m/s. The speed in a medium is $$\frac{e_0}{n}$$ where $$n$$ is the refractive index of the material .The relationship between the refractive index and dielectric constant is $$n=\sqrt{\epsilon_r\mu_r}$$ where $$\epsilon_r$$ and $$\mu_r$$ is the relative permitivitty (dielectric constant) and relative permeability of the material.

Thus the velocity of the wave is $$\frac{c_0}{\sqrt{\epsilon_r\mu_r}}$$

Stripped cable should show the same speed for the wave still confined in the dielectric. You can however, if you want to, dig deeper into group and phase velocity and try to see where that math takes you.

Responding here largely to the comment from OP that

I meant stripped of the conductive ground sheath with the dielectric still intact. Basically just a wire surrounded by the same dielectric.

Such a wire would not carry high frequency signals. So it doesn't make sense to talk about the propagation velocity.

In a very simple picture, to send a signal down a wire there must be a signal wire but also a return wire. If you remove the sheath there is no return so current can't flow and the cable is no longer a transmission line which can be used to send a signal.

In a more sophisticated picture which is necessary to truly understand how high frequency signals (wavelength appreciably shorter than length of cable) are transmitted in a coax cable you must think of the cable as a transmission line. In a transmission line the coaxial cable is thought of as a waveguide for an electromagnetic wave propagating down the cable's length. The simple picture in terms of voltage and current breaks down. One is better served by thinking about the electric and magnetic fields propagating as an EM wave down the cable. The shield serves to confine and guide these electromagnetic waves down the cable. Without the shield the EM waves are not confined and no signal is transmitted.

So far I have been discussing the shield and the center conductor serving as a waveguide for the wave. Of course, the electric and magnetic fields live in between the center conductor and the shield. This is why whatever dielectric fills that region of space is what determines the velocity of the EM wave.

So I think my answer to your questions is: The velocity factor is mainly influenced by the choice of dielectric in between the center conductor and the shield, however, the geometry of the center conductor and the shield is necessary for the cable to function at all. Thus you question "Would coax cables stripped of their tubular shielding (but not their dielectric) have the same velocity factor as a normal coax line?" doesn't quite make sense.