Roy Lewallen wrote:
. . .
I've taken the EZNEC model available there and modified it by replacing
the whip with a wire to ground from the top of the coil
(http://eznec.com/misc/test316_modified.EZ). I added a lumped impedance
in that wire to represent the impedance of the vertical wire I
deleted(*). The feedpoint impedance is the same as for the original
model, and the currents at the top and bottom of the inductor are almost
exactly the same as for the original model. Can the traveling wave
analysis be used to explain the inductor currents in this model? Is
traveling wave analysis necessary to explain them?

(*) The impedance inserted in the new wire isn't equal to the impedance
of the top wire driven against ground. The reason is that the new wire
to ground does radiate some, does have significant impedance itself, and
does interact with the inductor. The modified system, however, is quite
obviously very different in radiating properties from the original, and
isn't too different from a lumped RC load.

Notice that the current into the grounded wire at the bottom of the coil
is about 1 amp, and the current going into ground at the grounded end of
the added wire is about 0.56 amp. So where is the extra current for the
coil bottom wire coming from? The answer is displacement current from
the coil. That is, the coil is capacitively coupled to ground, and this
causes displacement current from the coil to ground. The effect is
greatest at the end of the coil which is farthest from the source. A
decent model of the coil is an L network, with a series L, and a shunt C
to ground from the far end. This is all that's necessary to explain the
drop in current from the bottom to the top; no current waves, standing
or traveling, no transmission line analysis are required.

If you're not convinced, try this. Change the ground type to free space.
Then connect the bottoms of the two formerly grounded wires together
with another wire. You'll see that the current at the top of the coil is
now very nearly the same as at the bottom. We haven't changed any waves,
antenna lengths, or anything else related to antennas or waves. All
we've done is to eliminate the other side of the capacitor -- we've
removed the C in the equivalent lumped L network.

A simple lumped component model explains the difference between grounded
and free space models just fine. How well does the traveling wave theory
do at it?

Roy Lewallen, W7EL