Roger Sparks wrote:
Thanks Keith. I see what you are doing now, although I still
don't understand your logic in faulting Cecil on the instantaneous
values. I agree with you that the instantaneous values can be
tracked, but don't see a fault in Cecil's presentation.

I made no assertions about instantaneous power at all and
have added a note in my article to that effect. My assertions
about instantaneous power cannot possibly be wrong because
I didn't make any. :-) Nothing in my article applies to or
is concerned with instantaneous power.

For the power density/irradiance/interference equation to
be applicable, certain conditions must be met. One of those
conditions is that all component powers must be *average*
powers resembling power density/irradiance from optics.
Another condition is that the phase angle between the two
waves being superposed must be constant and therefore the
two associated waves must be coherent (phase-locked) with
each other.

Roy and I went around a few times on whether the source reflects
in a case like this. The source reflection controls whether the
50 ohm source resistor acts like 50 ohms to the reflected wave,
or acts like a short circuit in parallel with the 50 ohm source
resistor.

What Roy (and others) are missing is that there is more than
one mechanism in physics that can cause a redistribution of
reflected energy back toward the load. An ordinary reflection
is not the only cause. In a one-dimensional environment,
e.g. a transmission line, there is an additional mechanism
present that can redirect and redistribute the reflected
energy back toward the load.

1. Reflection - what happens when a *single wave* encounters
an impedance discontinuity. Some (or all) of the reflected
energy reverses direction.

2. Wave interaction - what happens when *two waves* superpose,
interact, AND effect a redistribution of their energy components
as described on the FSU web page at:

http://micro.magnet.fsu.edu/primer/j...ons/index.html

"... when two waves of equal amplitude and wavelength that
are 180-degrees ... out of phase with each other meet, they
are not actually annihilated, ... All of the photon energy
present in these waves must somehow be recovered or
redistributed in a new direction, according to the law of
energy conservation ... Instead, upon meeting, the photons
are redistributed to regions that permit constructive
interference, so the effect should be considered as a
*redistribution of light waves and photon energy* ..."

In the simple ideal voltage source described in my article,
there are no reflections because the source resistance equals
the characteristic impedance of the transmission line.

In Part 1 of the article, there is also no wave interaction
because the forward wave and reflected wave are 90 degrees
out of phase. So for that special case, none of the reflected
energy is redistributed back toward the load. Therefore, for
that special case, all of the reflected energy is dissipated
in the source resistor because all conditions for a redistribution
of the reflected energy have been eliminated.

In the special case described in Part 1, because of the 90
degree phase difference, the forward wave and reflected
wave are completely independent of each other almost as if
they were not coherent. The result in that special case is
that the power components can simply be added because in
that special case, (V1^2 + V2^2) = (V1 + V2)^2, something
that is obviously NOT true in the general case.

Part 2 of the article will describe what happens when
the forward wave and reflected wave interact at the source
resistor and effect a redistribution of reflected energy
back toward the load *even when there are no reflections*.
This is the key concept, understood for many decades in the
field of optical physics, that most RF people seem to be
missing.
--
73, Cecil http://www.w5dxp.com