Roy:

[snip]
"Roy Lewallen" wrote in message
...
Not QED at all. You claimed to have proved that maximum power is
delivered to a load when a transmission line is terminated such that the
reflected voltage on the line is zero.
[snip]

No I did not! Never said that, never have. Where did you get that idea?

I said that for a general complex Zo the reflected voltage is generally
NOT zero at maximum power transfer.

To make myself perfectly clear, let me repeat that...

I said that for a general complex Zo the reflected voltage is generally
NOT zero at maximum power transfer.

I said that for a general complex Zo the reflected voltage is generally
NOT zero at maximum power transfer.

I said that for a general complex Zo the reflected voltage is generally
NOT zero at maximum power transfer.

[snip]
Here, you're agreeing that the
reflected voltage is zero when the line is terminated in its
characteristic impedance. So where's the proof that this condition leads
to maximum power to the load?

Roy Lewallen, W7EL
[snip]

What I was trying to prove was that the reflected voltage is NOT zero
at conjugate match for the case of complex Zo!

I proved that by setting up a transmission line with perfect image [not
conjugate]
matching on both ends [Zo is seen looking in both directions from any point
in
the system] and driven by a generator set up to create the incident wave.

That system has no impedance discontinuities anywhere. The impedance
is Zo all along the line and into the generator looking in either direction.
No impedance discontinuities no reflections, period!

I then calculated the classical reflection coefficient and showed it to be
zero
confirming that rho = 0 when there are no impedance discontinuities and the
classical formula for rho is used, rho = (Z - Zo)/(Z + Zo).

As the last step I changed the termination from Z0 to conj(Zo) i.e. a
conjugate
match, NOT an image match and showed that rho is NOT zero in this case.

QED!

Summarizing...

Image Match: A line of surge impedance Zo terminated in Zo has no impedance
discontinuities and no reflections.

Conjugate Match: A line of surge impedance terminated in conj(Zo) has an
impedance
discontinuity and hence has reflections. [Unless in the one unique case
that Zo is purely real]

BTW...

Aside: From the postings of Dave and yourself along this thread, I get the
impression that
ya'll beleive that lumped systems obey different laws and should should be
modeled
differently than distributed systems. I am surprised by that claim. Surely
you don't mean that!

Surely all electrical systems, lumped or distributed, must obey the laws of
electrodynamics as set
out by Maxwell-Heaviside. Do you know of any cases where they don't?

Regards,

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