Ian White GM3SEK wrote:

To all: Ian is not addressing the issue which is: Can a standing wave
current phase measurement be used to tell us anything about the phase
shift through a loading coil? The answer is NO! W7EL's phase measurements
are flawed. Therefore, they cannot be presented as evidence of anything
valid. They certainly cannot be used to prove that a coil is a point
inductance.

The question is not whether the two models agree on the low end - they
do agree. The question is whether they agree on the high end - they
don't and they are not supposed to. The differences I have presented in
the two models is where the lumped circuit model fails and the
distributed network model is valid.

There is an infinite range of real-life loading coils of various shapes
and sizes. Pure single-point inductive loading is the limiting case that
marks one end of that range. Any successful theory has GOT to get this
case right - and if it can't, it fails.

Since the distributed network model is a superset of the lumped circuit
model, it does get that case right. It also gets the case right at the
other end of the range where the lumped circuit model fails. 75m mobile
loading coils cannot be validly modeled using the lumped circuit model.

Regardless of the actual method used, any correct analysis of the whole
antenna MUST conclude that, for the limiting case of pure inductive
loading, the voltage/current/phase relationships at the loading
inductance are the SAME as those predicted by conventional circuit
analysis. This limiting case is where the two kinds of analysis come
together, and here they MUST agree.

And they do, no question about that.

That means a correct analysis for the whole antenna MUST predict zero
phase shift in the current (It = I0 cos wt) between the terminals of the
loading inductance.

Here you are allowing your model to dictate reality, not vice versa.
A practical antenna is a large structure, usually at least an electrical
1/4 wavelength. There is no such thing as a point inductance in a
real world mobile ham antenna.

Let's be clear: in this context, "current" is the plain ordinary
alternating current that we learned about in school: It = I0 cos wt. It
is the simple back-and-forth movement of electrons (charge) past a given
point.

Let's be clear. That model fails in a transmission line as it does in
standing wave antennas. Taking a simple-minded approach to physics
is where the air, earth, fire, and water elements came from.

Nobody denies that for real-life loading coils there can be a phase
shift in the current from end to end, and that it will become larger as
the coil becomes longer and skinnier. That isn't the question I'm
addressing here. But the question of what happens when the coil shrinks
down to become a single-point loading inductance is equally important:
it cannot be evaded, and it is a definitive deal-breaker.

In that case, both models give the same answer. But that case doesn't
exist in reality in real-world antennas. In reality, the lumped circuit
model fails when it is extended to large structures like transmission
lines and antennas.

It's hard to tell for sure from the avalanche of messages, but Cecil's
analysis apparently fails in the limiting case of pure inductance - or
rather, he seems to deny that the test is even a valid one.

The distributed network analysis works perfectly in the limiting case
since it is a superset of the lumped circuit model. There is absolutely
no disagreement between the distributed network analysis and the
lumped circuit analysis for point inductors. Anyone who says there is
is just attempting to set up a strawman.
--
73, Cecil http://www.qsl.net/w5dxp