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On Mon, 31 Mar 2008 13:08:59 -0700 (PDT)
Keith Dysart wrote:

On Mar 31, 2:22*pm, Roger Sparks wrote:
On Mon, 31 Mar 2008 10:03:52 -0700

Roger Sparks wrote:
On Sun, 30 Mar 2008 07:43:59 -0700 (PDT)
Keith Dysart wrote:

On Mar 29, 7:18 pm, Roger Sparks wrote:
On Sat, 29 Mar 2008 12:45:48 -0700 (PDT)

Keith Dysart wrote:
On Mar 27, 2:06 am, Roger Sparks wrote:
Cecil Moore wrote:
Roger Sparks wrote:
You need to take a look at the spreadsheets.
clip
http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf
clip

I doubt that this will satisfy your power location concerns because the spread sheet shows more power being delivered to the resistor than is present in the voltage. *This is because the impedance of the power equation has changed due to the contribution of the current component. Consider that for columns B and C, the same current flows whether the voltage in B is applied or the voltage in C is applied. *This can only happen if the impedance seen by each respective voltage is different. *This is interference at work *
--
73, Roger, W7WKB

After posting previosly, I got to thinking that interference here is wrecking the analysis of Column D. *The traveling wave analysis is correct (Column H). *Only one current is flowing through Rs, and the current is not enough to supply the power suggested in column D. *While it is logical to add the voltages from Column B and Column C, the two voltages are often in opposition so they are not "seen" by Rs. *As a result, we must have a reflection from Rs that I am not taking into account. *

Column B is correct; this being the voltage produced by the source
divided by two.
It is also the forward voltage on the line.
Vrs.source(t) = Vf(t) = 70.7 sin(wt)

Column C is the reflected voltage (not the reflected voltage impressed
across the
source resistor). The reflection coefficient is -1, and the delay is
90 degrees
so the reflected voltage at the generator is
Vr(t) = -1 * Vf(t - 90 degrees)
= - 70.7 sin(wt-90)
= 70.7 sin(wt+90)

But Vr is impressed across the resistor in the opposite direction to
that of
Vrs.source, so the equation for total Vrs is
Vrs.total(t) = Vrs.source(t) - Vr(t)
thus column D should be B31-C31.

Alternatively,
Vrs.reflect(t) = -Vr(t)
and then
Vrs.total(t) = Vrs.source(t) + Vrs.reflect(t)

Column E is correctly computing the instantaneous power from Column D
since
P(t) = V(t) * I(t)
= V(t) * V(t) / R
= V(t) * V(t) / 50 (in this example)
but has the wrong data because of the error in Column D.

Column F is integrating the power to yield either the energy in a
cycle or
the average power per cycle (though presented in unusual units).

I agree G is erroneous and I am not sure what H is computing.

...Keith

I made the change in Column D and the trend is more believable in Column E. I think the math here is noncommutative in the sense that time must rotate forward. I think this change does that even though the average power results stay the same.
--
73, Roger, W7WKB

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Cecil Moore wrote:
Roger Sparks wrote:
While it is logical to add the voltages from Column B and Column C,
the two voltages are often in opposition so they are not "seen" by
Rs. As a result, we must have a reflection from Rs that I am not
taking into account.

It's not a "reflection" of a single wave, Roger, it is
a "redistribution" of energy caused by superposition
of two waves accompanied by interference. Eugene Hecht
explains it all in Chapter 9: Interference in "Optics".

For anyone who thinks he is already omniscient
about EM waves, I would highly recommend reading
Hecht's chapter on interference.

Here's an even better idea.

Dump Hecht and read about interference in Born and Wolf. Chapter VII (in
the 7th edition) is one of the main contributions. I particularly like
Section 7.6. In this section the authors derive a general set of
equations that deal with all sorts of reflection configurations. There
is no need to worry about constructive or destructive interference. The
equations smoothly transition from one to the other as appropriate. The
equations don't fall apart as the reflection goes to zero. No
"redistribution" is needed.

This is the way physics typically works; it is not necessary to separate
superposition from interference or separate constructive from
destructive. If the analysis and the equations are correct they will
work for a wide range of parameters. Equations that must be fine-tuned
for every possible change in reflection coefficient or other parameters
are very limited and most troublesome.

73,
Gene
W4SZ

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On Mar 31, 8:04*am, Cecil Moore wrote:
Keith Dysart wrote:
You state that your hypothesis is that for this specific
circuit, "the energy in the reflected wave is dissipated in
the source resistor".

First, let's correct your out-of-context quotation.
Here is what you should have quoted: "When zero
interference exists at the source resistor, the
energy in the reflected wave is dissipated in the
source resistor."

This is actually a fact for both average powers
and instantaneous powers. Since all of your examples
are associated with a non-zero level of interference,
they are irrelevant to the stated conditions.

Since my example is *your* example (q.v. your Fig 1-1), your
example has non-zero interference (as you state above), so
you have just said that your example violates the stated
conditions.

Or are you going to say that the circuit exhibits interference
when an instantaneous analysis is performed, but knows that
it should refrain from doing so when only an average analysis
is done?

Here is a quote from that article:
"Please note that any power referred to in this paper is an AVERAGE
POWER. Instantaneous power is irrelevant to the following discussion."
The word "average" is implied in every statement I make.

Yes, "implied" is the word. Why not clearly state that, while the
average energy appears to be dissipated in the source resistor, the
actual energy is not.

Or *is* the intent to deceive?

This claim is amenable to analysis
using instantaneous energy flows. When so analyzed, the
hypothesis fails.

No, it doesn't fail. You have simply failed to satisfy
the zero interference precondition.

If the precondition fails for the circuit, then it fails for
the circuit.

If you wish to narrow your hypothesis to "the average energy
in the reflected wave is simply numerically equal to the
increase in the average dissipation in the source
resistor" I will not object since that hypothesis would
be completely accurate and not misleading.

That is, in fact, the only hypothesis presented in
my Part 1 article. Since my hypothesis never applied
to instantaneous power, I don't have to narrow the
hypothesis. My article stands as written. Please
cease and desist with the unfair innuendo.

You insist that the narrowing is "implied", but then
refuse to explicitly state such to make it clear to
the reader. Why?

Not a waste at all.

Obviously, your opinion differs from mine. To the best
of my knowledge, you are the first person to spend any
mental effort on instantaneous power. If that's what
you want to do, be my guest. I consider it to be little
more than mental masturbation, "of limited utility" as
Hecht said.

Yes. It does not support your hypothesis, so it is wise
to ignore it.

In fact, I proved my assertion was true even at the
instantaneous power level when the "zero interference"
precondition is met.

Ah, yes. X**2 + Y**2 = (X+Y)**2 only when X or Y equals 0,
which for the example at hand applies at exactly 4 instances
per cycle.

The rest of the time the circuit exhibits interference.

Since you start with an unshakeable belief in the
existance of energy in the reflected wave, this would be
your natural conclusion.

Since you are incapable of producing an EM wave devoid
of energy (or an angel dancing on the head of a pin) both
concepts are unrelated to reality IMO.

Your challenge is the same as it has always been. Just
produce an EM wave containing zero energy and get it
over with.

Tis a problem isn't it. You won't let go of energy in the
reflected wave long enough to even explore the circuit to
discover the inconsistencies that result from the belief.

You can not find a reason why instantaneous analysis should
not work, but the conclusions are uncomfortable, so you
decide that Hecht has told you not to bother, and you stop.
Without knowing why.

...Keith

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On Mar 31, 8:43*am, Cecil Moore wrote:
Keith Dysart wrote:
But the meaning of the disclaimer is not clear to the
reader. You really need to restate your hypothesis to
remove the possibility of misleading the reader.

What is it about "Please note that any power referred to
in this paper is an AVERAGE POWER. Instantaneous power
is irrelevant to the following discussion." that you
do not understand?

After many posts and back and forth, I understand. But the
poor first reader will miss the implications: that the
imputed energy in the reflected wave is not dissipated
in the source resistor.

Why not save the reader the challenge and just state it
clearly?

I would suggest ...

I would suggest that you write your own article.
Mine stands as written in the *stated context*
of zero interference and average powers. I am
not interested in attempting a unified theory
of everything.

Except that you have now indicated that there is
interference in the circuit of Fig 1-1.

I personally don't think
that anyone else cares about instantaneous powers.

I am sure some do not. But anyone interested in a full
understanding does.

Anyone interested in a *full* understanding would
take the discussion down to the quantum level which,
interestingly enough, you have chosen to ignore.

Yes. I have stopped at the level that disproves that the
imputed energy in the reflected wave is dissipated in
the source resistor. That is sufficient for me.

I do not think that deeper analysis will show this to
be wrong, but you are invited to do so.

On the other hand, average analysis can be shown to
produce misleading results by applying instantaneous
analysis. You should be interested because it disproves
that the imputed energy in the reflected wave is
dissipated in the source resistor.

It is convenient when you just ignore the analysis
that disproves your hypothesis. But it does not make
the hypothesis more correct.

If you think your unethical innuendo, out-of-context
quotes, and straw man arguments disprove anything,
I feel sorry for you.

Once again, the context of my Part 1 assertions is
*ZERO INTERFERENCE* and *AVERAGE POWERS*. You have
disproved nothing so far. You were even taken aback
when it was true at the instantaneous level in the
context of zero instantaneous interference.

I was? If so, I have now moved beyond. Especially since
you now assert that the circuit does exhibit interference,
the hypothesis becomes moot.

...Keith

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On Mar 31, 9:01*am, Cecil Moore wrote:
Keith Dysart wrote:
Perhaps, but it is highly improbable that it falls apart
in a manner that ends up supporting the original failed
hypothesis.

Since the original hypothesis is in the context of
zero interference (and average powers) it has not
failed. So far, I have made no assertions about
conditions when interference is present as it is
in all of your examples. None of your observations
are relevant to my Part 1 article because they are
all outside the stated context of the article.

The challenge for you is to present a zero interference
example for which my hypothesis is false. So far, you
have failed to do so.

We are talking about the same circuit, which you now
claim exhibits interference, rendering your hypothesis
moot.

I have asserted, "If zero interference exists, then 'A'
is true". You have said 'A' is not true when interference
exists. I actually agree with you but it is irrelevant
to the stated 'if' portion of my premise. Where did
you study logic?

Good that you agree. And now that you state that the
circuit exhibits interference, it might be best to
withdraw your example.

...Keith

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Keith Dysart wrote:
Since my example is *your* example (q.v. your Fig 1-1), your
example has non-zero interference (as you state above), so
you have just said that your example violates the stated
conditions.

Keith, if I send you $100, would you use it to buy
yourself some ethics?
--
73, Cecil http://www.w5dxp.com

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Keith Dysart wrote:
After many posts and back and forth, I understand.

Do you understand that you need to go out and buy
some ethics?
--
73, Cecil http://www.w5dxp.com

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Keith Dysart wrote:
We are talking about the same circuit, which you now
claim exhibits interference, rendering your hypothesis
moot.

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.
--
73, Cecil http://www.w5dxp.com

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Roger Sparks wrote:
The storage of the redistributed energy must be close to the
wires of the circuit so we should be able to describe it
mathmatically, if I just knew how.

The math is pretty easy, Roger. Keith seems to believe
that an inductor stores power which is, of course, a
ridiculous concept. As soon as I can see a character
that is smaller than 2 inches tall, I will respond.
--
73, Cecil http://www.w5dxp.com

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Gene Fuller wrote:
Dump Hecht ...

Dump Gene Fuller. :-)
--
73, Cecil http://www.w5dxp.com