wrote:
OK. I'm not sure what you are trying to say. It sounds like we all know
and agree a reasonable physial size lumped inductor with good flux
coupling between ends and stray C to the outside world that is small
compared to termination impedance works like a lumped inductor below
self-resonance of the inductor.

I absolutely agree about the characteristics of an inductor presupposed
by the lumped-circuit model. But one cannot use the presuppositions
of the model to prove the model is valid for all cases. The dissagreement
here is one of degree. I would have stated the assertion above, it behaves
"... like a lumped inductor *far* below self-resonance of the inductor." Dr.
Corum sets the "far below" range at 15 degrees or 1/6 the self-resonant
frequency.I previously showed that 15 degrees of 450 ohm transmission
line will change a load of 50+j0 into a load of 54+j100 ohms. That may
be accurate enough for Dr. Corum to start using the lumped-circuit model,
but not for me. I would be more inclined to set the limit at 5 degrees.

What are you trying to say? Can you give an example in you own words
explaining what you are trying to say and why it is meaningful or
useful to others?

What I am trying to say can best be illustrated by an example task that
I need to perform. I have a 180 foot dipole that I need to shorten so I
am going to install loading coils. I want the length of the loaded antenna
to be 90 feet. I'm pretty naive at this, so I am just going to build the
coil
out of the wire I remove from the antenna. My neighboring ham friend
says that will work just fine. And in the process of reducing the size of
my antenna, I want to learn something about antennas so I have borrowed
two toroidal current pickups to measure the current.

Note that at the frequency where the dipole is 1/2WL and resonant,
it is 180 feet long and 180 degrees long so the number of feet of
wire is also the number of degrees of antenna. Here is my 1/2WL
dipole with current pickup coils installed at points 'x' and 'y' and
FP is the feedpoint,the impedance of which is 60 ohms.

------------------------------FP-------x---------------y-------

Total length is 180 feet. The distance between 'x' and 'y' is 45 feet.
Since feet = degrees in this case, the number of degrees between
'x' and 'y' is known to be 45 degrees from antenna theory. Those
45 degrees are what I am going to attempt to replace with a coil.

So I adjust the feedpoint current to one amp at a reference phase
angle of zero degrees and measure the current at 'x' and the current
at 'y'. The current at 'x' is 0.92 amp at 0 deg. The current at 'y' is
0.38 amp at 0 deg. Already I am not understanding my measurements.
The electrical length between 'x' and 'y' is obviously 45 deg. Why is
there no phase shift at all in the measured current between 'x' and
'y' and the feedpoint current? But I want to complete this task so
I will wait until later for an explanation to that apparent paradox.

I take the 45 feet of wire from each side of the dipole, wind it
into two coils, and install them in each side. Now the 90 foot
long dipole looks like this.

-------//////-------FP------x-//////-y------

I make some more measurements with the feedpoint current set
to one amp at zero degrees. The resonant frequency of the dipole
has changed from the earlier resonant frequency. I have to adjust
the number of turns on the coil to return to the original frequency.
I discover that the feedpoint impedance has dropped to 45 ohms.
I measure the current at each end of the coil and at one end it is
1.1 amp at 0 deg and at the other end it is 0.6 amp at 0 deg

These are not the results predicted by my neighboring ham friend.
I'm confused but here are the things I know for sure.

1. The resonant frequency changed when I installed the coil so
the coil is not a perfect replacement for the wire.

2. The feedpoint impedance decreased from 60 ohms to 45
ohms. Since 45 ohms is closer to 50 ohms than is 60 ohms,
I'm not too interested in knowing why..

3. The current at 'x' increased from 0.92 amp at 0 deg in the
wire dipole to 1.1 amp at 0 deg in the loaded dipole. The phase
didn't change.

4.The current at 'y' increased from 0.38 amps at 0 deg in the
wire dipole to 0.6 amp at 0 deg in the loaded dipole. The phase
didn't change.

5. No matter where I measure the current in either system, the
phase always comes up zero degrees between any two points
from tip to tip anywhere on either dipole no matter how far
apart are the measurement points. My neighboring ham friend said the number
of degrees in the coil had to be the number of degrees in the
wire and indeed, both are measured to be zero degrees, but
I wonder if that's really what he had in mind when he said
the delay would be equal. Zero equals zero, but what does
that mean for me?

The change in feedpoint impedance and the different current
magnitudes don't much bother me but I am really bothered
by those phase measurements. The dipole is 180 degrees long
and the current should be changing phase, at least on the wire
if not through the coil. I need some expert to explain how those
phase measurements on the wire are possible on both antennas.
I know my phase measurements are correct but why are they
always zero degrees? And since they are always zero degrees,
what information are they providing?
--
73, Cecil, W5DXP