On Mar 27, 11:10 am, Cecil Moore wrote:
Keith Dysart wrote:
So you are having difficulty doing the math to justify
your hypothesis.

Actually no, the math is not difficult. I'm pre-
occupied with something else and think it's just
time to agree with Hecht that instantaneous power
is "of limited utility".

Have you taken a look at Roger's spreadsheets?

Yes.

Conservation of energy requires that the total
quantity of energy in the system not change.

:-) Isn't the whole purpose of a transmitting
antenna to radiate energy away from the antenna
system? And that radiation continues to be "lost"
from the system space for some time after the
source power is removed?

Wouldn't you have to define the "system" as the
entire universe for your statement to be true?

Sort of, but there is an easy work-around. Since we
are not particularly interested in what happens to
the energy going to the source resistor, for
example, we define the boundary of the system to
pass through the resistor and simply account for
the energy as a flow out of the system. And we
do the same for the source since we are not
particularly interested in where the energy for
the source comes from; we just account for it as
a flow into the system. And lastly, we don't
really care where the energy on the line goes to
or comes from, so we just account for it as a flow
out of the system. You may have noticed that we
have removed all the components from the system,
it is a null system, and all we are doing is
accounting for the flows into and out of the
system. Hence
Ps(t) = Prs(t) + Pg(t)

The powers must sum to 0 to satisfy conservation
of energy.

That may be true, but there's still no conservation
of instantaneous power principle.

To conserve energy however, i.e. to have no energy
accumulate in the null system described above, the
flows must balance at all times, that is,
instantaneously.

A hot resistor
continues to radiate heat long after any power
source is removed.

If you want to be that complicated you can; energy
is delivered instantaneously to the resistor according
to Vr*Ir (or equivalently, V**2/R), stored in the
resistor as heat and dissipated to the environment
later.

But for our purposes, we can stop that analysis at
the point where the energy enters the resistor and
use Vr(t) * Ir(t) to compute the instantaneous flow
into the resistor.

You could simply do the derivation for an example that
demonstrates your hypothesis.

Already done on my web page. My only actual hypothesis
concerns average power. I've wasted too much time
bantering about something that Hecht says is "of
limited utility".

Unfortunately for your hypothesis, average power is
insufficient to account for energy which might be in
the reflected wave. An average power analysis agrees
with your hypothesis, while a more detailed instaneous
analysis disproves it.

the idea that Pfor and Pref describe actual energy
flows is very dubious.

Again, look yourself in the mirror and tell yourself
that what you are seeing contains no energy. The
theory that some EM waves contain energy and some
do not is not new to you. Dr. Best was the first to
theorize that canceled waves continue to propagate
forever devoid of energy. Someone else asserted that
canceled waves never contained any energy to start
with. I strongly suspect that what you are seeing
in the mirror are the waves that didn't cancel and
that do contain energy. :-)

If it was just a 'suspicion' you could probably let
go of the idea long enough to learn what is really
happening and why it is not inconsistent with the
idea that reflected wave energy is a dubious concept.

So the energy is not being stored
in the reactive component of the line input
impedance.

Assuming you have not made an error,

You *have* found it hard to the do the math; otherwise,
you could detect an error, if there was one.

so what? Energy
stored in the reactance is only one of the possibilities
that I listed earlier. As I said in an earlier posting
which you declared a non-sequitor (sic), one or more of
the following is true:

1. The source adjusts to the energy requirements.

2. The reactance stores and delivers energy.

3. Wave energy is redistributed during superposition.

4. Something I haven't thought of.

Your explanation is not complete until you can identify
the element that stores and returns the energy and its
energy transfer function.

The ExH reflected wave energy exists and cannot
be destroyed. It goes somewhere and its average
value is dissipated in the source resistor in
my special case example.

Or not, as has been shown with the detailed analysis.

You are attempting to
destroy the reflected wave energy using words
and math presumably knowing all along that
reflected wave energy cannot be destroyed.

Energy can not be destroyed. This leads inexorably
to the conclusion that the reflected wave does not
necessarily contain energy.

....Keith