Peter, I am very familiar with what happens below 200 Khz.

Most of my transmission line progs cover from power freqs up to UHF.
And they only stop there because of problems with finding room on the
screen for numerical overflow and the programming trouble with
shifting decimal points around.

Very shortly I shall have a program about "Behaviour of Coaxial
Transmission Lines at Low Frequencies. It accepts frequencies in the
range 20 Hz to 5 MHz. Input data is kilo-Hertz in the range 0.02 to
5000. Originally I stopped at 500 KHz.

There's no point in extending frequency range up to 10 GHz because
there is no interest in the subject matter. Although the maths is
already built in. There's just not enough space on the screen.
Programs should be easy to use.

As a program writer yourself you should be familiar with all this.
----
Reg.
======================================

"Peter O. Brackett" wrote in message
nk.net...
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