Peter O. Brackett wrote:
. . .
Most [non-parametric] analytic skin effect models derived from Maxwell and
Heaviside's equations [such as those in Ramo and Whinnery] involve the use
of "transcendental" functions that although presented in a compact notation,
even still do not succumb to "simple" evaluation.

Surely though skin effect is easier to model below 200 kHz where the effect
becomes vanishingly smaller? And so I don't understand why your programs
cannot provide skin effects below 200 kHz.

If you are interested I can point you to some [lumped model] skin effect
models for wires [based upon concentric ring/cylindrical models] that,
although parametric and empirical, are very "compact" and easly evalutate
and which closely model skin effect, and other secondary effects such as
"proximity crowding", up to prescribed frequency limits as set by the
"parameters".

These models simply make empirical parametric corrections to the basic
R-L-C-G primary parameters by adding a few correction terms.

Thoughts, comments?

Calculation of skin effect in a round wire is simple, provided that you
have the ability to calculate various Bessel functions. Libraries in
Fortran are widely available, and probably in other languages also.
NEC-2 (and therefore EZNEC) does such a full calculation for evaluation
of wire loss. A side benefit of doing this is that you also get an
accurate evaluation of the internal inductance. However, in practical
terms, you can do quite well with the common skin depth approximation
based on the assumption that the wire diameter is at least several skin
depths, and an interpolation from there to the DC case.

Coaxial cable is more problematic than twinlead. Most analyses assume
that the resistance of the shield is negligible. But for an accurate
evaluation, you need to include it. At high frequencies it's simple, but
it's much more difficult at low frequencies than for a round wire, since
most equations you'll find require subtracting huge numbers from each
other, exceeding the capability of even double precision on modern PCs.
It's possible but requires some mathematical manipulation and trickery.

With coax at low frequencies, the fields from the two conductor currents
reach the outside of the cable. While they should still cancel, this
might cause some problems with the assumptions we normally make in the
analysis of coaxial transmission lines.

You're not likely to be able to do a very good job of predicting real
life transmission line behavior in any case, though, unless you account
for such real factors as the roughness of stranded conductors, braided
coax shield, and plated conductors. I'd also expect twinlead with solid
or punched polyethylene insulation between conductors to be somewhat
dispersive (that is, having a velocity factor which changes with
frequency), but I've never tried to measure it. Reg has said he's
measured many pieces of real cable and found its loss to agree with his
earlier coax program, but won't tell us where he buys it. Everything
I've ever been able to buy is considerably lossier.

Roy Lewallen, W7EL