Tom Donaly wrote:
This is just another way of writing 2Acos(kx+d/2)(e^i(wt+d/2). Notice
that the part cos(kx+d/2) still contains the phase information?
If Cecil were any kind of experimentalist he could easily tease the
phase information out of any standing wave on his antenna system.

I have previously teased that information from that equation.
Perhaps you forgot. It's how to determine the exact phase
shift along a thin-wire 1/2WL dipole. I showed how to do that
days/weeks/years ago. It's the *phase* of the standing wave
current that does not yield any phase information. I have been
very careful with that caveat in my statements.

cos(kx+d/2) indeed does still contain the phase information.
If you will re-read my postings, you will see that I said
the *PHASE* term of the reflected current doesn't contain any
phase information. FYI, that's the e^i(wt+d/2) term and that
part is what Roy used to make his phase measurements which
has been my objection for years. It's all archived on Google.

It is I, not Roy or Tom, who used the phase information in
cos(kx+d/2) to determine phase. When the term containing
the phase information is actually used, the delay through
the coil is shown to be in the tens of degrees.

In the 1/2WL thin-wire dipole, the phase shift between two
points is arc-cos(amplitude1) - arc-cos(amplitude2). The
only phase information is, as you and Gene Fuller rightly
assert, in the amplitude of the standing wave current, NOT
in the phase of the standing wave current that Roy measured.

If the e^i(wt+d/2) term is used, as Roy and Tom have done,
it suffers from the absence of any phase information at all.

Gene Fuller said it all days ago:
Gene Fuller, W4SZ wrote:
In a standing wave antenna problem, such as the one you describe, there is no
remaining phase information. Any specific phase characteristics of the traveling
waves died out when the startup transients died out.
Phase is gone. Kaput. Vanished. Cannot be recovered. Never to be seen again.

i.e. there's no remaining phase information in e^i(wt+d/2) term.

The only "phase" remaining is the cos (kz) term, which is really an amplitude
description, not a phase.

i.e. there is phase information in the cos(k+d/2) term, but
that's not the part of the wave that Roy and Tom were using
to determine delay through the coil. I have been hoping someone
would jump in who understood the math.

To summarize: cos(kx+d/2) is proportional to the *amplitude* of
the standing wave current. When I used the amplitude of the
standing wave current to estimate the phase, the gurus
objected.

e^i(wt+d/2) is proportional to the phase of the standing wave
current and, ironically contains no phase information, just as
Gene asserted. Yet, this is what Roy chose to measure in trying
to determine the phase shift through a coil and that's the entire
problem with his measurements. He was expecting to measure zero
phase shift and he did because there was no phase shift information
available from his measurement of the e^i(wt+d/2) term.

I told Roy a long time ago, in general, how to calculate the phase
shift from the cos(kx+d/2 amplitude term but he replied with
"gobbledygook" or some such.
--
73, Cecil http://www.qsl.net/w5dxp