Independence of waves
 

Owen Duffy wrote:
Richard Clark wrote:
Why would you think that superposition fails for this?

Richard, I don't... but the failure was to think that such an experiment
indicated that the two interfering waves could be isolated at a point.

Doesn't

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

indicate that the two interfering waves are isolated
to a point?
--
73, Cecil http://www.w5dxp.com

Independence of waves
 

Alan Peake wrote:

Owen Duffy wrote:
But is it possible to inject two coherent waves travelling
independently in the same direction?

In a transmission line? Wouldn't they both have the same propagation
velocity? If so, how would you distinguish between them?

They become indistinguishable, i.e. they interact. If they
interact destructively, they give up energy to constructive
interference in the opposite direction. If they interact
constructively, they require destructive interference
energy from the opposite direction. In a transmission line,
interference is one-dimensional.
--
73, Cecil http://www.w5dxp.com

Independence of waves
 

"Cecil Moore" wrote in message
et...
The fields cannot be separated from
the energy necessary for them to exist. Such is the basic
nature of EM waves.
--
I would go the other way... the energy can not be separated from the fields.
the fields are the 'more basic' components, energy and power can always be
calculated from them... but you can't always go the other way without
carrying along extra phase information that isn't necessary when talking
about (scalar) power or energy.

Independence of waves
 

that favours one or other of the waves will result in higher received
power. This indicates that both waves are independent and available to
the receiving antenna, the waves do not cancel in space, but rather the
superposition occurs in the antenna.

It's really very simple:

at each point in free space at a specific time t, there is only ONE
value of the (vector) electric and magnetic fields,

E=(E_x(x,y,z,t),E_y(x,y,z,t),E_z(x,y,z,t))
B=(B_x(x,y,z,t),B_y(x,y,z,t),B_z(x,y,z,t))

to find those values, you simply add up what comes from various sources
of the fields. Separate antennas do not have their "own" E and B that
is independent.

Tor
N4OGW

Independence of waves
 

Roy Lewallen wrote:
Well, let's see. Begin with two identical, phase locked generators with
fixed 50 ohm output resistances. Connect the output of generator A to a
one wavelength 50 ohm transmission line, and the output of generator B
to a half wavelength 50 ohm line. Connect the far ends of the lines
together, and to a third transmission line of any length. Let's properly
terminate the third line for simplicity. Superposition should work with
this system, so begin by turning off generator A. The one wavelength
line is now perfectly terminated and looks just like a 50 ohm resistor
across the third line. Generator B puts half its power into generator
A's output resistance and half into the third line's load.

If generator A has 100 watts available to a 50 ohm load, how
much power is being dissipated in the resistor at the end of
the third transmission line?

Did you account for the fact that the generator sees 25 ohms,
not 50 ohms? Are you ignoring the reflections on generator
A's feedline?

There's a
wave traveling down that line. Now turn off B and turn on A, and note
that half of A's power is going to B's source resistance and half into
the third line's load.

With either source turned off, the voltage reflection coefficient at
the junction of the three lines is rho = (25-50)/(25+50) = -0.33.
Did you account for the resulting reflections?

If you believe as I do that waves don't interact in a linear medium and
believe in the validity of superposition in such a medium, then you
believe that when both generators are on there are two waves going down
that third line. They're exactly equal but out of phase, so they add to
zero everywhere along the line. With the system on and in steady state,
there's absolutely no way you can tell the difference between this sum
of two waves and no waves at all. *They are the same.* If you look at
the input to the third line, you'll find a point with zero voltage
across the line, and zero current entering or leaving it. Where you will
get into serious trouble is if you assign a power to each of the
original waves.

Would you agree that the waves are EM waves? Would you agree
that the waves each have an E-field and a B-field? Would you
agree that the joules/sec in each wave is proportional to
ExB and that the waves could not exist without those joules/sec?
There is absolutely no problem assigning joules/sec to each
EM wave. In fact, the laws of physics demands it.

Then you'll have a real job explaining where the power
in one of the waves went when you turned on the second generator --
among other problems.

It's no problem at all. Optical physicists have been doing it
for over a century. The energy analysis at the feedline junction
point is very straight forward. It simply obeys the wave reflection
model, the superposition principle, and the conservation of
energy principle.

A solution to the problem based on the assumption that there are no
waves on the third line and one which claims there are two canceling
waves are equally valid, and both should give identical answers.

EM waves cannot exist without ExB joules/sec, i.e. EM waves
cannot exist devoid of energy. Those two waves engaged in
destructive interference which redirected the sum of their
energy components back toward the sources as constructive
interference. They interacted at the physical impedance
discontinuity and ceased to exist in the third feedline.

In your example, with both sources on, the SWR on the two
generator feedlines is infinite. There is exactly enough joules
stored in each line to support the forward and reflected powers
measured by a Bird directional wattmeter.
--
73, Cecil, w5dxp.com

Independence of waves
 

On Fri, 20 Apr 2007 00:46:07 -0700, Roy Lewallen
wrote:

Richard Clark wrote:

Hi Owen,

And you have already allowed that superposition does not fail. Thus
there must be some other failure to be found in the choice of antenna.
From other correspondence, it is asserted that a gain antenna, by
virtue of its size, cannot be placed in null space (that point wherein
all contributions of energy sum to zero) which is planar and
equidistant between sources (there being two of them for the purpose
of discussion).

Have I described this accurately?

I think it might be more fundamental and perhaps subtle than just a
limitation of size. If the null space is a whole plane, as with the two
radiating elements of my example, you have an infinite area on which to
construct your antenna, although it would have to have zero thickness.
But even allowing infinitely thin elements, I don't see any way you can
construct it entirely on the plane so it will be more sensitive to
signals coming from one side of the plane than the other.

Hi Roy,

I presume by your response that it affirms my description. Moving on
to your comments, it stands to reason that the reduction of the
argument proves you cannot build an antenna with directivity within a
very specific constraint - the null space. As there is zero dimension
on the axis that connects the two sources, then no directivity can be
had from a zero length boom as one example. Other examples would
demand some dimension other than zero along this axis is where I see
the counter-argument developing.

... But if I'm
right, then there's no way to do as Owen originally proposed, namely to
determine entirely from a null space that the null is the sum of
multiple fields, let alone the nature of those fields -- at least with a
directional antenna. It has to extend out where it can a sniff of the
uncanceled fields to do that.

This then suggests that there is something special about null space
that is observed no where else. That is specifically true, but not
generally. What is implied by null is zero, and in a perfect world we
can say they are equivalent. Even a dipole inhabiting that null space
would bear it out, whereas an antenna with greater directivity along
that axis would not.

However, if we open up the meaning of null to mean a point, or region,
within which we find a minimum due to the combination of all wave
contributions, then I would say a directive antenna is back in the
game, and that it exhibits Owens proposition (if I understand it - but
I still need to see Owen's elaboration).

73's
Richard Clark, KB7QHC

Independence of waves
 

Richard,

As often happens, I don't think we're fully communicating.

Richard Clark wrote:

I presume by your response that it affirms my description. Moving on
to your comments, it stands to reason that the reduction of the
argument proves you cannot build an antenna with directivity within a
very specific constraint - the null space. As there is zero dimension
on the axis that connects the two sources, then no directivity can be
had from a zero length boom as one example. Other examples would
demand some dimension other than zero along this axis is where I see
the counter-argument developing.

In the two antenna example, the null space is a plane. Since the plane
is infinite in extent, you can create in that plane an antenna with a
boom of any length, and therefore with arbitrarily high directivity.
However, if you restrict that antenna to lie entirely in the null plane,
that directivity won't be in a direction such that the antenna will
favor one radiator over the other. Therefore it can't tell if the null
plane is simply an area in space with no field, or whether it's the
result of two superposing fields. And I believe this is true for any
antenna, of any size, orientation, or design that you can construct
which lies completely in that plane.

This then suggests that there is something special about null space
that is observed no where else. That is specifically true, but not
generally. What is implied by null is zero, and in a perfect world we
can say they are equivalent. Even a dipole inhabiting that null space
would bear it out, whereas an antenna with greater directivity along
that axis would not.

But I'm claiming you can't get directivity such that you can favor one
radiator over the other, by any antenna lying entirely in the null
space. In other words, any antenna you build in that null space will
detect zero field. The special thing about null space is simply that
it's a limit, and it makes a good vehicle for illustration because we
can more easily distinguish between nothing and something than between
two different levels.

However, if we open up the meaning of null to mean a point, or region,
within which we find a minimum due to the combination of all wave
contributions, then I would say a directive antenna is back in the
game, and that it exhibits Owens proposition (if I understand it - but
I still need to see Owen's elaboration).

I'll extend my hypothesis to include all such regions. Create a null
space or region of any size or shape by superposing any number of waves.
I claim that any antenna, regardless of size or design, lying entirely
in that space or region will detect zero signal. In fact, no detector of
any type which you can devise, lying entirely within that null space or
region, will be able to detect anything or otherwise tell the difference
between the superposition and a simple region of zero field. It will
take only a single contrary example to prove me wrong.

Roy Lewallen, W7EL

Independence of waves
 

Roy Lewallen, W7EL wrote:
"With the system on and in steady state, there`s absolutely no way you
can tell the difference between this sum of two waves and no waves at
all."

With the constraint of where Roy would let me check, I think he is
right.

Terman`s first sentence in the 1955 (4th edition) of "Electronics and
Radio Engineering" is: "Electrical energy that has escaped into free
space exisrs in the form of electromagnetic waves."

Other definitions say: "All entities that carry force, whether one
marble striking another or sunlight moving molecules of air, act
sometimes as particles and sometimes as waves."

Thyere is an analogy of Roy`s null plane in public address where two
loudspeakers are placed together and driven out-of-phase. The microphone
is placed on the centerline to avoid feedback.

I agree that two wires in a plane with the plane of the source antennas
perpendicular to the plane of of those wires and the reception point
equidistant from the antennas cannot select between those antennas
without occupying some space outside the plane. A patch antenna might do
it but it has depth or thickness so it partially falls outside the
plane.

Waves may be only a mathematical convenience but are visible in water
and in powders on vibrating surfaces. They are also visible in
synchronized illumination on vibrating surfaces and in synchronized
photos.

Waves in-phase and traveling in the same direction are inseparable so
might as well be a single wave.

Best regards, Richard Harrison, KB5WZI

Independence of waves
 

On Fri, 20 Apr 2007 12:46:50 -0700, Roy Lewallen
wrote:

But I'm claiming you can't get directivity such that you can favor one
radiator over the other, by any antenna lying entirely in the null
space. In other words, any antenna you build in that null space will
detect zero field.

Hi Roy,

No dispute there either.

The special thing about null space is simply that
it's a limit, and it makes a good vehicle for illustration because we
can more easily distinguish between nothing and something than between
two different levels.

That is distinctive as being binary, certainly; but I am sure there is
something between two different levels that are distinguishable to the
same degree. The difference between 0 and 1 is no greater than
between 1 and 2.

However, if we open up the meaning of null to mean a point, or region,
within which we find a minimum due to the combination of all wave
contributions, then I would say a directive antenna is back in the
game, and that it exhibits Owens proposition (if I understand it - but
I still need to see Owen's elaboration).

I'll extend my hypothesis to include all such regions. Create a null
space or region of any size or shape by superposing any number of waves.

But this says nothing of the quality of "null" as I extended it above
which could be supported by a directional antenna. As I am still
unsure of the nature of Owen's proposition, I will leave the quality
of "null" for Owen to discuss or discard.

73's
Richard Clark, KB7QHC

Independence of waves
 

Richard Clark wrote in
:

On Fri, 20 Apr 2007 05:38:37 GMT, Owen Duffy wrote:

"I maintain that there is
actually zero field at a point of superposition of multiple waves
which sum to zero, and that no device or detector can be devised
which, looking only at that point, can tell that the zero field is a
result of multiple waves."

Hi Owen,

This seems to be in distinct contrast to what appeared to be your goal
earlier - insofar as the separation of sources (you and others call
them waves). I am trying to tease out just what it was that impelled
you upon this thread.

Richard

I still have a problem reconciling the resultant E field and H field,
including their direction, with the concept that they are not evidence of
another wave. I am not suggesting there is another wave, there is good
reason to believe that there isn't, but that if there isn't another wave,
is the resultant E field, and H field (including direction) a convenient
mathematical representation of something that doesn't actually exist.

In answer to your last question, a quest for understanding. I don't know
the answer, but the discussion is enlightening.


And we haven't mentioned power, not once!

Not specifically so, but inferentially, certainly. We see the term
detector employed above, and it cannot escape the obvious implication
of power to render an indication. Perhaps the relief expressed by
your sentiment is in not having to have had added or subtracted power
(or any other expressions of power).

Basically. Some of the problems in the analysis are as a result of trying
to determine conditions at a point, which can have no area, and
presumably no power, but yet E field and H field.

I think the discussion is mainly exploring a detailed definition of the
concept of superposition of radio waves. It seems to mean different
things to different people, but it is used as if it has a shared meaning.

Owen