On Nov 16, 12:34 pm, Cecil Moore wrote:
The following is from an email to which I replied today.

Given two coherent EM waves superposed in a 50 ohm environment
at considerable distance from any source:

Wave#3 = Wave#1 superposed with Wave#2

Wave#1: V = 50v at 0 deg, I = 1.0a at 0 deg, P = 50 joules/sec

Wave#2: V = 50v at 45 deg, I = 1.0a at 45 deg, P = 50 joules/sec

These two waves superpose to V = 92.38v and I = 1.85a
Note: P = 171 joules/sec

*During each second*, Wave#1 supplies 50 joules of energy and
Wave#2 supplies 50 joules of energy for a total of 100 joules of
energy being supplied *every second* to the superposition process.
Yet the results of that superposition process yields 171 joules
of energy *during each second*, 71 joules more than is being
supplied to the process. Where are the extra 71 joules per second
coming from?
--
73, Cecil http://www.w5dxp.com

Nice "when are you going to stop beating your mother" sort of
question. And what was your reply?

K7ITM wrote:
Nice "when are you going to stop beating your mother" sort of
question. And what was your reply?

It's a rhetorical question, Tom. What is your reply?
When someone (besides Eugene Hecht) explains it to
my satisfaction I will stop beating that dead horse.
--
73, Cecil http://www.w5dxp.com

On Nov 16, 3:10 pm, Cecil Moore wrote:
K7ITM wrote:
Nice "when are you going to stop beating your mother" sort of
question. And what was your reply?

It's a rhetorical question, Tom. What is your reply?
When someone (besides Eugene Hecht) explains it to
my satisfaction I will stop beating that dead horse.
--
73, Cecil http://www.w5dxp.com

From your original posting, "The following is from an email to which I
replied today." There was no indication than anything following that
was your reply, and I was curious what your reply was. You're welcome
to beat dead horses as much as you like, but that doesn't mean I need
to.

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. Right now I'm not accepting that you will be able
to combine two independent waves carrying 50 watts each into a single
wave carrying more than 100 watts. Thus, it's a "when are you going
to stop beating your mother" problem, as posed. There's really
nothing interesting except at the point at which the waves combine.
But then that's already been explained more than once.

K7ITM wrote:
From your original posting, "The following is from an email to which I
replied today." There was no indication than anything following that
was your reply, and I was curious what your reply was.

The posting was my reply to that original email.

Right now I'm not accepting that you will be able
to combine two independent waves carrying 50 watts each into a single
wave carrying more than 100 watts.

It happens all the time at a Z0-match in a transmission
line. Please reference Dr. Best's article in the Nov/Dec
2001 QEX. He combines a 75 joule/sec wave with an 8.33
joule/sec wave to get a 133.33 joule/sec wave.

Ptotal = 75 + 8.33 + 2*SQRT(75*8.33) = 133.33 joules/sec

Dr. Best's article was the first time I had ever seen
the power density irradiance equations from the field
of optical physics used on RF waves.
--
73, Cecil http://www.w5dxp.com

On Nov 17, 12:15 am, Cecil Moore wrote:
K7ITM wrote:
From your original posting, "The following is from an email to which I
replied today." There was no indication than anything following that
was your reply, and I was curious what your reply was.

The posting was my reply to that original email.

Right now I'm not accepting that you will be able
to combine two independent waves carrying 50 watts each into a single
wave carrying more than 100 watts.

It happens all the time at a Z0-match in a transmission
line. Please reference Dr. Best's article in the Nov/Dec
2001 QEX. He combines a 75 joule/sec wave with an 8.33
joule/sec wave to get a 133.33 joule/sec wave.

Ptotal = 75 + 8.33 + 2*SQRT(75*8.33) = 133.33 joules/sec

Dr. Best's article was the first time I had ever seen
the power density irradiance equations from the field
of optical physics used on RF waves.
--
73, Cecil http://www.w5dxp.com

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.

Adios,
Tom

"K7ITM" wrote
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.
__________

The physics of EM radiation.

As an example, consider an array comprised of two, identical radiators on
the same vertical axis, in the same physical orientation, with a vertical
separation of 1 wavelength, each driven with equal r-f power and relative
phase by the same r-f source.

The fields from the two radiators are generated and radiated separately, but
once well past the near-field boundary of the array, the EM field existing
at every point in free space will be the vector sum of those separate
fields.

When the net field at the radiation peak of the array is measured in the far
field, there will be no way to determine from that measurement whether the
field was generated using a single radiator with X power input, or the
described 2-element array having about 1/2 that power input.

RF

Richard Fry wrote:
"K7ITM" wrote
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.
__________

The physics of EM radiation.

As an example, consider an array comprised of two, identical radiators
on the same vertical axis, in the same physical orientation, with a
vertical separation of 1 wavelength, each driven with equal r-f power
and relative phase by the same r-f source.

The fields from the two radiators are generated and radiated separately,
but once well past the near-field boundary of the array, the EM field
existing at every point in free space will be the vector sum of those
separate fields.

When the net field at the radiation peak of the array is measured in the
far field, there will be no way to determine from that measurement
whether the field was generated using a single radiator with X power
input, or the described 2-element array having about 1/2 that power input.

RF

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

Richard Fry wrote:
The physics of EM radiation.

It seems strange to me that people who know that
antenna gain in one direction comes at the expense
of gain in another direction cannot carry that
concept over to transmission lines. Constructive
interference in one direction means destructive
interference in another direction. That's what
creates the radiation pattern for antennas. It
is also exactly the same thing that routes
energy toward the antenna instead of toward the
source in a Z0-matched transmission line.

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

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 at http://www.w5dxp.com/thinfilm.gig
--
73, Cecil http://www.w5dxp.com

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.