K7ITM wrote:
Roy wrote, "... That is, the coil is capacitively coupled to ground,
and this
causes displacement current from the coil to ground."

In fact, if there were no such current -- if there were no capacitance
from the coil to the world outside the coil -- then the time delay
through the coil, calculated from tau = sqrt(L*C), would be zero. It
is exactly this current that allows there to be a transmission-line
behaviour and a corresponding time delay.

Yes. And this, not the C across the coil, is what should be used for
transmission line formulas when treating an inductor as a transmission
line. When the ground was removed and replaced by a wire, the
transmission line properties of the coil changed dramatically, while the
C across the coil didn't change significantly.

That's not to say, however, that a physically very small loading coil
with practically no capacitance to ground would not work as a loading
coil. It just wouldn't have a transmission line behaviour worth
mentioning.

It is also exactly this displacement current from a large coil that
allows the current at one end of the coil to be substantially different
from the current at the other end.

Yes again, with one slight modification. You'll note from the EZNEC
models that the current actually increases some as you go up from the
bottom of the inductor. This is the effect noted by King which is due to
imperfect coupling between turns. It results in currents at both ends
being less than at the center.

A transmission line can be represented by a series of L networks with
series L and shunt C. You can achieve any desired accuracy by breaking
the total L and C into enough L network sections. The requirement for
validity is that the length of line represented by each section must be
very small relative to a wavelength. For the example coil, a single
section is entirely adequate at the 5.89 MHz frequency of analysis.
However, at some higher frequency this model won't be adequate, and
either more L sections or a distributed model is necessary. If the
reasons for this aren't obvious, many texts cover it quite well. No
special "traveling wave" analysis is required.

I spent several years of my career designing very high speed TDR and
sampling circuits, which involved a great deal of modeling. At the tens
of GHz equivalent bandwidths of the circuitry, even very small
structures such as chip capacitors and short connecting runs often had
to be treated as transmission lines. One of the skills important to
building an accurate model which would run in a reasonable amount of
time, particularly on the much slower machines being used in the earlier
part of that period, is determining when a lumped L, pi, or tee model is
adequate and when a full-blown transmission line model has to be
used(*). My models were used in the development of quite a number of
circuits that were successfully produced in large numbers.

(*) One of the characteristics of the SPICE programs at the time was
that the time step was never longer than the delay of the shortest
transmission line in the model. So if you willy-nilly modeled everything
as a transmission line, you'd end up with an excruciatingly short time
step and consequently unnecessarily long calculation time.

Roy Lewallen, W7EL