The Rest of the Story
 

On Mar 30, 8:43*pm, Cecil Moore wrote:
Keith Dysart wrote:
Perhaps you should complete part one so that it fully
accounts for the energy flows before progressing to
writing part two. Average is not a full accounting.

Average is the only accounting that I consider to
be important and the only accounting that I am going
to do. I have added a disclaimer about instantaneous
power to my Part 1 article.

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.

I would suggest something along the lines of "My
hypothesis is that the average energy in the reflected
wave is *numerically* equal to the increase in dissipation
of the source resistor. It should be noted that this
says nothing about whether the energy in the reflected
wave is actually dissipated in the source resistor."
That would be completely accurate and very unlikely to
be misconstrued by the reader.

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.

If you need an instantaneous power article written,
please feel free to write it yourself. I wish you luck
but I personally consider it to be a waste of time.

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

...Keith

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On Mar 30, 8:48*pm, Cecil Moore wrote:
Keith Dysart wrote:
Using averages, the computed powers support the hypothesis,
but when examined with finer granularity, they do not.

Well Keith, yours also falls apart at finer granularity
where you are required to determine the position and
momentum of the individual charge carriers.

Perhaps, but it is highly improbable that it falls apart
in a manner that ends up supporting the original failed
hypothesis.

...Keith

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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.

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.

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 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.

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.

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

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

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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?

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.

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.

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

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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.

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?

Maybe you don't realize that if the 'if' portion of
an 'if/then' statement is false, the entire statement
is true, by definition.

My assertions about conditions when interference is
present will appear in Parts 2 and 3 (which would have
been completed by now if I had ignored your diversions).
--
73, Cecil http://www.w5dxp.com

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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 am still having difficulty matching these equations with mine. Just
to make sure we are discussing the same problem....

As I tried to understand your problem, I finally realized that it was really my problem. As a result, I redid the spreadsheet. I now label "my formula" as being erroneous, this because it does relate to the current, not the voltage, and must be displaced by 45 degrees.

My formula (labeled erroneous) was the result of the formulas of columns B and C added with trig identities. What I did not realize was that the adding, while correct, rotates the phase. The formula is wrong because it does not recognize the phase shift that had been assumed for line one.

The spreadsheet addresses the following issues:

Does the traveling wave carry power? Yes. The spreadsheet was built
assuming that power is carried by traveling waves. Because the
resulting wave form and powers seem correct, the underlaying assumption
seems correct.

It was not obvious which columns were used to draw this correlation.

Column E and column F display power. Column F recognizes that if 100 watts is applied continueously (on the average) over an entire 360 degree cycle, the final power applied over time would be 360 * 100 = 36000 watt-degrees. Part of the power comes from the reflection, part comes directly. Obviously, interference is very much at work in this example.

Column E is the power dissipated in the resistor, and Column F
is the integral of Column and represents the total energy which
has flowed in to the resistor over the cycle. It is also the
average energy per cycle.

If you were to extend your analysis to compute the energy
in each degree of the reflected wave and add it to the energy
in each degree of Vrs.source(t) and sum these, you would
find that the instantaneous energy from Vrs.source and
Vrs.reflected does not agree with the instantaneous energy
dissipated in the source resistor. It is this disagreement
that is the root of my argument that the power in the
reflected wave is a dubious concept.


I think the energy adds correctly now. Of course it depends upon how we measure the energy because energy is stored in the transmission line at all times, but the stored energy is only measured across either Rs or the transmission line. We do not measure the energy within the transmission line in this example, which is the sum of the applied power for 90 degrees.

Using averages, the computed powers support the hypothesis,
but when examined with finer granularity, they do not.

I think each degree has the correct power now. I apologize for the errors, and hope that I have them all removed.

However, even if this experiment is consistent with the hypothesis
it only takes one experiment which is not to disprove the hypothesis.

True!

Is power conserved on the transmission line, meaning, can the energy
contained in power be conserved and located over time on the
transmission line? Yes, the spreadsheet was built assuming that power
could be conserved and traced over time so the underlaying assumption
seems correct.

Does interference occur in this example? The spreadsheet was built
assuming that voltage and currents from superpose in a manner consistent
with constructive and destructive interference, so the underlaying
assumption seems correct.

Is power stored in the reactive component for release in later in the
cycle or during the next half cycle? Yes, power is stored on the
transmission line during the time it takes for power to enter the line,
travel to the end and return. The time of wave travel on the
transmission line is related to the value of the reactive component.

Does the direction of wave travel affect the measurement of voltage and
the application of power to a device? Yes. A wave loses energy (and
therefore voltage) as it travels through a resistance. As a result,
power from the prime source is ALWAYS applied across the sum of the
resistance from the resistor AND transmission line.

I am not sure that I would describe this as the wave losing energy,
but rather as the voltage dividing between the two impedances.
If the source resistance was replaced by another transmission,
which could easily be set to provide a 50 ohm impedance, would
you still describe it as the wave losing energy?

It should be OK to think of the voltage dividing between two impedances. The important thing is to consider how the reflected voltage sums with the forward voltage where it is measured. Because the two waves are traveling in opposite directions, the measured voltage is not the voltage applied to either Rs or the transmission line. This is why columns B and C must be added to find the total voltage across Rs.

Whether one needs to add or subtract is more a matter of the
convention
being used for the signs of the values. When Vf and Vr are derived
using
Vtot = Vf + Vr; Itot = If + Ir
one would expect to have to add the negative of Vr to the contribution
from Vs to arrive at the total voltage across the source resistor.

The spreadsheet was
built using this assumption and seems correct. (At times during the
cycle, the forward and reflected waves oppose, resulting in very little
current through the resistor. During those times, the power applied to
the transmission line is much HIGHER because the reflected wave reflects
from the load and source, and merges/adds to the forward wave from the
source.)

I am not convinced. When there is very little current through the
resistor,
there is also very little current into the transmission line. This
suggests to me that the power applied to the transmission line is low.

I don't follow you here. Right, power into the transmission line is low when the current in is low, and it is high when the current is high. It is clear that peak current and peak voltage do not occur at the same time except when measured across the resistor in column D.

Power into the transmission line is low when either the voltage or
the current is low; when either is zero, the power is zero.

Since the highest voltage occurs with zero current and the highest
current occurs with zero voltage, maximum power into the transmission
line occurs when the voltage and current are both medium; more
precisely, when they are both at .707 of their maximum values.

This is just one example, but it seems like the power is accounted for here. We need another example where power can NOT be accounted for.

I suggest it is the same example, but the granularity of the
analysis needs to be increased.

...Keith

I hope I have the spread sheet displaying correct values now. Thank you for your careful analysis.

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

The Rest of the Story
 

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.
--
73, Roger, W7WKB

The Rest of the Story
 

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

The Rest of the Story
 

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

The Rest of the Story
 

On Mon, 31 Mar 2008 19:11:56 -0500
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.
--
73, Cecil http://www.w5dxp.com

I had to chuckle when I read this Cecil. First I looked up the word "omniscient" to refresh my memory about meaning, but then I thought "anyone who thinks he is omniscient is not about to read the works of others and learn new tricks". Just human nature.

You can see from my postings that I am still trying to better understand the wave and reflections, still looking how to describe the energy distribution within the cycle. 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. We are probably close on the spreadsheet, but it is not yet crystal clear in my mind.

--
73, Roger, W7WKB