I read the analysis earlier, and didn't and don't see how it constitutes
the proof I proposed.

Permit me to repeat the entirety of what I said, and not just the last
sentence. I said:

I'll restate something I mentioned before (first incorrectly, then
corrected). Connecting a load to a transmission line which is the
complex conjugate of the transmission line Z0 does *not* guarantee
maximum power delivery from the source, or to the load. The load
impedance which provides maximum load power is the complex conjugate of
the impedance looking back from the load toward the source. That
impedance is the source impedance transformed through the transmission
line between source and load, and it's not generally the same as the
line's Z0, or its complex conjugate. When this condition of maximum load
power is met, there will almost certainly be voltage and current wave
reflections on the line -- there would be none only if the optimum load
impedance coincidentally happened to be equal to the line Z0. So the
argument that there can be no reflection of the voltage wave under the
condition of maximum power transfer is wrong.

You didn't show differently in your analysis, and no one has stepped
forward with a contrary proof, derivation from known principles, or
numerical example that shows otherwise.


Now let's see if this constitutes such a proof.

Peter O. Brackett wrote:
Roy:

[snip]

You didn't show differently in your analysis, and no one has stepped
forward with a contrary proof, derivation from known principles, or
numerical example that shows otherwise.

Roy Lewallen, W7EL

[snip]

Yes I did. I guess that you missed that post.

I'll paste a little bit of that posting here below so that you can see it
again.

[begin paste]
We are discussing *very* fine points here, but...

[snip]
ratio of the reflected to incident voltage as rho = b/a would yeild the
usual formula:

rho = b/a = (Z - R)i/(Z + R)i = (Z - R)/(Z+ R).

Here I'll assume that you've defined a and b as equalling the forward
and reverse voltages in a transmission line, which is a different
definition than in your other posting. With that definition of a and b,
and if R is the transmission line characteristic impedance, then the
equation is valid for a transmission line, and ok so far. Otherwise,
you're talking about something other than a transmission line, so the
"proof" doesn't apply at all.

In which no conjugates appear!

Now if we take the internal/reference impedance R to be complex as R = r +
jx then for a "conjugate match" the unknown Z would be the conjugate of the
internal/reference impedance and so that would be:

Z = r - jx

So the load impedance is the complex conjugate of the transmission line
characteristic impedance. Ok.


Thus the total driving point impedance faced by the incident voltage a would
be 2r:

R + Z = r + jx + r - jx = 2r

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