lu6etj wrote in
:

....
I am not interested yet to make questions about real rigs, but reduce
at first only one specific problem at the most simple theorical model
I can think: an ideal constant voltage source in series with an ideal
resistence loaded at first with simple resistive loads connected
directly and late via ideal lossless TL of differents simple
wavelenghts 1/2, 1/4, 1/8 (I have formed idea about this, but I am not
interested in my concept but your concept about it).
For example, I want to know if you (all) would predict identical Rs
and Rl dissipation in that reduced and theorical context with direct
and remotely connected loads (vinculated via TL).

To this point K1TTT -seem to me- tell me you all would agree to settle
the problem with Telegrapher's equations to obtain TL input Z and then
apply simple circuit theory solution to calculate Rs-Rl dissipation
(before begin Thevenin misleading issue).
I do not want to advance more from here for fear to complicate the
question with my translation.

Yes, if you are looking for a steady state solution, that is a valid
solution, and almost the easiest solution.

If you are using lossless lines, then the solution can be simpler than the
Telegrapher's Equation which uses hyperbolic trig functions. Simple trig
functions suffice if the line is lossless... but of course, the hyperbolic
functions will also work.

The reason I said "almost the easiest solution" above is that a trig based
simplification of the Telegrapher's Equation is simpler than the hyperbolic
Telegrapher's equation.

Implicit in this is that for the steady state, it doesn't matter how an
external network dictates V/I (Z) at the source/load terminals, whether or
not transmission lines are involved, or their length, the power delivered
by the source to its immediate load is determined by Veq, Zeq of the
source, and Zl of the load.

If an experiment indicates othewise, the experiment is flawed (eg something
is wrong with the assumed values for circuit components, measurement error
etc).

Taking Walt's example, he connected three 50 ohms loads in parallel, then
attached a nominal 50 ohm line of 13.5° electrical length. If you use TLLC
(http://www.vk1od.net/calc/tl/tllc.php) to solve this problem at 4MHz using
RG213 (though I don't know what he used), Zin is 17.78+j10.58. A lossless
solution will have very slightly lower R. Walt measured 17.98 + j8.77 which
suggests that the load at the end of the 50 ohm line was not exactly
16.6667+j0, or the line a little shorter, Zo off spec etc.

Whilst the above focuses on steady state analysis, understand that steady
state analysis is not appropriate for some types of transmitters, but for
systems where the transmission line propagation delay is small compared the
the highest modulating frequency, steady state analysis should be adequate.

Owen