Ian White GM3SEK wrote:

So.. Terman's equation probably holds for coax where the inner
conductor is 20 skin depths,


Sorry, Jim, you lost me: why such a large number as 20?

At 2.5 skin depths, the current density is 10% of the surface value; at
5 skin depths, 1%. If at least 5 skin depths are available, we can be
confident in the accuracy of the standard, uncorrected equation for most
purposes.


But it's round... (unless Terman rolled that into his constants)

Consider if you peeled that 2.5 skin depth layer and made it flat. It
would look like a pyramid, not a rectangular bar.

Of course, if you assume that the cross sectional area is an annulus
(the pi*( r^2-(r-skindepth)^2) style calculation) this partially gets
taken into account.

The other factor is that in a wire that is comparable to skin depth in
radius, the current on the far side of the wire also contributes to
squeezing the current towards the near side surface. (and that's why
the actual math gets hairy.. you can't use a simple exponential
approximation for the current density)

At 20 skin depths, the difference is negligble.

As a practical matter, if you have an application that actually cares
about this level of detail, you probably have the resources to deal with
the exact calculations, so the simple "thin layer on the surface" is
close enough.

For what it's worth, this kind of thing is why the loss in coax doesn't
follow a nice k1*f + k2*sqrt(f) characteristic at low frequencies. The
second term is essentially assuming that the skin depth in the
conductors is "small" compared to conductor size.



A more serious effect of insufficient conductor depth may be in
estimating the effectiveness of shielding. The residual fields at the
opposite side of an extremely thin shield can be very significant if
we're looking for attenuations of 40dB, 60dB or more.

Especially at low frequencies... (shielding mains frequency
interference, or PWM switcher noise, for instance)