Thanks for hanging in there. Let's see where this one goes. . .

Peter O. Brackett wrote:
Roy:

[snip]

Here you've lost me. a is the forward voltage in the transmission line.
What can be the meaning of its facing a driving point impedance? The
forward wave sees only the characteristic impedance of the line; at all
points the ratio of forward voltage to forward current is simply the Z0
of the line. So I don't believe that it sees 2r anywhere.

This is where I'm stuck. If you can show where along the line the
forward voltage wave "faces" 2r, that is, Vf/If = 2r, I can continue.

Roy Lewallen, W7EL

[snip]

I appologize if I am "going to fast" for the limitations inherent in
NewsGroup postings.

Let me take it a little more slowly here...

To see that there is essentially no difference between my (apparently two)
different
definitions of the incident and reflected waves a and b, consider the
following scenario
of an actual transmission line having surge impedance [characteristic
impedance] Zo.
Let Zo be in general complex. i.e. Zo = sqrt[(R + jwL)/(G + jwC)] where R,
L, G,
and C are the primary parameters of R Ohms, L Henries, G Siemens, and C
Farads
per unit length.

Now at any particular frequency w = 2*p*f you will find that this general
complex
surge impedance Zo evaluates to a complex number, say Zo(jw) = r + jx.
Later
let's let r = 50 Ohms and x = 5 Ohms so that we can work out a numerical
example.

The numbers aren't necessary, but that's fine.


Consider either a semi-infinite length of this Zo line, or even a finite
length of the Zo line
terminated in an impedance equal to Z0. I am sure that you will agree that
both the
semi-infinite Zo line or the finite length Zo line terminated in Zo have the
same
driving point impedance namely Zo.

The terminated line I'm comfortable with. "Semi-infinite" isn't in my
lexicon, but I'll see where it goes.

Now excite this semi-infinte Zo line by an ideal generator of open circuit
voltage
Vi = 2*a behind an impedance equal to the surge impedance Zo. In other
words
this is a Thevenin generator of ideal constant voltage 2a behind a complex
impedance
of Zo. And so... since an ideal voltage source has zero impedance, the
termination
at the source end of this semi-infinite Zo line is Zo,
. . .

Maybe the trouble is with the "semi-infinite" aspect, but here we part
company again. The termination at the source end of the line is, by
definition, the source impedance, which is zero, not Z0.

Can't you do this analysis with a plain, ordinary, transmission line of
finite length? Lossless is ok, lossy is ok. Or is your proof true only
if the line is "semi-infinite" in length (whatever that is)?

Roy Lewallen, W7EL