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

On Nov 16, 4:10 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.

Yes, no, yes, no fights won't get you anywhere.

"Cecil Moore" wrote in message
et...
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:

Can we take this to mean that this is not the steady state condition?

Tam/WB2TT

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

Tam/WB2TT wrote:
"Cecil Moore" wrote:
Given two coherent EM waves superposed in a 50 ohm environment
at considerable distance from any source:

Can we take this to mean that this is not the steady state condition?

Sorry if I somehow gave you that idea. It is a steady-state
problem.
--
73, Cecil http://www.w5dxp.com

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

50 joules/s are carried by Wave#1 if alone. The same applies to Wave#2

But if both waves are sumultaneouly present, the power carried by each wave when
alone is no longer a meaningful number. As a matter of fact when superposing two
coherent waves (same frequency, fixed phase relationship), one MUST first sum
voltages (or currents) and then calculate power.

Summing wave powers could only be done in case of incoherent waves.

In conclusion, the answer to your question is that the apparent extra 71
joules/s come front the fact that 100 joules/s taken as reference is a number
having no physical meaning.

73

Tony I0JX

Antonio Vernucci wrote:
But if both waves are sumultaneouly present, the power carried by each
wave when alone is no longer a meaningful number.

Why is the ExB Poynting vector of each wave no longer
proportional to the energy content? Why does the energy
content of the component waves have to change when they
superpose? Where does that energy change go? Do the
necessary joules disappear and/or appear from thin air?

As a matter of fact
when superposing two coherent waves (same frequency, fixed phase
relationship), one MUST first sum voltages (or currents) and then
calculate power.

That's what I did and the result was 171 joules/sec.
The Poynting vector for each of the two source waves
is 50 joules/sec. Why is the energy content of the
component waves not a meaningful number?

Summing wave powers could only be done in case of incoherent waves.

No, there is a special equation to be used for summing coherent
waves, i.e. the irradiance equation from optical physics. For
power density:

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

where 'A' is the angle between the two E-fields.

In conclusion, the answer to your question is that the apparent extra 71
joules/s come front the fact that 100 joules/s taken as reference is a
number having no physical meaning.

For every second that passes, 50 + 50 = 100 joules has no
physical meaning? Are you saying that an EM wave is not
associated with ExB joules/sec?
--
73, Cecil http://www.w5dxp.com

Why is the ExB Poynting vector of each wave no longer
proportional to the energy content? Why does the energy
content of the component waves have to change when they
superpose? Where does that energy change go? Do the
necessary joules disappear and/or appear from thin air?

Joules do not disappear, they just get distributed over the free space in a
non-uniform manner.

In certain regions of the space the two waves add up (apparently creating extra
power), in other regions they cancel out (apparently destroying power). The
integral of total radiated power does not change.

In your example you considered a location where the two waves have a 45 deg.
shift. At another location, where the two waves have a zero deg. shift, you
would observe an even higher apparent power creation. Conversely, at locations
where the two waves have a 180 deg. shift you would observe absence of power.

The principle causing the apparent power creation at your location is the same
principle by which an antenna formed by two stacked dipoles features a gain of
up to 3 dB with respect to a single dipole, and can then deliver up to twice the
power to a receiver placed at the maximum radiation heading (and zero power at a
receiver placed at 90 degrees from that heading). .

That's what I did and the result was 171 joules/sec.
The Poynting vector for each of the two source waves
is 50 joules/sec. Why is the energy content of the
component waves not a meaningful number?

Each wave produces 50 joules/s when alone. When the two waves are superimposed,
each wave produces not only its 50 joules/s but also 35.5 more joules that it
"robs" from other regions of the space. If you would plainly sum the power of
two components (i.e. 50 + 50), you would neglect the fact that coherent waves
necessarily interfere with each other in the space, in constructive or
destructive manner depending on the receiver location.

Summing wave powers could only be done in case of incoherent waves.

No, there is a special equation to be used for summing coherent
waves, i.e. the irradiance equation from optical physics. For
power density:

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

where 'A' is the angle between the two E-fields.

Please re-read my sentence more carefully. My statement was that summing powers
(that is. Ptotal = P1 + P2) would only be correct for incoherent waves.

For coherent waves, plainly summing powers would generally be incorrect (apart
from one particular phase angle), and one must nstead use the equation you have
shown.

For every second that passes, 50 + 50 = 100 joules has no
physical meaning? Are you saying that an EM wave is not
associated with ExB joules/sec?

see previous remarks.

73

Tony I0JX

Antonio Vernucci wrote:
Each wave produces 50 joules/s when alone. When the two waves are
superimposed, each wave produces not only its 50 joules/s but also 35.5
more joules that it "robs" from other regions of the space.

My point exactly! The same thing is true when it happens
in a transmission line at a Z0-match point. The region of
constructive interference toward the load (forward energy
wave) "robs" energy from the region of destructive
interference toward the source (reflected energy waves).
That's how antenna tuners work.
--
73, Cecil http://www.w5dxp.com