steveeh131047 wrote:
As a newcomer to the group I'm hesitant to join a discussion which has
been running for almost 200 postings, and where the protagonists
understand the topic in much greater depth than I do. But here
goes ....

My starting assumption is that EZNEC can model a helical inductor
reasonably accurately, with the exception of the increase in AC
resitance caused by proximity effects.

Yes, that's correct. Fortunately, proximity effect is generally
negligible unless the turn spacing is very close.

If I take an EZNEC model of a coil - 40 turns #14 wire, 6" diameter,
12" long - I discover it has a characteristic impedance of about 2550
ohms at a self-resonant frequency of around 6.1 MHz.

A single conductor doesn't have a characteristic impedance -- it's the
impedance between the two conductors of a transmission line. You can
measure a characteristic impedance between, say, a coil and ground, but
its value depends on the spacing between the two. If the coil is tilted
with respect to the ground, the impedance of this two-conductor system
will change with the position along the coil.

If I use it as
the base loading coil for a short vertical antenna with a 6ft whip
above it, I notice that EZNEC shows a difference in the current at the
top of the coil compared with the bottom of about 0.69:1, and a
resonant frequency of 3.79MHz.

I then look to see which of the various models might reasonably
predict the values observed in the EZNEC modelling.

Clearly, a simple lumped-element inductor doesn't get close. I've read
various web pages and postings which argue qualitatively that things
like "distributed capacitance" might explain some of the observations,
but as yet I've seen no quantitative analysis which attempts to
predict the numbers.

It's difficult or impossible to do with lumped elements. A vertical
loading coil has not only series inductance, but also capacitance to
ground or, in the case of a dipole, to the other half of the dipole.
This capacitance varies along the coil, being greatest at the bottom and
increasing toward the top. (This is the cause of the varying Z0 I
mentioned above.) But there's also a delay associated with the
capacitance which complicates the interaction to the point where you
can't easily model it with lumped elements. And the coil radiates, which
alters its current distribution.

That said, a lumped inductor makes a fairly decent model for a
physically very small (in terms of wavelength) toroidal loading coil,
since it has minimal capacitance to ground and a minimal amount of
radiation. I actually built a vertical, loaded it with one, and made
careful measurements which I posted on this newsgroup several years ago.
Cecil is still complaining about it.

The displacement current flowing through those capacitances, not some
"effective degrees of antenna" phenomenon, is what causes the current
along a solenoidal loading coil to vary. If you reduce the capacitances
to a low value as I did in my measurement, the currents at the ends
become nearly the same, which is what the measurement showed.

In contrast, I look at the work of Corum & Corum and of G3YNH who
insist that "coils are best regarded as transmission lines", and I get
quantitative results which closely match the EZNEC results. For my
example coil, I get a self resonant frequency of 6.3MHz (cf 6.1MHz),
a characteristic impedance of 2792 ohms (cf 2550 ohms) and an Iout/Iin
ratio of 0.72 (cf 0.69)

Not only that, the transmission line model predicts an inductive
reactance very close to that needed for antenna resonance at 3.79 MHz

You've kind of lost me here, since I can't see how you've replaced a
two-terminal coil with a four-terminal transmission line. And a
transmission line doesn't radiate, so that sometimes-important property
of a solenoidal coil is ignored.

I'm a simple soul, and I don't pretend to understand all the maths
involved; I merely observe that the transmission line approach
delivers "hard numbers" that closely match those predicted by EZNEC.
I've yet to see another model get close. So, until I do, I guess I
have to favour the approach of Corum & Corum, G3YNH et al.

Be sure to test the approach with other configurations, such as longer
and shorter coils, frequencies well away from resonance, etc. to find
the limits of applicability of the approach. Does it correctly predict
the field strength? Efficiency? Bandwidth?

If someone can show me similarly accurate results from an approach
based on a lumped-element model, I'd be interested to see them.

Me, too. The thing which prompted me to add the automated helix
generation feature to EZNEC was the realization that lumped loads so
often did a poor job of simulating solenoidal loading inductors.

Roy Lewallen, W7EL