Roy Lewallen wrote:

Jim Kelley wrote:


The way it looks to me, the speed of propagation is pretty much the
inverse of the squareroot of the product of mu and epsilon for the
dielectric between conductors.


That's almost correct, but not quite. You need to modify it by changing
"the dielectric between conductors" to "the medium containing the
fields". Inside a coaxial cable, both are the same, so you can easily
calculate the velocity factor from the dielectric constant (relative
epsilon) of the dielectric. In the case of ladder line, TV twinlead, or
microstrip line, though, part of the field is in the dielectric and part
is in the air.

Yes, air is obviously also a dielectric.

So the velocity factor is a function of the dielectric
constants of both. Often, an "effective" dielectric constant is
calculated that fits the rule you mentioned(*). For the types of line I
mentioned, it's between those of air and the dielectric material. It's
not at all trivial to calculate, so it's usually determined by
measurement or a field-solving computer program.

Exactly. That's why I chose to adhere as strictly as possible to
absolute generalities. ;-)

In the case of an insulated antenna wire or one with a ferrite core on
the outside, the "other conductor" is usually a very great distance away
so the vast majority of the field is in the air. Also, the simple
formula you refer to might not apply when the distance between
conductors is a substantial fraction of a wavelength or more. If you
take a piece of coax with solid polyethylene dielectric and measure its
velocity factor, you'll find it to be around 0.66 (following the formula
you mention). But if you strip off the shield and use the same center
wire and insulation for an antenna, you'll find the insulation slows the
wave on the antenna by only a few percent (almost certainly less than
five).

I think in the case where the distance between conductors is much larger
than the diameter of the conductor, a better form would probably be one
over the squareroot of the product of inductance per unit length and
capacitance per unit length.

(*) In the case of microstrip line, the field distribution changes with
frequency. This results in an effective dielectric constant, and hence
velocity factor, which changes with frequency. With something like
Teflon dielectric, which has a relatively low dielectric constant, this
change isn't much. But it sure gave me grief when designing time-domain
circuitry using microstrip lines on an alumina substrate (dielectric
constant ~ 10), where the change was much greater.

Roy Lewallen, W7EL

Thanks for the excellent tutorial, Roy.

73, ac6xg