Ian White GM3SEK wrote:
I am not your offshore lab service, Cecil. If you want to back up your
speculations, do your own work.

I posted my measurements but I am handicapped by not being able to
measure any impedance above 650 ohms. But I can sure see those series
resonant points with my MFJ-259B. You know, the points that your lumped
circuit model says do not exist?

I know what a parallel LC circuit does. The point you continue to evade
is that, from VLF up to about 20MHz, this coil of cable behaves in
exactly the same way.

And falls apart above 20 MHz because of transmission line effects. Your
lumped circuit model is a subset of the distributed network model. Of
course, they will give similar results up to the point where the lumped
circuit model falls apart.

The circuit looks inductive below the resonant frequency and capacitive
above it, and passing through resonance the phase angle of the
impedance flips from +90deg to -90deg... and then it stays very close to
90deg, clear up to about 20MHz.

Yes, both models give similar results up to 20 MHz which is about half
way around the Smith Chart. Then your model falls apart. The fact that
the phase angle departs radically from -90 degrees in reality when your
model predicts that it should stay at -90 degrees is prima facie
evidence that your model has fallen apart. Your own phase graphs
contradict what you are saying.

That is the usual mixture of selective quoting and false logic. What
you continue to overlook is that the behaviour all the way from DC
through the 4.7MHz resonance and onward up to about 20MHz can be
accurately represented by nothing more elaborate than a simple LCR
circuit. The fall in impedance from the resonant frequency up to about
20MHz is completely accounted for by just those three simple parameters:
two reactances and one fixed loss resistance in parallel.

Just proving that the lumped circuit model is a subset of the
distributed network model and the two results are expected to be
similar. But your model falls apart above 20 MHz where the transmission
line effects are obvious.

Above that frequency there are effects that the simple LCR model cannot
account for. I have always said so, and yes, a transmission-line model
could account for those.

I certainly don't remember you ever saying that but we are making
progress. You are agreeing with me and we seem to have little argument
left. What I seem to remember you saying is that it is "ridiculous" to
model a parallel self-resonant choke as a transmission line. But my
memory is not as good as it once was.

That is simply not true. The limitation in working range is simply the
shunting effect of the self-capacitance, which becomes increasingly
important above resonance and causes a long progressive fall in
impedance. This effect is very simple and entirely predictable. By 20MHz
it has reduced the impedance to a hundred ohms or less, which means that
the coil of cable is no use as a feedline choke for that frequency.

Your rose colored glasses are giving you false images. In the earlier
example, the 12 turn choke had a maximum choking impedance at 15 MHz.
At 23 MHz, the phase angle goes to -88 degrees just as both models
predict. At 32 MHz, the phase angle is back to +20.4 degrees. Using
your lumped circuit model, how does the phase angel get back to +20.4
degrees with that lumped capacitance dominating???

Ian, IF YOU ANSWER ONLY ONE QUESTION, PLEASE ANSWER THIS ONE. Exactly
how does the phase angle get to +20.4 degrees at the exact time that
your lumped circuit model is predicting -90 degrees??? (That's a 541%
error!)

The series resonances above 20MHz cause further dips in impedance to
only a few ohms, but those dips are quite localized in frequency. They
are not the cause of the long progressive fall in impedance above the
parallel resonance, which is what limits the usable bandwidth of the
choke.

You are attempting to use petitio principii to prove the validity of
your model and I think you know that is a no-no. A similar long
progressive fall happens with the distributed network model but it
accurately predicts the transmission line effects proved by the bumps
in the phase graphs that you provided.

Back to the previously discussed 12 turn choke. The impedance at 23 MHz
is 955 ohms at -88 degrees, almost purely capacitive. Your "long
progression" model would predict 686 ohms at -89 degrees for 32 MHz.
Yet at 32 MHz, the impedance is measured to be 258 ohms at +20.4
degrees. Your lumped circuit "long progressive fall" model could not be
any more wrong. Your impedance is off by 166% and your phase is off by
541%.

Please note that if your lumped circuit model were correct, the choke
would still be performing pretty well at 32 MHz with a choking
impedance of 686 ohms. Your above statement is thus proved false by the
measured data.

The challenge is still on the table, Cecil, for YOU to develop a
quantified transmission-line model that will predict all the measured
properties of a resonant choke over that wider range of frequencies.

My model, although not perfect, yields more accurate results than your
model over that wider range of frequencies. My model predicts the bumps
in the phase graphs. Your model predicts zero bumps in the phase
graphs. Yet the bumps are obvious on your phase graphs. My model, a
superset of yours, sure doesn't produce errors like 541%.
--
73, Cecil, w5dxp.com