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

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.

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

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

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

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

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

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

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

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