For closewound coils, with length to diameter ratios around 5:1, a series of
fairly careful measurements have been made with the coils arranged
vertically above a ground plane, fed at the base, with a capacitive load on
the other end, and the driving frequency arranged to be at the resonant
frequency of the whole assembly. The measurements were made with carefully
designed fiberoptic probes that were specifically designed to avoid
perturbing the magnetic and electric fields.
These measurements were made by tesla coil researchers trying to establish
whether the secondary coil acts as an open circuited quarter wavelength
transmission line (where there would be a 90 degree phase shift between top
and bottom) or whether it was best modeled as a lumped circuit (big L C
circuit)
In most cases, the phase shift in the current at top and bottom was on the
order of 10-20 degrees.
Subsequently, rigorous calculation and numerical modeling were done to
understand the exact voltage and current distribution within the system;
i.e. to explicitly calculate the capacitance and inductance of each segment
of the coil, and, as well, to calculate the mutual coupling of each segment
of the coil to the others. For inductance the signficant thing is that the
magnetic field of one segment pretty much links to the adjacent segments,
and less so for the rest. For capacitance, the significant thing is the
capacitance to "ground" or "free space" (self C), and less so the
capacitance to adjacent segments.
At this time, the models are sufficiently well developed that they predict
the actual currents and voltages to substantially better than one percent
(if not several more significant figures... I've not been following the
developments that closely). The models have also been developed to model
the current flow on the surface of and within the inductors, using
rigorously (in the mathematical sense) validated closed form analytical
expressions. Over the past 5 or 6 years, there has been an extensive amount
of quite painstaking experimental verification of these models with a lot of
attention to experimental methods and quantifying uncertainty. This is a
huge amount of work.
The take home message here, regarding loading coils, is that simple lumped
approximations of a loading coil may do just fine for an initial design cut,
but do not adequately reflect reality. The other message is that
measurement uncertainties can be quite large in an experimental setup. I'd
venture to guess that there has been NO ham measurements or analysis of the
loading coil problem that even approaches what has been done in the case of
the tesla coil secondary world, especially in terms of experimental and
analytical rigor.
I'd also give my opinion that it probably wouldn't be worth it to do such
analysis or experiments, except perhaps to settle a "bar bet". Most all
tesla coils are essentially identical in design and form, so the analysis
that has been done is generally applicable to tesla coils, but that's a very
narrow applicability. Amateur antennas vary so much in installation and
design that a rigorous treatment of one case would not, in general, be
applicable to others.
I think it's best to leave it at:
Loading coils are not isolated lumped elements and cannot be modeled as
such.
A lumped model serves as a decent design tool to determine a starting point,
which will have to be further iterated empirically.
To give credit where it's due, the research work I've described above was
primarily done by Terry Fritz (in the US), Paul Nicholson (in the UK), and
Antonio Carlos M. de Queiroz (in Brazil). I can come up with some links to
papers if needed.
Jim W6RMK
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