On Dec 13, 5:57 am, Cecil Moore wrote:
It does not seem to be a concept that is
particularly useful for the solving of problems.

Looks like you haven't thought it through. If one
wants to create a shortened dual-Z0 stub with
equal lengths of each section of Z0High and Z0Low,
here is the corresponding chart for different
ratios of Z0High/Z0Low.

http://www.w5dxp.com/DualZ0.gif

As an example, one can create an electrical 1/4WL
stub that is 1/3 the normal physical length by
using 600 ohm line and 50 ohm line.

There are many ways to create the impedances
for matching, each with different advantages. As
you point out, one of the benefits of using two
different impedance lines is a reduction in material,
though, you could go all the way to just using
a lumped capacitor and save even more.

This reality, however, does not demonstrate any
value for the *concept* of phase shift at a
discontinuity. For the concept to be useful it
should facilitate understanding or problem
solving. As far as I can tell, you always solve
the problem in the conventional way (change
the angle on the Smith chart, un-normalize
the impedance, re-normalize the impedance
to the new Z0, measure the angle to get to
the desired impedance) and then work out
the "phase shift" at the discontinuity. It sure
looks like additional work that adds no value
since the important and useful information
has already been derived before computing the
"phase shift".

As such, I declare it "not particularly useful".

....Keith