Gene Fuller wrote:
Cecil Moore wrote:
It seems that you are contradicting yourself by saying that all
the information in the component waves is still there after
superposition yet you say the phase is gone. Both statements
cannot be true.

Both statements are true. Superposition does not favor one description
over the other. If there is no phase information remaining in the
superposed result (the standing wave) then there is no phase information
remaining at all, regardless of your mathematical manipulations. There
are no hidden variables.

But you said (and for some unknown reason trimmed):

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

I agree with you. The phase of the underlying forward and
reflected traveling waves can be deduced from the *amplitude*
of the standing wave. Here is a graphic excerpted from the
recently available PDF 1st edition of "Antennas" by Kraus.
EZNEC can also be used with the same results.

http://www.w5dxp.com/krausdip.jpg

As you can see, the current amplitude is a ~cosine function.
The phase of the forward traveling wave relative to a source
wave of 1.0 amp at 0 degrees (EZNEC standard) is an ARC-COSINE
function of the current amplitude. For instance, at 45 degrees
away from the feedpoint, the current is ~0.707 amps. ARC-COSINE
of 0.707 is 45 degrees. You were correct when you said that
the information in the forward and reflected waves is preserved
in the standing waves. Kraus' graphic proves it.

But it has yet to be explained how Roy (and Tom R.) could
use the essentially unchanging *phase* of the standing wave
current to "measure" the phase shift through a loading coil
- since the phase of the standing wave current cannot even
be used to determine the phase shift through a wire. This
question has been asked many times. The absence of an answer
stands out like a sore thumb.

Roy said:
What I measured was a 3.1% reduction in magnitude from input to output,
with no discernible phase shift.

Of course there was no discernible phase shift as can be seen from
Kraus' graphic above. But Kraus' graph gives us a way to deduce
the phase shift from the amplitudes. Assuming a reference amplitude
of 1.0 amp at the bottom of the coil, a 3.1% reduction would give
us 0.969 amps at the top of the coil. ARC-COSINE(0.969) = 14.3 deg.
That's a close approximation of the phase shift through the coil
being undergone by the forward current and reflected current.

If the forward current at the bottom of the coil is 0.55A @ 0 deg,
and the reflected current at the bottom of the coil is
0.45A @ 0 deg, the total current at the bottom of the coil
is 1.0A @ 0 deg. With a 14.3 degree phase shift through the
coil, the forward current at the top of the coil would be
0.55A @ -14.3 deg and the reflected current would be
0.45A @ +14.3 deg. Adding those two phasors together yields

0.55A*cos(-14.3) + 0.45A*cos(+ 14.3) = 0.533A + 0.436A = 0.969A
at the top of the coil. 0.969A is 3.1% lower than the 1.0 amp
at the bottom of the coil. Everything is perfectly consistent
with a 14.3 degree phase shift through the coil for the two
traveling waves.
--
73, Cecil http://www.w5dxp.com