On Jun 18, 10:49*am, walt wrote:
Now where is the impedance-matching point on the line?

By definition, the Z0-match point is where the reflections toward the
source are first eliminated, i.e. Vtot/Itot=Z0, which is on the source
side of the inductive stub. If reflections were eliminated anywhere
else (closer to the load) then there would be no need for that section
of feedline. An energy analysis is possible but would no doubt be
messy. For instance, what is the SWR at the stub short? Where is the
ground reference at the stub short? Since the series stub is a certain
number of degrees long, the two currents at the mouth of the stub
cannot possibly be 100% differential, i.e. common-mode currents exist
on the series stub. Since there is a phase shift in the series stub
that doesn't exist in the main coax braid, common-mode current must be
flowing in the rest of the system. Electrically, how long is the
series stub in degrees? Does an impedance discontinuity exist at the
short at the end of a series stub like it does at the end of a shorted
stub - or not? What is the characteristic impedance of a series stub?
(It is probably not the Z0 of the transmission line being used.)

There is obviously a multiple-port impedance discontinuity at the Z0-
match point but I don't know what it is or how to measure it. I don't
even know how to measure the multiple-port s11 at the Z0-match point.
IMO, this example is just too complicated for 99.9% of the readers
here, including myself.

If we put the series stub (or inductive coil) into a two-port black
box and performed s-parameter measurements on it, we could come up
with the s-parameter equations.

Source--50 ohm line--x--black box--y--150 ohm load

Reckon what s11 we would measure if we replaced the 150 ohm load with
a 50 ohm resistor?
--
73, Cecil, w5dxp.com