Keith Dysart wrote:
This reality, however, does not demonstrate any
value for the *concept* of phase shift at a
discontinuity.

It may indeed have little value for stubs. But
for loaded mobile antennas the value is obvious.

The value is that it explains the phase shift
through a loading coil in a loaded mobile
antenna and the phase shift at the coil to
stinger junction. Using dual-Z0 transmission
line stubs we are ready to understand loaded
mobile antennas, the phase shift through the
loading coil, and the "missing degrees" at the
coil to stinger junction.

According to Dr. Corum, my 75m Texas Bugcatcher
coil has a Z0 of ~4000 and a VF of ~0.02.

The stinger has a Z0 in the ballpark of 400 ohms
and a VF close to 1.0

Knowing what we know about a dual-Z0 1/4WL stub,
we can now use that knowledge to analyze a base-
loaded mobile antenna with coil and stinger.

---Z0=4000 ohm coil---+---10 deg 400 ohm stinger

Now it's a piece of cake. How many degrees of
loading coil do we need to make the configuration
90 electrical degrees long?

Arctan((400/4000)*cot(10)) = ~30 degrees

What is the impedance at the coil to stinger
junction?

400*cot(10) = ~ -j2300 ohms

What is the phase shift at the coil to stinger
junction?

90 - 30 - 10 = ~50 degrees

I stumbled upon the dual-Z0 stub idea in trying to
understand the phase shifts and delays in a loaded
mobile antenna. The same general principles apply.
Using traveling-wave current to measure the delay
through my Texas Bugcatcher coil agreed within 15%
with these calculated values.

One side said the coil had to make up the missing 80
degrees of antenna that necessarily had to be there
with a 10 degree stinger. This side did not understand
the phase shift at the coil to stinger junction.

The other side said the coil, like a lumped inductor,
has ~zero phase shift through it. This side did not
understand the limitations of the lumped circuit
model.

The delay through a coil is what it measures and
calculates to be within a certain accuracy. It is not
80 degrees and it is not ~zero degrees.
--
73, Cecil http://www.w5dxp.com