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

On Apr 20, 5:54 pm, Owen Duffy wrote:

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.

It is usual, I believe, to talk about power density. Volts per meter
times amps per meter is watts per square meter. It's not watts at a
point, or along a line, but over an area. Of course, you have to be
careful what you mean by that. The actual value of the power density
will be a function of position and time, of course, and will in
general be different at one point than at a point a meter, a
millimeter, or a micron removed. It can also be useful to add the
dimension of frequency: the power density is also a function of
frequency.

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.

One of the points of the "fields are interpreted by some as physical,
and by others as mathematical abstractions," which is a preamble to
further antenna discussions in the book I'm thinking of, is that it
doesn't matter which way you view them; if both camps describe their
behaviour the same way, the observable result is the same.

Cheers,
Tom

Owen Duffy wrote:
. . .
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.

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation (x
+ y) is f(x + y). This is a very clear and unambiguous definition which
you can find in a multiplicity of texts. It's an extremely valuable tool
in the analysis of linear systems.

To put it plainly in terms of waves and radiators, it means that if one
radiator by itself creates field x and another creates field y, then the
field resulting when both radiators are on is x + y.

What other meaning do you think it has?

Roy Lewallen, W7EL

Correction:

Roy Lewallen wrote:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation (x
+ y) is f(x + y). . .

That should read:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation
(x + y) is f(x) + f(y). . .
^^^^^^^^^^^
I apologize for the error. Thanks very much to David Ryeburn for
spotting it.

Roy Lewallen, W7EL

On Apr 20, 10:10 pm, Roy Lewallen wrote:
Correction:

Roy Lewallen wrote:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation (x
+ y) is f(x + y). . .

That should read:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation
(x + y) is f(x) + f(y). . .
^^^^^^^^^^^
I apologize for the error. Thanks very much to David Ryeburn for
spotting it.

Roy Lewallen, W7EL

I guess that's the definition of linearity. I'm not sure I've heard
it called superposition before, but rather that the superposition
theorem is a direct result of the linearity of a system. I trust
that's a small definitional issue that doesn't really change what
you're saying.

Cheers,
Tom

"K7ITM" wrote in message
oups.com...
On Apr 20, 10:10 pm, Roy Lewallen wrote:
Correction:

Roy Lewallen wrote:

Superposition means the following: If f(x) is the result of excitation
x
and f(y) is the result of excitation y, then the result of excitation
(x
+ y) is f(x + y). . .

That should read:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation
(x + y) is f(x) + f(y). . .
^^^^^^^^^^^
I apologize for the error. Thanks very much to David Ryeburn for
spotting it.

Roy Lewallen, W7EL

I guess that's the definition of linearity. I'm not sure I've heard
it called superposition before, but rather that the superposition
theorem is a direct result of the linearity of a system. I trust
that's a small definitional issue that doesn't really change what
you're saying.

Cheers,
Tom


linearity of the system is VERY important. it is what prevents the
waves/fields from interacting and making something new. empty space is
linear, air is (normally) linear, conductors (like antennas) are linear.
consider a conductor in space. if 2 different waves are incident upon it
you can analyze each interaction separately and just add the results.
However, if there is a rusty joint in that conductor you must analyze the
two incident waves together and you end up with not only the sum of their
resultant fields, but also various mixing products and other new stuff. so
yes, linearity is a very important consideration when talking about multiple
waves or fields and assuming superposition is correct.

K7ITM wrote:
On Apr 20, 10:10 pm, Roy Lewallen wrote:
Correction:

Roy Lewallen wrote:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation (x
+ y) is f(x + y). . .
That should read:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation
(x + y) is f(x) + f(y). . .
^^^^^^^^^^^
I apologize for the error. Thanks very much to David Ryeburn for
spotting it.

Roy Lewallen, W7EL

I guess that's the definition of linearity. I'm not sure I've heard
it called superposition before, but rather that the superposition
theorem is a direct result of the linearity of a system. I trust
that's a small definitional issue that doesn't really change what
you're saying.

Cheers,
Tom



Tom,

For most purposes the terms superposition and linearity are
interchangeable. However, for the purists there is a difference.

A system that is deemed linear requires that it has the properties of
both superposition and scalability. These properties are essentially the
same for simple systems, but they are not necessarily the same when
considering complex values. I found some clear examples in a book, "The
Science of Radio", by Paul Nahin.

One example, y(t)=Re{x(t)} describes a system which obeys superposition,
but not scaling. Hint: try a scaling factor of "j". That system is not
linear.

Another example is y(t)=[1/x(t)]*[dx/dt]^2. That system obeys scaling,
but not superposition. Again, it is not linear.

The bottom line is that superposition is necessary, but not sufficient
to ensure linearity.

You are correct that the definitional issue is not relevant to the
current RRAA discussion.

73,
Gene
W4SZ

On Apr 21, 7:24 am, Gene Fuller wrote:
K7ITM wrote:
On Apr 20, 10:10 pm, Roy Lewallen wrote:
Correction:

Roy Lewallen wrote:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation (x
+ y) is f(x + y). . .
That should read:

Superposition means the following: If f(x) is the result of excitation x
and f(y) is the result of excitation y, then the result of excitation
(x + y) is f(x) + f(y). . .
^^^^^^^^^^^
I apologize for the error. Thanks very much to David Ryeburn for
spotting it.

Roy Lewallen, W7EL

I guess that's the definition of linearity. I'm not sure I've heard
it called superposition before, but rather that the superposition
theorem is a direct result of the linearity of a system. I trust
that's a small definitional issue that doesn't really change what
you're saying.

Cheers,
Tom

Tom,

For most purposes the terms superposition and linearity are
interchangeable. However, for the purists there is a difference.

A system that is deemed linear requires that it has the properties of
both superposition and scalability. These properties are essentially the
same for simple systems, but they are not necessarily the same when
considering complex values. I found some clear examples in a book, "The
Science of Radio", by Paul Nahin.

One example, y(t)=Re{x(t)} describes a system which obeys superposition,
but not scaling. Hint: try a scaling factor of "j". That system is not
linear.

Another example is y(t)=[1/x(t)]*[dx/dt]^2. That system obeys scaling,
but not superposition. Again, it is not linear.

The bottom line is that superposition is necessary, but not sufficient
to ensure linearity.

You are correct that the definitional issue is not relevant to the
current RRAA discussion.

73,
Gene
W4SZ

Thanks, Gene--those examples are helpful. I'll retract what I posted
last night.

Based on the "necessary but not sufficient" statement above, we can
say that superposition does hold in a linear system, so if we specify
a linear system, we do have that guarantee.

Cheers,
Tom

K7ITM wrote:

Thanks, Gene--those examples are helpful. I'll retract what I posted
last night.

Based on the "necessary but not sufficient" statement above, we can
say that superposition does hold in a linear system, so if we specify
a linear system, we do have that guarantee.

And my thanks to both of you.

Roy Lewallen, W7EL

Roy Lewallen wrote in
:

Correction:

Roy Lewallen wrote:

Superposition means the following: If f(x) is the result of
excitation x and f(y) is the result of excitation y, then the result
of excitation (x + y) is f(x + y). . .

That should read:

Superposition means the following: If f(x) is the result of excitation
x
and f(y) is the result of excitation y, then the result of
excitation
(x + y) is f(x) + f(y). . .
^^^^^^^^^^^
I apologize for the error. Thanks very much to David Ryeburn for
spotting it.


Fine Roy, the maths is easy, but you don't discuss the eligible
quantities.

As I learned the superposition theoram applying to circuit analysis, it
was voltages or currents that could be superposed.

Presumably, for EM fields in space, the electric field strength and
magnetic field strength from multiple source can be superposed to obtain
resultant fields, as well as voltages or currents in any circuit elements
excited by those waves.

For avoidance of doubt, power is not a quantity to be superposed, though
presumably if it can be deconstructed to voltage or current or electric
field strength or magnetic field strength (though that may require
additional information), then those components may be superposed.

The resultant fields at a point though seem to not necessarily contain
sufficient information to infer the existence of a wave, just one wave,
or any specific number of waves, so the superposed resultant at a single
point is by itself of somewhat limited use. This one way process where
the resultant doesn't characterise the sources other than at the point
seems to support the existence of the source waves independently of each
other, and that there is no merging of the waves.

Is anything above contentious or just plain wrong?

Owen