steveeh131047 wrote:
. . .
And finally, finally, to Roy: I struggle with the "mental gymnastics"
needed to move from the simple stub model outlined above, to one where
the "transmission line" is a single wire, not two wires, and "in-line"
with the antenna elements. If you read the Curum & Corum paper I'm
sure it will be clearer to you than to me! But until I can understand
it better, I content myself with this thought: if we removed 56ft of
wire from our full-sized quarter-wave vertical to leave just the 6ft
whip, we'd be happy to analyse this 56ft straight piece of wire using
a transmission line approach (including considering forward &
reflected waves, and the resultant standing wave along it), and to
ascribe to it an equivalent inductive reactance. I don't understand
why I (we?) find it intellectually any more difficult to take the same
approach with a piece of wire once it is wound into a helix.

Regards,
Steve G3TXQ

The similarities between an antenna and transmission line have been
known for a very long time and described in a number of papers. (See for
example Boyer, "The Antenna-Transmission Line Analog", _Ham Radio_,
April and May 1977, and Schelkunoff, "Theory of Antennas of Arbitrary
Size and Shape", _Proc. of the I.R.E., Sept. 1941.) It's a useful
conceptualization tool but, like comparing electricity to water in a
pipe, has its limitations. 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. 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. Boyer deals with this by
simply adding a resistance at the model feedpoint, noting that the
resistance doesn't change very rapidly with frequency. So this is one
inherent shortcoming of the transmission line analog. As long as you
incorporate the increasing Z0 with distance from the feedpoint and the
limitations of the resistive part, the model does reasonably well in
predicting the feedpoint characteristics of simple antennas. 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.

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. (L and C are per unit length in both cases.) But
don't forget the C which is an essential part of this analysis, and
don't forget that the C is decreasing from the bottom to the top of the
coil, resulting in an increasing characteristic impedance. A very short
coil like a toroid will raise the Z0 only for a very short distance, so
behaves differently from a long solenoidal coil.

Models or analogs can be very useful in gaining insight about how things
work. You have to remain vigilant, though, that you don't extend the
analogy beyond it realm of validity.

Roy Lewallen, W7EL