Dave:

[snip]
these discussions always seem to end up in this same quagmire, one group
trying to solve everything with wave equations, sinusoidal steady states,
transmission line transformations, and the other holding on to the lumped
models and trying to make them fit the wrong problem domain. one thing i
did learn in ee classes was to use the right model for the job, choosing
the
wrong one will give you wrong answers most of the time.... the real
problem
is that sometimes you can get the right answer from the wrong model just
because the numbers work out... and when you have to show your work you
lose
credit for using the wrong method but still getting the right numerical
answer. that is what i see here, someone has started with a simplified
case
that just happens to work out to the same answer and has tried to
generalize
it... -10 points for the wrong method!
[snip]

Dave:

I disagree, I feel that for measurements and calculations involving the
impedance matching
dynamics at any reference plane in such systems the differences between
lumped and
distributed systems is trivial and unimportant.

The impedance matching dynamics at the reference plane/junction point are
the same for
distributed and lumped systems, they obey all the same equations, their
electrodyanamics
is the same, one simply cannot tell the difference at the driving point.

If you don't like lumped models, then make the internal resistance of the
Thevenin
generator out of a distributed line. It will work just the same way.

The disagreements that occur when there are discussions/arguments occur
because folks
often assume they are different situations, but they are not.

Every line has a driving point impedance of Zo and at that point the voltage
and current
are related by Ohms Law v = Zo*i just as for a lumped system of impedance
Zo.
It simply doesn't matter if Zo is lumped or distributed when making
observations at the
driving point. And this is what one is doing when making impedance matching
calculations.

I agree that if you move off down the line in distance/space that you will
find
differences, but you certainly can't observe them at the driving points.

A slotted line device for measuring VSWR is a physical example of a
measurement
system that works on a distributed system that won't work for a lumped
system.
However you can exactly correlate the measurements taken with the slotted
line
to measurements taken at the driving point.

And so, although I agree with you that some can't seem to be able to see
that these
situations are the same, I don't agree that makes them different. They are
the same
at the driving point.

--
Peter K1PO
Indialantic By-the-Sea, FL.