Reg et al:

[snip]
The reason why both programs stop at 200 KHz has nothing to do with
the foregoing. It is due to skin effect not being fully operative at
lower frequencies which complicates calculations.
There are other programs which go down to audio and power frequencies.
----
Reg, G4FGQ
[snip]

It's a pity that your programs don't work all the way down to DC.

Maxwell's celebrated [I really should say Heaviside's] equations do!

Aside: It is Heaviside's vector formulation of Maxwell's complicated
quaternic formulation with which most of we [modern] "electricians" are most
familiar.

In fact the common/conventional mathematical formulation of the reflection
coefficient rho and its' magnitude gamma as derived from the
Maxwell/Heaviside equations are indeed valid from "DC to daylight".

Notwithstanding the views of some, there are indeed "reflected waves" at DC
and even these "DC reflections" are correctly predicted by the widely
accepted and celebrated common/conventional mathematical models of
electro-magnetic phenomena, formulated by Maxwell and Heaviside.

Reg I assume the reason for your programs failure to give [correct] answers
below 200 kHz is because your "quick and dirty" programs do not utilize full
mathematical models for skin effect below 200 kHz. As you know, solving
Maxwell's equations for analytical solutions of practical problems is
fraught with great difficulties and so often numerical techniques [MoM, FEM,
etc...] or empirical parametric methods are used.

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?

--
Pete k1po
Indialantic By-the-Sea, FL