Superposition
 

On Sat, 17 Nov 2007 15:34:34 -0500, "Stefan Wolfe"
wrote:

it is possible
for there to be a plus power differential from the sum of the source powers
at any given segment as long as there is equal power subtracted at another
location.

Talking about taking Cecil's sucker bait. The string of conditionals
above should convince any rational mind that something in the
underlying premise is broken. - I explained this in another part of
the thread.

73's
Richard Clark, KB7QHC

Superposition
 

Cecil Moore wrote:
Tom Donaly wrote:
Hiding behind authority again, Cecil? Using a few carefully edited
quotes from Hecht doesn't prove anything. Ian hit the nail on the
head: Vague philosophical arguments using second and third order
abstractions that you can't prove to have any connection to reality
aren't going to convince anyone.

The void technical content of your objection is noted, Tom.
Why don't you present some theory and math that prove me
wrong instead of just waving your hands and uttering ad
hominem attacks?

Because I don't have to prove you wrong, Cecil, you have to prove
yourself right. So far, you've given us nothing but a few
untestable assumptions and little else. A series of declarative
sentences and obscure analogies does not a theory make. When you can
work out 1. A logical framework, using vector calculus, in order to show
us, logically, why we should pay attention to you, and 2. A series of
easily replicated experiments that you've performed, and we can perform
in turn, to see how well your ideas are supported by reality, then,
maybe we should give you a hearing, but a series of unsupported
statements followed by a barrage of objection stoppers just isn't good
enough. This may be fun for you, but, for anyone dealing with you, it's
just a waste of time.
73,
Tom Donaly, KA6RUH

Superposition
 

Dave wrote:
Dave wrote:
Tom Donaly wrote:

So in the limit, as the number of radiators is increased to infinity,
the amount of power it would take to produce the measured sum would
go to zero. Nice logic.
73,
Tom Donaly, KA6RUH


Mathematica 6.0 for Sun Solaris SPARC (64-bit)
Copyright 1988-2007 Wolfram Research, Inc.

In[1]:= 0 Infinity

Infinity::indet: Indeterminate expression 0 Infinity encountered.

Out[1]= Indeterminate
0 Infinity
is interpreted as zero times infinity


That's the rule all right. Notice, however, that I said, "in the limit."
Does Mathematica teach you about taking limits and such?
73,
Tom Donaly, KA6RUH

Superposition
 

Dave wrote:

You can do the same with DC - you don't need to use AC at all. Put a 50 V
battery in series with the pure 50 Ohm load and it supplies 50 W. Put it in
series with another load, consisting of a 50 Ohm voltage source in
consisting of a 50 volt voltage source, not a 50 Ohm voltage source!
series with a 50 Ohm load, and it is no surprise it delivers a different
power. Depending on what way you connect the two batteries, the current would
be 0 A or 4 A, and so the power 0 or 200W.
As I said before, 0 or 2A, which gives 0 or 200 W.

Your example, though correct, has little to do with the case being discussed.

In your example it is true that power varies depending on what way you connect
the two batteries, but in all cases the total power dissipated in the loads
remains equal to the total power delivered by the sources.

In the case being discussed instead the power dissipated in the load varies with
NO CHANGE in total power delivered by the sources.

73

Tony I0JX

Superposition
 

On Sat, 17 Nov 2007 22:05:57 +0100, "Antonio Vernucci"
wrote:

In the case being discussed instead the power dissipated in the load varies with
NO CHANGE in total power delivered by the sources.

Hi Tony,

Buying into a blighted argument (what Cecil presented) leads to some
very strange contortions such as you describe above. That, or there
are some strained language problems here.

73's
Richard Clark, KB7QHC

Superposition
 

Antonio Vernucci wrote:
Dave wrote:

You can do the same with DC - you don't need to use AC at all. Put a
50 V battery in series with the pure 50 Ohm load and it supplies 50
W. Put it in series with another load, consisting of a 50 Ohm voltage
source in
consisting of a 50 volt voltage source, not a 50 Ohm voltage source!
series with a 50 Ohm load, and it is no surprise it delivers a
different power. Depending on what way you connect the two batteries,
the current would be 0 A or 4 A, and so the power 0 or 200W.
As I said before, 0 or 2A, which gives 0 or 200 W.

Your example, though correct, has little to do with the case being
discussed.

In your example it is true that power varies depending on what way you
connect the two batteries, but in all cases the total power dissipated
in the loads remains equal to the total power delivered by the sources.

yes

In the case being discussed instead the power dissipated in the load
varies with NO CHANGE in total power delivered by the sources.

no way. Prove there is no change in the power delivered by the sources.

Superposition
 

Tam/WB2TT wrote:

You can come up with a lot simpler example that at first might look like a
paradox. Consider two DC current sources of 1 amp each. Each current source
will deliver 50 W to a 50 Ohm resistor. Now connect the two current sources
in parallel, and the resultant 2 amps will deliver 200W to the same 50 Ohm
resistor. There is nothing wrong here.

I see Cecil is still superposing his waves of average power.

I have an example that's more fun yet.

Take a 10 volt source and connect it through a 10 ohm resistor to
another 10 volt source. The positive terminals of the sources are
connected to the ends of the resistor, and the negative terminals are
connected together -- "grounded", if you prefer. Turn on one source,
leaving the other off. (An "off" voltage source is a short circuit.)
Result: 10 watts of dissipation in the resistor. Turn off the first
source and turn on the second. Result: 10 watts of dissipation in the
resistor. Now turn both sources on. Result: An exercise for the reader.

This is a linear circuit for which superposition holds.

Roy Lewallen, W7EL

Superposition
 

On Sat, 17 Nov 2007 16:20:15 -0500, "Stefan Wolfe"
wrote:


"Richard Clark" wrote in message
.. .
On Sat, 17 Nov 2007 15:34:34 -0500, "Stefan Wolfe"
wrote:

it is possible
for there to be a plus power differential from the sum of the source
powers
at any given segment as long as there is equal power subtracted at another
location.

Talking about taking Cecil's sucker bait. The string of conditionals
above should convince any rational mind that something in the
underlying premise is broken. - I explained this in another part of
the thread.

Hello Richard, with all due respect to your background on this, which is
much much greater than mine, I do have fundamental concepts that were
modeled in my mind many years ago at the University and even to some extent
in high school. No need to try to align me with other posters who I may
agree with, as you would political parties. Nobody is running for office
here. I tend to see no violations of physical laws provided they are held
true for the system as a whole, *provided you have defined a closed system*,
and he has. That is the way laws of science behave.

A largely rambling response. It describes, but doesn't actually
answer how
"a plus power differential from the sum of
the source powers at any given segment"
is so overly elaborate to be a fundamental concept supporting an
erroneous speculation Cecil is offering.

If you in fact think that the issue of accepting a broken argument is
on par with High School homecoming elections, that is not the race I
am competing in. If you want to stick with a technical issue in a
technical forum, then strict language and solid logic is still a
requirement.

73's
Richard Clark, KB7QHC

Superposition
 

K7ITM wrote:

In typical Cecil fashion, you trimmed out the only part I really cared
about having you answer: "Assuming the two "waves" existed
independently at some points in space, you'll have to first tell us
_exactly_ what was done to combine them into one wave." Depending on
how _I_ do that, I can get various answers, since some power goes
elsewhere in some of the methods, but I _never_ get more power out of
a steady-state system than I put in. Barring stupid math mistakes,
anyway.

*No matter how* you combine two waves in space or a transmission line in
such a way that they add, the process will result in other regions in
which they cancel, and vice-versa. The result is the correct net power
in the *whole system*. Long ago I issued a challenge for someone to
describe a system for which this isn't true, and re-issued it recently.
No takers.

Attempting to apply the law of conservation of energy, or anything else,
to one region while ignoring the others is certain to lead to bogus
conclusions, as we've seen over and over.

Roy Lewallen, W7EL

Superposition
 

Stefan Wolfe wrote:
I believe in the case at
hand (a transmission line far removed from the source) that it is possible
for there to be a plus power differential from the sum of the source powers
at any given segment as long as there is equal power subtracted at another
location.

Yes, at least someone understands. The "plus power" is
needed by constructive interference. The "power subtracted"
is given up by destructive interference somewhere else.
Apparently, none of the gurus on this newsgroup have ever
considered where the "plus power" comes from while
belittling anyone who wonders where it comes from.
--
73, Cecil http://www.w5dxp.com

Superposition
 

On Sat, 17 Nov 2007 17:16:11 -0500, "Stefan Wolfe"
wrote:

"a plus power differential from the sum of
the source powers at any given segment"
is so overly elaborate to be a fundamental concept supporting an
erroneous speculation Cecil is offering.

In a closed system, this is so un-elaborate that I can even take this down
to grade school artithmetic, Richard. When I add all of the power
differentials from source power with a plus sign in front of them, to the
power differentials from source power with a negative sign in front of them,
the sum must be zero. We're talking about power so I don't even have to go
to high school to learn about summing vectors.

What am I missing here?

Well, for one powers do not add, just energies.

The point of the matter is that the method of Superposition does not
reveal the nature of reality by parts, only by its whole.
Superposition is an artifice, a method, where reality is suspended
pending completing the analysis. To stop in the middle and proclaim a
new reality is a fraud. But then I've already explained this
elsewhere (did you follow that lead?).

If you in fact think that the issue of accepting a broken argument is
on par with High School homecoming elections, that is not the race I
am competing in.
If you want to stick with a technical issue in a
technical forum, then strict language and solid logic is still a
requirement.

Then I am sure you will agree that using terms like "taking Cecil's sucker
bait" is not the type of "strict language" and "solid logic" appropriate in
a technical forum.

In fact, it is in the strictest language par excellence! Strict
allows for no wiggle room, nothing nebulous. You completely
understood what it meant and technical forums are assaulted with a lot
of bankrupt theories- sometimes innocently offered, but not in this
case. You might complain of style, but not substance.

If you want it in another style, I could easily comply, but evoke
groans from many following this (and more complaints of style). On
the other hand, the substance of the issue is that the origin of this
thread is a patchwork of unremittingly failed logic that many here
have accepted as a point from which to argue. Tom has already
identified it in the class of argument "Have you stopped beating your
mother?" The crew here picks the theme up and starts asking for
definitions of mother, beating, "when does stop actually occur?", and
the rest. It does have its amusement, however. ;-)

73's
Richard Clark, KB7QHC

Superposition
 

Richard Clark wrote:
Talking about taking Cecil's sucker bait. The string of conditionals
above should convince any rational mind that something in the
underlying premise is broken.

Anything for which you cannot provide a technical answer
appears to you to be "sucker bait". No underlying premise
is broken. EM waves interacting at a Z0-match simply obey
the laws of physics including the conservation of energy
principle. For every packet of additional energy needed
for constructive interference to occur, a packet of energy
becomes available from destructive interference.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Tom Donaly wrote:
Because I don't have to prove you wrong, Cecil, you have to prove
yourself right.

Sorry, I don't, Tom. Hecht, Born and Wolf have already
proven those fundamentals of physics to be true. You
have to prove me, Hecht, and Born and Wolf wrong.

And of course, you will mount every diversion known to
man to avoid facing the technical facts as explained by
Hecht, Born & Wolf, Melles-Groit, and the FSU web page.
--
73, Cecil http://www.w5dxp.com

Superposition
 

no way. Prove there is no change in the power delivered by the sources.

Making reference to the case under discussion (Wave#1 produces 50 joules/s at
the receiver when alone, and so does Wave#2 when alone), imagine that the two
waves are generated by two remote transmitters (+antennas) and that you measure
the power of the two superimposed waves on a receiver (+antenna) that you can
move in the space as you like.

If you put your receiver/antenna in a point where the two waves have equal
amplitude and opposite phase, your receiver will measure zero joules/s.

If you instead put your receiver/antenna in a point where the two waves have
equal amplitude and same phase, your receiver will measure 200 joules/s (i.e.
four times the power produced by each wave alone, not just two times).

Finally, if you put your receiver in a point where the two waves have equal
amplitude and a 45 deg. shift (as in the proposed case), your receiver will
measure 171 joules/s (still more than twice the power produced by each wave
alone).

Moving your receiver here and there will obviously cause no change in the power
delivered by the two remote transmitters.

The trick is due to the fact that the two waves interfere each other in
constructive or destructive manner depending on the particular receive point.
So, in the "lucky" points you get some extra power, which is however compensated
for by the power loss occurring at the "unlucky" points.

The original question is deceiving, because it attracts the reader's attention
on just one particular point of the space, where energy can unexplicably appear
to be created or destroyed. But instead considering the power distribution over
the whole space, the mistery disappears.

73

Tony I0JX

Superposition
 

Richard Clark wrote:
"Antonio Vernucci" wrote:
In the case being discussed instead the power dissipated in the load varies with
NO CHANGE in total power delivered by the sources.

Buying into a blighted argument (what Cecil presented) leads to some
very strange contortions such as you describe above.

Sorry Richard, but if you listen to Antonio, you might learn
something about conservation of energy. He is one of the few
posters who seems to have a grasp of the technical facts that
have, so far, eluded you and other gurus.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Dave wrote:
In the case being discussed instead the power dissipated in the load
varies with NO CHANGE in total power delivered by the sources.

no way. Prove there is no change in the power delivered by the sources.

Piece of cake. The sources are beams of light from Alpha Centauri.
Now tell us exactly how Alpha Centauri adjusts its power output
from 11 light-years away.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Forgot to also mention that, obviously, shutting off one of the two remote
transmitters causes no change in the power delivered by the other transmitter.

73

Tony I0JX

Superposition
 

Roy Lewallen wrote:
I see Cecil is still superposing his waves of average power.

That's at least unfair and at most unethical, Roy. I am not
superposing power. I am using the accepted irradiance equations
from optical physics to predict the energy result of superposing
EM waves, something that was being done by physicists before you
were born.

I have an example that's more fun yet.
Take a 10 volt source ...

It may be more fun but irrelevant. Please explain how the sun
can adjust its energy output depending upon what might or might
not be happening on earth. If you can do that, I will retract
everything I have said about this subject.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Roy Lewallen wrote:
*No matter how* you combine two waves in space or a transmission line in
such a way that they add, the process will result in other regions in
which they cancel, and vice-versa.

That is my argument, Roy, not yours. You are on record as
not caring what happens to reflected power.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Richard Clark wrote:
... reality is suspended ...

That's obvious but why are you proud of it?
--
73, Cecil http://www.w5dxp.com

Superposition
 

I reinforce what Roy has said with different words: Superposition and
linearity are one and the same. If a circuit or process is linear, then
superposition gives correct results. If superposition works, then the
circuit or process is linear. Power is not a linear process. Power
involves multiplication.

When investigating the results of multiple voltage and/or current sources
(including E or H from an antenna) all at the same frequency, one performs
an addition (vector addition). Then, and only then, one may (note the
permissive form) use the resultant voltage or current or impedance (two of
the three) to calculate (complex) power. (In the antenna case, recall that
Z is near 377 ohms only in the far field.)

73, Mac N8TT

--
J. McLaughlin; Michigan, USA
Home:
"Roy Lewallen" wrote in message
snip

I see Cecil is still superposing his waves of average power.

I have an example that's more fun yet.

Take a 10 volt source and connect it through a 10 ohm resistor to another
10 volt source. The positive terminals of the sources are connected to the
ends of the resistor, and the negative terminals are connected together --
"grounded", if you prefer. Turn on one source, leaving the other off. (An
"off" voltage source is a short circuit.) Result: 10 watts of dissipation
in the resistor. Turn off the first source and turn on the second. Result:
10 watts of dissipation in the resistor. Now turn both sources on. Result:
An exercise for the reader.

This is a linear circuit for which superposition holds.

Roy Lewallen, W7EL

Superposition
 

On Nov 17, 10:36 am, Cecil Moore wrote:
K7ITM wrote:
In typical Cecil fashion, you trimmed out the only part I really cared
about having you answer: "Assuming the two "waves" existed
independently at some points in space, you'll have to first tell us
_exactly_ what was done to combine them into one wave."

They were confined to a transmission line. Coherent
waves traveling in the same direction in a transmission
line are forced to also be collinear. Unlike space, a
transmission line forces collinearity upon the EM waves.
But the same thing happens at a 1/4WL thin-film non-
reflective coating on glass. Assuming one brings the
Poynting vectors into collinearity, one can see what
is happening athttp://www.w5dxp.com/thinfilm.gig
--
73, Cecil http://www.w5dxp.com

Of course it was obvious from the base posting in this thread that the
"waves" must be on a TEM transmission line. But you still haven't
said anything about HOW you launched two distinct waves but got them
to combine into one.

You're working WAY too hard on this one if you have to bring Poynting
vectors into it.

Superposition
 

On Sat, 17 Nov 2007 18:28:21 -0500, "Stefan Wolfe"
wrote:


"Richard Clark" wrote in message
.. .


Well, for one powers do not add, just energies.

Well, power is a vector quanity subject to the rules of vector math. But
look at it in terms of the energy domain:

The total energy in the system over any time interval is equal to the sum of
the each power integrated over each segment of the transmission line during
the same time interval.

This isn't getting any better.

73's
Richard Clark, KB7QHC

Superposition
 

J. Mc Laughlin wrote:
Power is not a linear process. Power involves multiplication.

Nobody has said that power is a linear process.
The equation for adding EM powers has been known
for decades and if it didn't work, it would have
been discarded. As it is, one can find the power
density equation in any appropriate physics textbook.
The method of adding powers associated with two
coherent collinear EM waves is:

Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

where 'A' is the phase angle between the E-fields
of the two waves.
--
73, Cecil http://www.w5dxp.com

Superposition
 

K7ITM wrote:
Of course it was obvious from the base posting in this thread that the
"waves" must be on a TEM transmission line. But you still haven't
said anything about HOW you launched two distinct waves but got them
to combine into one.

The waves are launched by the external reflection from a
Z0-match and the internal reflection from the load.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Antonio Vernucci wrote:
. . .
The original question is deceiving, because it attracts the reader's
attention on just one particular point of the space, where energy can
unexplicably appear to be created or destroyed. But instead considering
the power distribution over the whole space, the mistery disappears.

Exactly. Misdirection is the primary tool used by magicians
(illusionists) to distract us into thinking something is occurring which
really isn't. Its utility hasn't been lost on those wanting to divert
our attention from the flaws in their arguments.

Pay no attention to the man behind the curtain. . .

Roy Lewallen, W7EL

Superposition
 

On Sat, 17 Nov 2007 18:56:46 -0500, "Stefan Wolfe"
wrote:

Well, for one powers do not add, just energies.

Well, power is a vector quanity subject to the rules of vector math. But
look at it in terms of the energy domain:

The total energy in the system over any time interval is equal to the sum
of
the each power integrated over each segment of the transmission line
during
the same time interval.

This isn't getting any better.

Since Energy is the integral of power over time,

Now from bad to worse.

You are going to have to unwind a lot of your own problems before you
can get to Cecil's tricks of subterfuge.

73's
Richard Clark, KB7QHC

Superposition
 

On Sat, 17 Nov 2007 20:30:54 -0500, "Stefan Wolfe"
wrote:

Well, for one powers do not add, just energies.

Well, power is a vector quanity subject to the rules of vector math. But
look at it in terms of the energy domain:

The total energy in the system over any time interval is equal to the
sum
of
the each power integrated over each segment of the transmission line
during
the same time interval.

This isn't getting any better.

Since Energy is the integral of power over time,

Now from bad to worse.

You are going to have to unwind a lot of your own problems before you
can get to Cecil's tricks of subterfuge.

What are the units you use to express the integral of watts over time?

Watt-Hours?

Worst yet (or perhaps finally), we are now at the end of superlatives
for this round. This chain of mistaken identities has every link
competing as its weakest link.

73's
Richard Clark, KB7QHC

Superposition
 

Richard Clark wrote:
You are going to have to unwind a lot of your own problems before you
can get to Cecil's tricks of subterfuge.

No tricks or subterfuge, Richard, just a simple energy
analysis based on the conservation of energy principle.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Cecil Moore wrote:
Tom Donaly wrote:
Because I don't have to prove you wrong, Cecil, you have to prove
yourself right.

Sorry, I don't, Tom. Hecht, Born and Wolf have already
proven those fundamentals of physics to be true. You
have to prove me, Hecht, and Born and Wolf wrong.

And of course, you will mount every diversion known to
man to avoid facing the technical facts as explained by
Hecht, Born & Wolf, Melles-Groit, and the FSU web page.

Cecil,

Have you ever seriously read a copy of Born and Wolf? I have a couple of
editions right beside me, and I just read through the chapter on
interference again.

You would not recognize any of your claims in that chapter. B&W never
mention "interaction" at all, not even once. They completely avoid all
of the elementary Hecht-like handwaving. They don't even mention energy.
It is simply not necessary to do so. Classical physics is quite self
consistent. Assuming one does not make an error in the setup of the
problem (perhaps a poor assumption) or in the math, the energy will
always come out correctly. It is not an independent consideration.

It is possible to solve problems entirely in a framework of energy
analysis, as I have pointed out previously. Much of quantum mechanics is
done that way. However, energy consideration are not more or less
important than any other formulation. Use the method that is easiest.

In this case the problem is overspecified with impossible conditions.
Tom, Tom, and Roy have pointed out the difficulty. I agree with them.

You have specified voltage, current, and impedance at the same time.
These items cannot be arbitrary and independent.

You got it wrong. Try again.

73,
Gene
W4SZ

Superposition
 

Cecil Moore wrote:
Tom Donaly wrote:
Because I don't have to prove you wrong, Cecil, you have to prove
yourself right.

Sorry, I don't, Tom. Hecht, Born and Wolf have already
proven those fundamentals of physics to be true. You
have to prove me, Hecht, and Born and Wolf wrong.

And of course, you will mount every diversion known to
man to avoid facing the technical facts as explained by
Hecht, Born & Wolf, Melles-Groit, and the FSU web page.

Sorry Cecil, quoting sources you can't possibly understand, yourself,
won't prove anything. Let me know if you ever plan on doing it right.
73,
Tom Donaly, KA6RUH

Superposition
 

On Sat, 17 Nov 2007 21:46:30 -0500, "Stefan Wolfe"
wrote:


"Richard Clark" wrote in message
.. .
On Sat, 17 Nov 2007 20:30:54 -0500, "Stefan Wolfe"
wrote:

Well, for one powers do not add, just energies.

Well, power is a vector quanity subject to the rules of vector math.
But
look at it in terms of the energy domain:

The total energy in the system over any time interval is equal to the
sum
of
the each power integrated over each segment of the transmission line
during
the same time interval.

This isn't getting any better.

Since Energy is the integral of power over time,

Now from bad to worse.

You are going to have to unwind a lot of your own problems before you
can get to Cecil's tricks of subterfuge.

What are the units you use to express the integral of watts over time?

Watt-Hours?

OK, fine. I prefer joules. Stay calm, Richard.

Joules is the integral of watts over time? Beyond superlatives!

Now consider the equation

Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

For energy, integrate Ptotal for 1 second:

= (50 - 0) + (50 - 0) - 2SQRT P1*P2 sine(A)
= 100 - 2*SQRT*P1*P2(sine(0 - n*2*pi)) = 100- 0 = 100

The integral of one full sine or cosine cycle totals zero assuming zero
reference.
It isn't in integral form.

No ENERGY lost, even though at certain times the power was greater than 100W
while at other times it was less.
that's not the meaning of integration

Let's rewind up that list of charades to revisit:
Well, power is a vector quanity subject to the rules of vector math.
and ponder the implication of a negative power, for simplicity:
P1 = 50W @ 90deg
P2 = 50W @ 270deg
what does the math reveal?

73's
Richard Clark, KB7QHC

Superposition
 

Gene Fuller wrote:
Assuming one does not make an error in the setup of the
problem (perhaps a poor assumption) or in the math, the energy will
always come out correctly. It is not an independent consideration.

Energy has not been a consideration at all for many
people such as yourself. That's why you guys have
missed the boat as far as energy is concerned. You
have only given lip service to the conservation of
energy principle. When you are pressed for details,
you whole argument falls apart.

You got it wrong. Try again.

Please point out in detail what is wrong with it.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Tom Donaly wrote:
Sorry Cecil, quoting sources you can't possibly understand, yourself,
won't prove anything. Let me know if you ever plan on doing it right.

The technical content of your objection is noted, Tom.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Richard Clark wrote:
and ponder the implication of a negative power

Power to the load equals forward power minus reflected power.

The negative sign for power in that case is associated with
direction of the Poynting vectors, positive for forward and
negative for reflected.

Constructive interference power minus destructive interference
power equals zero.

The negative sign for power is associated with destructive
interference.

Both of those cases are simply mathematical conventions.
--
73, Cecil http://www.w5dxp.com

Superposition
 

Richard Clark wrote:
and ponder the implication of a negative power, for simplicity:
P1 = 50W @ 90deg
P2 = 50W @ 270deg
what does the math reveal?

Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

Ptotal = 50 + 50 + 2*SQRT(2500)cos(180)

Ptotal = 50w + 50w - 100w = 0

There's 100 watts of destructive interference.
The two waves are canceled in their original direction
of flow. The energy in the two waves is redistributed
to regions that permit 100 watts of constructive
interference to occur. If the above happens in a
transmission line, the "lost" energy in the canceled
waves will simply be redistributed in the only other
direction available.

micro.magnet.fsu.edu/primer/java/scienceopticsu/interference/waveinteractions/index.html

"... when two waves of equal amplitude and wavelength that are
180-degrees ... out of phase with each other meet, they are not actually
annihilated, ... All of the photon energy present in these waves must
somehow be recovered or redistributed in a new direction, according to
the law of energy conservation ... Instead, upon meeting, the photons
are redistributed to regions that permit constructive interference, so
the effect should be considered as a redistribution of light waves and
photon energy rather than the spontaneous construction or destruction of
light."
--
73, Cecil http://www.w5dxp.com

Superposition
 

On Sun, 18 Nov 2007 00:16:47 -0500, "Stefan Wolfe"
wrote:

Let's rewind up that list of charades to revisit:
Well, power is a vector quanity subject to the rules of vector math.
and ponder the implication of a negative power, for simplicity:
P1 = 50W @ 90deg
P2 = 50W @ 270deg
what does the math reveal?

I am not trying to define power as negative with respect to zero
Negative with respect to zero? What about with respect to positive?
Or even a smaller negative! How about half negative (only 90 degrees
shift instead of 180)?
What happened to:
Well, power is a vector quanity subject to the rules of vector math.

I was so wanting to see your solution, much less how:
Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)
migrated into the negated sine in:
= (50 - 0) + (50 - 0) - 2SQRT P1*P2 sine(A)

I never expected such a trove of mistakes cascading through successive
replies. This is a troll, right?

No wonder you embrace anonymity, this would be embarrassing,
otherwise.

73's
Richard Clark, KB7QHC

Superposition
 

On Nov 17, 4:03 pm, Cecil Moore wrote:
K7ITM wrote:
Of course it was obvious from the base posting in this thread that the
"waves" must be on a TEM transmission line. But you still haven't
said anything about HOW you launched two distinct waves but got them
to combine into one.

The waves are launched by the external reflection from a
Z0-match and the internal reflection from the load.
--
73, Cecil http://www.w5dxp.com

So the waves are going opposite directions along the line??

Superposition
 

Exactly. Misdirection is the primary tool used by magicians (illusionists) to
distract us into thinking something is occurring which really isn't. Its
utility hasn't been lost on those wanting to divert our attention from the
flaws in their arguments.

Anyway, re-thinking on the case being here discussed, we must admit that the
issue could have been readily solved considering the basic antenna theory.

We know that two stacked dipoles yield a gain of up to 3 dB with respect to a
single dipole. In other words, two dipoles each fed with power P/2 produce, in
some regions of the space, a higher field than that produced by a single dipole
fed with power P, although the total transmit power has not changed.

The extra power measured at the receiver is obviously "created" at the expense
of power taken away from other regions of the space (according to the transmit
antenna pattern).

Too fundamental to deserve further discussions!

73

Tony I0JX

Superposition
 

What are the units you use to express the integral of watts over time?
Joules


Frank GM0CSZ / KN6WH