Roy Lewallen wrote in
:

Owen Duffy wrote:
Roy Lewallen wrote in
:

...
Sorry, I don't think so. The very first equation, Vf=Vs/2, would be
true only if the load = Ro or for the time between system start and
when the first reflection returns. For the specified steady state
and arbitrary load, Vf would be a function of the impedance seen by
the source which is in turn a function of the line length and load
impedance.

Vf means the 'forward wave' voltage equivalent voltage at the source
terminals.

I provide the mathematical development of the case that Vf=Vs/2 where
Rs=Ro=Zo at http://vk1od.net/blog/?p=1028 .

Can you fault that development?

Owen

I stand corrected. In the special case of Rs = Z0, the steady state
forward voltage and therefore "forward power" become independent of
the transmission line length and load impedance, just as you said and
show in your analysis.

Thanks Roy.

There may have been some misunderstanding. I thought your challenge was
issued in the context of the ideal 50 ohm source that Miguel was using as
a test case.

The maths for the ideal 50 ohm source test case is so simple, that it is
evident the |Vr|^2/Ro is not simply summed into Rs's dissipation.

Of course, in the general case, the maths is uglier, but since the
special case of Rs=Ro=Zo proves the 'reflected power' is not simply
dissipated in Rs, it (the general case) must give the same outcome.

Owen