Roy Lewallen wrote:
If you look at the transmission line
properties of a vertical, you see that the two conductors (the antenna
and ground plane) get farther and farther apart as the distance from the
feedpoint increases. This behaves like a transmission line whose
impedance increases with distance from the feedpoint and, in fact, a TDR
response shows just this characteristic. It's open circuited at the end,
so it behaves pretty much like an open circuited transmission line,
resulting in the same reflections and resulting standing waves you see
on a real antenna.

The Z0 characteristic impedance that matters is the
one that exists at the coil-stinger junction which
can be estimated from the single-wire transmission
line Z0 equation. It's usually in the neighborhood
of a few hundred ohms. For instance, a #14 horizontal
wire at 30 feet has a Z0 very close to 600 ohms
according to the formula.

One difficulty is accounting for the radiation, which
adds resistance to the feedpoint. I've never seen an attempt at
simulating it with distributed resistance, which I don't think would
work except over a narrow frequency range.

I have simulated such using EZNEC's wire resistivity
option. The resistance wire simulates the radiation
"loss" from the antenna. But for a standing wave
antenna, the "loss" to radiation is only about 20%
of the total energy stored on the standing wave
antenna. Therefore, a qualitative conceptual analysis
can be done assuming lossless conditions just as it
can be done with transmission lines.

But one
shortcoming of many antenna transmission line analogies is the attempt
to assign a single "average" or "effective" characteristic impedance to
the antenna, rather than the actual varying value. This is where a lot
of care has to be taken to assure that the model is valid in the regime
where it's being used.

Seems EZNEC automatically compensates for the varying Z0
so all we need to estimate is the single effective Z0 at
the coil to stinger impedance discontinuity.

There's no reason you can't also include a loading coil in the
transmission line model, and Boyer devotes much of the second part of
his article to doing just that. A solenoidal coil raises the
characteristic impedance of the length of "line" it occupies, because of
the increase in L/C ratio in that section. The traveling wave delay in
that section of the transmission line also increases due to the
increased LC product.

Are you saying the physics of the delay through a loading
coil changes between a traveling wave and a standing wave???
The standing wave is composed of a forward traveling wave
and a reflected traveling wave. They would experience the
same delay that you are talking about above.

So why didn't you use a traveling wave to measure the delay
through a loading coil??? Exactly how can the following
antenna current (from EZNEC) be used to calculate delay? The
current changes phase by 2.71 degrees in 90 degrees of
antenna. If the antenna was lossless, i.e. no radiation,
that current would not change phase at all.

EZNEC+ ver. 4.0
thin-wire 1/4WL vertical 4/23/2009 6:52:13 AM
--------------- CURRENT DATA ---------------
Frequency = 7.29 MHz
Wire No. 1:
Segment Conn Magnitude (A.) Phase (Deg.)
1 Ground 1 0.00
2 .97651 -0.42
3 .93005 -0.83
4 .86159 -1.19
5 .77258 -1.50
6 .66485 -1.78
7 .54059 -2.04
8 .40213 -2.28
9 .25161 -2.50
10 Open .08883 -2.71

--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com