On Mon, 09 Apr 2007 18:01:05 GMT, Gene Fuller
wrote:

You are quite prolific at manufacturing even more crystalline spheres.

Hi Gene,

Wait until they are embroidered with epicycles.

73's
Richard Clark, KB7QHC

Richard Fry wrote:

"Cecil Moore"

Still there are those nagging assertions of Born
and Wolf that for two equal magnitude signals,
the total intensity possible for incoherent
signals is double the intensity of one signal.
The total intensity possible for coherent
signals is four times the intensity of one signal.

________

It is a fairly common practice in broadcast designs to combine the
outputs of two r-f amplifiers of equal power rating, using a 4-port, 3
dB coaxial hybrid. The two amplifiers are driven by a single exciter
through a suitable splitter. The antenna connects to one output port of
the hybrid, and the other output port is connected to a dummy load.

When the relative r-f phases of the two txs are suitably set, the
antenna connection of the hybrid receives the total output power of the
two txs, and the dummy load port receives zero. When the relative r-f
phases of the txs are changed by 90 degrees from that setting, then the
conditions at the output ports are reversed.

The total average power available at the hybrid output for both of these
conditions is twice that of a single tx without the hybrid.

Does the quote from Born and Wolf support this?

RF

The quote from Born and Wolf that Cecil cites supports the 'profound'
notion that (E1 + E2)^2 / (E1 + E2) = 4.

73, Jim AC6XG

Gene Fuller wrote:
I am still waiting to learn the technical details of "cancellation",
including the proper units and the characteristic equations. There has
been deafening silence in response to my similar query about
"interference".

I have posted the details of cancellation more than
once and you haven't disagreed except in an ad
hominem way with zero technical content.

Once again here is the S-Parameter equation for
the reflected wave at a Z0-match impedance
discontinuity in a transmission line:

b1 = s11(a1) + s12(a2) = 0

b1 is the normalized reflected voltage at the
Z0-match. |b1|^2 is the reflected power in
the direction of the source.

s11(a1) is the normalized external reflected
voltage at the Z0-match.

s12(a2) is the normalized internal reflected
voltage making it through the Z0-match back
from the mismatched load.

Since b1 = 0, s11(a1) and s12(a2) have canceled.
s11(a1) and s12(a2) are of equal magnitudes and
opposite phases. Those waves are canceled toward
the source. Their combined energy components join
the forward wave toward the load.

Wave cancellation is what happens when a ham tunes
his antenna tuner for zero reflected power. I dare
say you have engaged in that very behavior leading
up to wave cancellation of reflections in the
direction of the source.
--
73, Cecil http://www.w5dxp.com

Jim Kelley wrote:
The quote from Born and Wolf that Cecil cites supports the 'profound'
notion that (E1 + E2)^2 / (E1 + E2) = 4.

There sure appears to be something wrong with that
equation, Jim. If E1 = E2 = 1 volt, then you have
4 / 2 = 4 which seems a bit wrong, if you don't
mind me saying so. What dimensions does your '4'
above have? Seems it would have to be 4 volts.

Assuming E1 = E2, I think what you meant to say was:

(E1 + E2)^2 / E1^2 = 4 (dimensionless)

which is what Born and Wolf say in equation (17)
chapter 7. Please note that is total constructive
interference as defined by Hecht in "Optics"

Also please note that if those signals are the opposite
phase:

(E1 - E2)^2 / E1^2 = 0

That's total destructive interference as defined
by Hecht.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
Richard Clark wrote:

Walter Maxwell wrote:

It is true, however, that two non-coherent fields from two different
sources would just plow through each
other with no effect on either.


Does the binary transition from a one micro-degree longer
cycle (non-coherent) to 0 (coherence) same length cycle really
plunge us into a new physical reality of waves colliding with
rebounds and caroms where formerly there was absolutely no
interaction before?


Of course, you are being facetious but the answer is simple.
If the two signals are mutually incoherent, they don't
interfere. Permanent wave cancellation is impossible
between two waves that are not coherent. Hecht in "Optics"
devotes an entire chapter to the "Basics of Coherence Theory".
So do Born and Wolf in "Principles of Optics". Here is what
Walt was obviously saying except in Born and Wolf's words:

"If the two beams originate in the same source, the fluctuations
in the two beams are in general correlated, and the beams are
said to be completely or partially *coherent* depending on
whether the correlation is complete or partial. In beams from
different sources, the fluctuations are completely uncorrelated,
and the beams are said to be mutually *incoherent*. When such
beams from different sources are superposed, no interference is
observed under ordinary experimental conditions, the total intensity
being everywhere the sum of the intensities of the individual beams."

In case you missed it, that says *NO INTERFERENCE* between mutually
incoherent waves. Seems reasonable to say that "no interference"
means the same thing as "no effect".

The last paragraph above is a perfect example of your tendancy to
misinterpret these texts, Cecil. Born and Wolf does not (and would
not) assert that there is "no effect" when mutually incoherent waves
are superposed. It's not reasonable to say that. There is certainly
an effect. In fact Walt and I use the effect whenever we tune our basses.

An illustration can be viewed at:

http://www.kettering.edu/~drussell/D...rposition.html

73, Jim AC6XG

Cecil Moore wrote:

With mutually coherent equal-magnitude sources,
the maximum possible peak intensity is four times
the intensity of a single wave, i.e. there is total
constructive interference. (This can happen
at a Z0-match in an RF transmission line.)

For "largely coherent sources" the peak intensity
would be slightly less than four times.

So according to your theory I can take a 1 watt laser, split the beam
into two coherent beams, recombine the beams in-phase together along
the same path thus creating constructive interference, and obtain 2
watts of laser power. Or would it be 4 watts?

:-)

ac6xg

Cecil Moore wrote:

Jim Kelley wrote:

The quote from Born and Wolf that Cecil cites supports the 'profound'
notion that (E1 + E2)^2 / (E1 + E2) = 4.


There sure appears to be something wrong with that
equation, Jim. If E1 = E2 = 1 volt, then you have
4 / 2 = 4 which seems a bit wrong, if you don't
mind me saying so. What dimensions does your '4'
above have? Seems it would have to be 4 volts.

Assuming E1 = E2, I think what you meant to say was:

(E1 + E2)^2 / E1^2 = 4 (dimensionless)

which is what Born and Wolf say in equation (17)
chapter 7. Please note that is total constructive
interference as defined by Hecht in "Optics"

Also please note that if those signals are the opposite
phase:

(E1 - E2)^2 / E1^2 = 0

That's total destructive interference as defined
by Hecht.

Right. So do you get the point, or not?

73, ac6xg

Jim Kelley wrote:
The last paragraph above is a perfect example of your tendancy to
misinterpret these texts, Cecil. Born and Wolf does not (and would not)
assert that there is "no effect" when mutually incoherent waves are
superposed. It's not reasonable to say that. There is certainly an
effect. In fact Walt and I use the effect whenever we tune our basses.

One wave has no effect on the other wave, Jim.
Please pay attention.
--
73, Cecil http://www.w5dxp.com

"Keith Dysart" wrote
The promoters of junk science fulfill an important role in this
process and I can't decide if their net effect is good or bad.
The bad effects are, of course, when they successfully lead
others astray.

On the whole, good or bad? I haven't decided.

Keith, I really like when junk science gurus exibit
constructive interference, the bafflegab sums to
four times the normal power!

Mike W5CHR

Jim Kelley wrote:
So according to your theory I can take a 1 watt laser, split the beam
into two coherent beams, recombine the beams in-phase together along the
same path thus creating constructive interference, and obtain 2 watts of
laser power. Or would it be 4 watts?

If it were total constructive interference, two 1/2W
beams would yield an intensity of 2 watts. Of course,
at another location, total destructive interference
would have to occur where the intensity was zero.

Put another way, the bright interference rings would
contain two watts per unit area while the flat black
rings would contain zero watts per unit area thus
averaging out to the original total of one watt.

As I said before, this ain't rocket science.
--
73, Cecil http://www.w5dxp.com