Well, Cecil, I think we're zeroing in on the flaw in your perception of
how the powers add. I hope you won't just keep saying it's impossible,
and will instead sharpen your pencil to show, as I have, the forward,
reverse, and total voltages, currents, and powers at both ends of the
line. And how everything can work together consistently to fit into your
view of power addition and subtraction.

A number of people have been trying for a long time to convince you
there's a flaw in your logic, but so far you haven't been able to see
it. Hopefully, in the process of deriving the values for this circuit,
you'll see where your logic has gone astray. Or, perhaps, you'll come up
with a completely consistent set of voltages, currents, and powers that
do fit within your view. And we'll all learn from it as we see where the
difference arises between your analysis and mine. Until you come up with
your analysis, though, I won't pay much attention to your complaints
that it's wrong unless you're able to show where in the analysis the
error lies.

I've posted the derivation of the total power formula on this thread. In
going through it, I found an error in the formula posted with my
numerical example. I've posted a correction for that on the same thread
as the example. In the correction posting, I also show how the formula
produces the same result as I got by directly calculating the total
power from the load voltage and current.

A closing quotation, from Johnson's _Transmission Lines and Networks_:

"[For a low loss line] P = |E+|^2 / Z0 - |E-|^2 / Z0. We can regard the
first term in this expression as the power associated with the
forward-traveling wave, and the second term as the reflected power. This
simple separation of power into two components, each associated with one
of the traveling waves, can be done only when the characteristic
impedance is a pure resistance. Otherwise, the interaction of the two
waves gives rise to a third component of power. Thus, the concept
applies to low-loss lines and to distortionless lines, but not to lossy
lines in general."

Something for you to think about. Or maybe you subscribe to Reg's view
that these texts are written by marketeers and salesmen. After all, as
Chairman of Princeton's EE department, I suppose Johnson's job was
primarily PR.

I'm quite sure that if you look carefully at any text where the author
subtracts "reverse power" from "forward power" to get total power, that
somewhere prior to that the assumption is made that loss is zero and/or
the line's characteristic impedance is purely real.

Roy Lewallen, W7EL

Cecil Moore wrote:
Roy Lewallen wrote:

No, the average Poynting vector points toward the load.


That automatically says Pz- is not larger than Pz+. There are only
two component Poynting vectors, 'Pz+' forward and 'Pz-' reflected.

If so, surely you came up with the same result, including the third
power term. If you haven't done the derivation, or if you'd like to
compare your derivation of total average power with mine, I'll be glad
to post it.


Assuming coherent waves, all wave components flowing toward the load
superpose into the forward wave and all wave components flowing away
from the load superpose into the reflected wave. Since there are only
two directions, there cannot exist a third wave. If your average Poynting
vector points toward the load, Pz- cannot possibly be larger than Pz+.
But feel free to post the derivation.