On Apr 1, 8:08 am, Cecil Moore wrote:
Keith Dysart wrote:
Cecil Moore wrote:
If the average interference is zero, the average
reflected power is dissipated in the source resistor.
All of your unethical lies, innuendo, and hand-waving
will not change that fact of physics.

More precisely, the average value of the imputed reflected
power is numerically equal to the increase in the average
power dissipated in the source resistor.

More precisely, at the *exact* time of arrival of the
reflected wave, the average power dissipated in the
source resistor increases by *exactly* the magnitude
of the average reflected power. Do you think that is
just a coincidence?

Not quite, but close. And averages can not change instantly.

But your phraseology suggests another way to approach
the problem. Let us consider what happens just after
the arrival of the reflected wave. For computational
convenience, we'll use a frequency of 1/360 hertz so
that 1 degree of the wave is one second long.

The reflected wave arrives at 90 seconds (or 90 degrees)
after the source is turned on. If the line is
terminated in 50 ohms, then no reflection arrives and
during the one second between degree 90 and degree 91,
the source resistor dissipates 0.01523 J of energy. The
line also receives 0.01523 J of energy and the source
provides 0.03046 J.
Esource.50[90..91] = 0.03046 J
Ers.50[90..91] = 0.01523 J
Eline.50[90..91] = 0.01523 J
Esource = Ers + Eline
as expected.
Efor = Eline
since Eref is 0.

Now let us examine the case with a 12.5 ohm load and
a non-zero reflected wave.
During the one second between degree 90 and degree 91,
the source resistor dissipation with no reflection
is still 0.01523 J and the imputed reflected wave
provides 99.98477 J for a total of 100.00000 J.

But the source resistor actually absorbs 98.25503 J
in this interval.

Ooooopppps. It does not add up. So the dissipation
in the source resistor went up, but not enough to
account for all of the imputed energy in the
reflected wave. This does not satisfy conservation
of energy, which should be sufficient to kill the
hypothesis.

But Esource = Ers + Eline as expected.
Esource.12.5[90..91] = -1.71451 J
Ers.12.5[90..91] = 98.25503 J
Eline.12.5[90..91] = -99.96954 J
Note that in the interval 90 to 91 degrees, the source
is absorbing energy. This is quite different than what
happens when there is no reflected wave.

You said earlier "Do you think that is just a coincidence?"
It is to be expected that the dissipation in the source
resistor changed; after all, the load conditions changed.
But it is mere happenstance that the average of the
increase in the dissipation is the same as the average
power imputed to the reflected wave; an ideosyncratic
effect of the selection of component values.

It is not obvious why you reject this more precise, less
misleading description.

Why do you use such unfair ill-willed debating techniques
based on innuendo and not on facts in evidence?

IMO, our two statements above say the same thing
with mine being the more precise and detailed.
I don't reject yours - I just prefer mine.

Authors often do have difficulties detecting when
their words mislead. Excellent authors, and there
are not many, use the feedback from their readers
to adjust their wording to eliminate misleading
prose.

If the source of the increased dissipation in the
source resistor is not the reflected energy, exactly
where did that "extra" energy come from at the exact
time of arrival of the reflected wave?

Exactly. This is what calls into question the
notion that the reflected wave is transporting
energy. This imputed energy can not be accounted for.

Now the energy that can be accounted for is the
energy that flows in or out of the line. This
energy, along with the energy dissipated in the
source resistor will *always*, no matter how
you slice and dice it, be equal to the energy
being delivered by the source; completely satisfying
the requirements of conservation of energy.

The best that can be said for the imputed power in
the reflected wave is that when it is subtracted
from the imputed power in the forward wave, the
result will be the actual energy flow in the line.
But this is just a tautology; a result from the
very definition of Vforward and Vreflected.

Hint: Since the only other source of energy in the
entire system is the reflected wave, any additional
source would violate the conservation of energy
principle.

Alternatively, since it turns out that trying to
use this imputed power to calculate the power
dissipated in the source resistor results in a
violation of conservation of energy, this
energy flow imputed to the reflected wave is
a figment. The only thing that is real is the
total energy flow.

Now you have asked repeatedly about the reflection
from the mirror because you are sure that this
is proof of the energy in the reflected wave.

The energy in the light entering your eye is
the total energy; it is not imputed energy of a
wave that is a partial contributor to the total.
If the eye were also a source, such that there
was a Pfor to go along with Pref, then your
question would align with the situation under
discussion. But when the energy flow is only
in one direction, that flow is a total flow
and it definitely contains energy.

To recap, it is when a total flow is
broken into multiple non-zero constituent flows
that energy flow imputed to the constituents
is a dubious concept.

....Keith