I have to agree with what Richard and some others have said.

First, that you've done a tremendous job of sharing your extensive
knowledge and experience, and explaining transmission line phenomena in
such a clear and understandable manner. We all owe you a great debt for
this.

But second, that there's something which you do state that I and some
others can't accept. And that is that a "virtual" short (or open)
circuit causes reflections, or that waves reflect from it. I maintain
that for either to happen requires that traveling waves interact with
each other. The "virtual" short or open is only the result of the sum --
superposition -- of traveling waves. Those traveling waves, and hence
their sum, cannot cause a reflection of other waves, or alter those
other waves in any way. Only a physical change in the (assumed linear)
propagating medium can alter the fields in a traveling wave and cause a
reflection. A real short circuit is in this category; a virtual short
circuit is not. It doesn't matter if the waves are coherent or not, or
even what their waveshapes are or whether or not they're periodic -- as
long as the medium is linear, the waves cannot interact.

You have clearly shown, and there is no doubt, that waves behave *just
as though* a virtual short or open circuit were a real one, and this is
certainly a valuable insight and very useful analysis tool, just like
the "virtual ground" at the summing junction of an op amp. But I feel
it's very important to separate analytical tools and concepts from
physical reality. If we don't, we're led deeper and deeper into the
virtual world. Sooner or later, we reach conclusions which are plainly
wrong.

There are many other examples of useful alternative ways of looking at
things, for example differential and common mode currents in place of
the reality of two individual currents, or replacing the actual
exponentially depth-decaying RF current in a conductor with an imaginary
one which is uniform down to the skin depth and zero below. But we have
to always keep in mind that these are merely mathematical tools and that
they don't really correspond to the physical reality.

Unless I've incorrectly read what you've written, you're saying that
you've proved that virtual shorts and opens reflect waves. But in every
example you can present, it can be shown that all waves and reflections
in the system can be explained solely by reflections from real impedance
changes, and without considering or even noticing those points at which
the waves superpose to become virtual short or open circuits. That, I
believe, would disprove the conjecture that virtual shorts or opens
cause reflections. Can you present any example which does require
virtual shorts or opens to explain the wave behavior in either a
transient or steady state condition?

If I've misinterpreted what you've said, I share that misinterpretation
with some of the others who have commented here. And if that's the case,
I respectfully suggest that you review what you've written and see how
it could be reworded to reduce the misunderstanding.

Once again, we all owe you a great deal of thanks for all you've done.
And personally, I owe you thanks for many other things, including
setting such an example of courtesy, civility and professionalism here
in this group (as well in everything else you touch). It's one I strive
for, but continually fall far short of.

Roy Lewallen, W7EL