On Dec 6, 8:59 am, Cecil Moore wrote:
Keith Dysart wrote:
Perhaps there is just no reason why the "phase shifts" should add
to 90. That would make the problem go away.

But there is every reason why the phase shifts *must*
add up to 90 degrees (or 270 or 450 or ...).

The only way you can get zero ohms looking into an
open stub is if the phase shift end-to-end is 90
degrees (or 270 or 450 or ...). The reflected current
must arrive back at the feedpoint in phase with
the forward current for the stub to be 1/4WL resonant.

In a typical loaded mobile antenna, the only way
to get a resistive feedpoint impedance is if the
antenna is electrically 90 degrees long.

Take a 1/4WL straight monopole wire. It is
electrically 90 degrees long. Put one turn of
loading in it. Is it still electrically 90 degrees
long or not? Proceed until the antenna is all
coil, i.e. self-resonant. Is it still electrically
90 degrees long or not?

You are good at building scenarios that align with
your hypotheseses. To test your hypothesis for
correctness you need to examine the scenarios
that may not align rather than those that do.

And you already have one. You have needed to
invent a phase shift occuring at an impedance
discontinuity to explain the missing "electrical
length".

You should also consider a shortened monopole
where lumped elements are used to tune out
the reactance.

Also consider a lengthened monople where
either distributed or lumped elements are used
to tune it.

You should consider a pure lumped element
circuit that presents the same impedance.
Identify the locations that sum to a 90 degree
"electrical length".

Lastly, for real fun, find the 90 degree
"electrical length" in a crystal.

....Keith