On 12 jun, 10:10, Cecil Moore wrote:
On Jun 11, 11:24*pm, lu6etj wrote:

As a courtesy to me, a foreigner tourist ham, would you mind stop for
a brief moment your more general differences and tell me if you agree
on the behavior of a Thevenin generator with a series resistance of 50
ohms in relation to changes in impedance of a lossless TL predicted by
the Telegrapher's equations solutions in terms of the power dissipated
on the load resistance and series resistence of Thevenin source?
I am pretty serious about this: until today I could not know if you
agree in that!! :)

Miguel, I don't think there is much disagreement about things that are
easily measured, like voltage and current. One solution to the
telegrapher's equations involves forward and reflected waves of
voltage and current. The conventional way of handling power (energy/
unit-time) is to use the voltages and currents to calculate the power
at certain points of interest. The telegrapher's equations do not tell
us *why* the power is what it is and the energy is where it is. To
obtain the why, one must study the behavior of electromagnetic waves.
How does the energy in electromagnetic waves behave? The telegrapher's
equations and Thevenin source do not answer that question.

For instance: Most readers here seem to think that the only phenomenon
that can cause a reversal of direction of energy flow in a
transmission line is a simple EM wave reflection based on the
reflection model. When they cannot explain what is happening using
that model, they throw up their hands and utter crap like, "Reflected
wave energy doesn't slosh back and forth between the load and the
source". But not only does it "slosh back and forth", it sloshes back
and forth at the speed of light in the medium because nothing else is
possible.

These are the people who have allowed their math models to become
their religion. They will not change their minds even when accepted
technical facts are presented. One response was, "Gobblydegook". (sic)

There is another phenomenon, besides a simple reflection, that causes
reflected energy to be redistributed back toward the load and that is
wave cancellation involving two wavefronts. If the two wavefronts are
equal in magnitude and opposite in phase, total wave cancellation is
the result which, in a transmission line, redistributes the wave
energy in the only other direction possible which is, surprise, the
opposite direction. This is a well known, well understood,
mathematically predictable phenomenon that happens all the time in the
field of optics, e.g. at the surface of non-reflective glass. It also
happens all the time in RF transmission lines when a Z0-match is
achieved.

Using the s-parameter equations (phasor math) at a Z0-match point in a
transmission line:

b1 = s11*a1 + s12*a2 = 0 = reflected voltage toward the source
Square this equation to get the reflected power toward the source.

These are the two wavefronts that undergo total wave cancellation,
i.e. total destructive interference.

b2 = s21*a1 + s22*a2 = forward voltage toward the load
s22*a2 is the re-reflection. Square this equation to get the forward
power toward the load.

If one squares both of those equations, one can observe the
interference terms which indicate why and where the energy goes. All
of the energy in s11*a1 and s12*a2 reverses direction at the Z0-match
and flows back toward the load. All the things that Roy is confused
about in his food-for-thought article on forward and reflected power
are easily explained by the power density equation (or by squaring the
s-parameter equations).

Ptot = P1 + P2 + 2*SQRT(P1*P2)*cos(A)
--
73, Cecil, w5dxp.com

Sorry and thanks Cecil I do not see this kind answer (I still using
normal Google groups reader and loss tracking of your message).
Tomorrow I will analize it with care, now is late here but I do not
want delay my aknowledge.

Miguel