Owen Duffy wrote:
It has been proposed that a helix can be represented by a transmission
line with certain parameters including Beta (the phase part of the
complex propagation constant), and solution of the transmission line
gives meaningful numbers for the inductance and self resonance of the
helix.

Some seem to state that the behavior of a physically short loading coil
demands the above transmission line solution for adequate accuracy, and
that the electrical length of the transmission line (Beta*CoilLength)
simply replaces the equivalent physical length of straight conductor and
so shortens the "quarter wave resonant" antenna.

Tom has described an experiment
(http://www.w8ji.com/inductor_current_time_delay.htm) where he has
measured the S21 delay of a 10" (254mm) long coil typical of a loading
coil for an 80m antenna. He hasn't described how the measurement is
actually made.

If the coil is represented as a transmission line with the load end
shorted to ground (as in the style of a helical resonator) it is much
shorter than a quarter wave transmission line.

Tom did not describe any form of directional coupler that would
effectively isolate and measure the forward and reflected waves at each
of the measurement points. Such a thing would be a considerable challenge
since Zo of the equivalent line varies with frequency and he sweeps from
0.3 to 30MHz in his measurement.

If a simple current probe was used to sample the magnitude and phase of
the current at each end of the coil, the samples are each of the sum of
the forward and reflected current components at each point.

It is the nature of a low loss transmission line less than an electrical
quarter wave and terminated in a short circuit, that the phase of the
(net) current at all points on the line is almost uniform.

Is it any surprise that Tom's measurement of delay indicates an apparent
phase change much smaller than the value of Beta*CoilLength?

Owen

I suggest you email Tom and ask him about his experiment. It doesn't
matter, though. Cecil will always argue, that, because Tom is wrong,
he, Cecil, must be right. In point of fact, Tom doesn't have to prove
Cecil wrong, Cecil has to prove himself right, which he can't possibly
do because he refuses to use either mathematics or experiment to bolster
his claims. He expects us to believe what is, basically, a philosophical
fantasy masquerading as theory. Again, get in touch with Tom. He may not
correspond with you, but then again, he may. Trying to second guess an
experiment from a web page is a difficult proposition.
73,
Tom Donaly, KA6RUH
(P.S. By now, you, and everyone else, should know that Cecil never
argues in good faith, so there's little point in bothering your head
about his theories. Dealing with Cecil should only done for
entertainment, and then in small quantities. A little of his fantasmic
fulminations go a long way.)