On Mar 4, 10:27*pm, Cecil Moore wrote:
Keith Dysart wrote:
Thus these examples do not demonstrate that the reflected power
is dissipated in the source resistor.

There are no reflections at the source so the reflected
energy flows through the source resistor. There is no
interference to redistribute any energy. There is no
other place for the reflected energy to go.

That is the conundrum, isn't it?

And yet the analysis of instantaneous energy flows definitely
shows that the reflected energy is not the energy being dissipated
in the source resistor.

Encountering this conundrum, and not wanting to give up on
conservation of energy, is what helped me form my views on
the nature of reflected energy.

...Keith

Keith Dysart wrote:
On Mar 4, 10:27 pm, Cecil Moore wrote:
Keith Dysart wrote:
Thus these examples do not demonstrate that the reflected power
is dissipated in the source resistor.
There are no reflections at the source so the reflected
energy flows through the source resistor. There is no
interference to redistribute any energy. There is no
other place for the reflected energy to go.

That is the conundrum, isn't it?

And yet the analysis of instantaneous energy flows definitely
shows that the reflected energy is not the energy being dissipated
in the source resistor.

Your analysis seems to be flawed. You are adding average
power terms to instantaneous power terms which is mixing
apples and oranges.
--
73, Cecil http://www.w5dxp.com

On Mar 5, 11:11*am, Cecil Moore wrote:
Keith Dysart wrote:
On Mar 4, 10:27 pm, Cecil Moore wrote:
Keith Dysart wrote:
Thus these examples do not demonstrate that the reflected power
is dissipated in the source resistor.
There are no reflections at the source so the reflected
energy flows through the source resistor. There is no
interference to redistribute any energy. There is no
other place for the reflected energy to go.

That is the conundrum, isn't it?

And yet the analysis of instantaneous energy flows definitely
shows that the reflected energy is not the energy being dissipated
in the source resistor.

Your analysis seems to be flawed. You are adding average
power terms to instantaneous power terms which is mixing
apples and oranges.

I do not think that is the case.

The expression for instantaneous power in Rs before the reflection
(or, if you prefer, when a 50 ohm load is used), is

Prs(t) = 50 + 50cos(2wt)

It is trivial to compute the average of this since the average
of a sine wave is 0, but that does not make the expression the
sum of an average and an instantaneous power.

As an exercise, compute the power in a 50 ohm resistor that has
a 100 volt sine wave across at, that is
V(t) = 100 cos(wt)

You will find the result is of the form shown above.

So when you add the instantaneous power in Rs before the reflection
arrives with the instantaneous power from the reflection it will
not sum to the instantaneous power dissipated in Rs after the
reflection returns.

Thus conveniently showing that for this example, the reflected
power is not dissipated in Rs.

...Keith

Keith Dysart wrote:
Thus conveniently showing that for this example, the reflected
power is not dissipated in Rs.

The *average* reflected power is certainly dissipated in Rs
because there is nowhere else for it to go. Your instantaneous
power, according to Eugene Hecht, is "of limited utility" which
you have proved with your straw man assertion above.

I have made no assertions about instantaneous power. All of
my assertions have been about average power and you have proved
none of my assertions about average power to be false.

Here is what you are doing:
Cecil: My GMC pickup is white.
Keith: No, your GMC pickup has black tires.

Your diversions are obvious. Instantaneous power is irrelevant
to my assertions.
--
73, Cecil http://www.w5dxp.com

On Mar 5, 1:58*pm, Cecil Moore wrote:
Keith Dysart wrote:
Thus conveniently showing that for this example, the reflected
power is not dissipated in Rs.

The *average* reflected power is certainly dissipated in Rs
because there is nowhere else for it to go. Your instantaneous
power, according to Eugene Hecht, is "of limited utility" which
you have proved with your straw man assertion above.

Hecht seems to have sufficient reputation that I trust that he made
this statement in the context of optics and not in the context of
electrical circuits.

I have made no assertions about instantaneous power. All of
my assertions have been about average power and you have proved
none of my assertions about average power to be false.

True. But analysis using instantaneous power reveals a different
answer.
Which is more likely to be correct?

Here is what you are doing:
Cecil: My GMC pickup is white.
Keith: No, your GMC pickup has black tires.

Your diversions are obvious. Instantaneous power is irrelevant
to my assertions.

Only if you give up on conservation of energy in instantaneous flows.

...Keith

Keith Dysart wrote:
Hecht seems to have sufficient reputation that I trust that he made
this statement in the context of optics and not in the context of
electrical circuits.

EM waves are EM waves, Keith, no matter what the frequency.
EM waves all obey the laws of reflection physics, superposition,
and conservation of energy principle. If you want to prove those
laws to be invalid and replace them with ones of your own design,
be our guest.

But analysis using instantaneous power reveals a different
answer. Which is more likely to be correct?

Analysis using an MFJ-259B on an antenna system reveals a
different impedance than is indicated by a DC ohm-meter.
So what? You used an average power tool, known to be
invalid for instantaneous powers, to incorrectly analyze
instantaneous powers. You are the one who made the error
- not the model. Your error was the (deliberate?) misuse
of the tool in order to try to create your straw man.

Using the power equation, derived from RMS values of
voltage, on instantaneous powers is an invalid thing
to do and will give known erroneous results which are
not the fault of the average power model. The fault is
in the *misuse* of the average power model.

We have already laid your straw man argument to rest
when we discussed the power in standing waves.

1. There is non-zero instantaneous power in standing waves.
2. There is zero average power in standing waves.

Does statement 1 contradict statement 2? Of course not.
They are both true. The same holds true for the present
discussion.

I have a probable explanation for your calculations. I
set the example up such that the average interference
is zero inside the source. It is entirely possible that
localized interference exists within each cycle such
that there is destructive interference for part of the
cycle and constructive interference in another part of
the cycle. In fact, based on the conservation of energy
principle, I am willing to state that is a fact and the
destructive interference magnitude exactly equals the
constructive interference magnitude for each cycle.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
Keith Dysart wrote:
Hecht seems to have sufficient reputation that I trust that he made
this statement in the context of optics and not in the context of
electrical circuits.

EM waves are EM waves, Keith, no matter what the frequency.
EM waves all obey the laws of reflection physics, superposition,
and conservation of energy principle. If you want to prove those
laws to be invalid and replace them with ones of your own design,
be our guest.

Cecil,

It is likely that all of these interference-related items you like to
quote from Hecht are cast in an environment of lossless optical
components. The characteristic impedance is set by the index of
refraction of the various layers, but none of the optical layers have
any absorption.

Soooo, how does any of this optical stuff extend to making arguments
about the absorption or re-reflection of energy in the source resistor
for the HF case?

The laws of physics may be inviolate, but it is not quite so clear that
your derived and extended models share the same characteristic.

73,
Gene
W4SZ