Independence of waves
 

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

Independence of waves
 

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

Independence of waves
 

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

Independence of waves
 

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

Independence of waves
 

Owen Duffy wrote:

I can see that we can deal mathematicly with two or more coherent
components thought of as travelling in the same direction on a line (by
adding their voltages or currents algebraicly), but it seems to me that
there is no way to isolate the components, and that questions whether
they actually exist separately.

I reckon that if you can't see them, measure them separate them etc,
then they don't exist.
It's different to being in a null between two antennae. The signals
don't appear to exist where you are, but move directly away from either
antenna, and there they are. So they exist at the null even though you
can't see them there.
Alan

Independence of waves
 

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

Independence of waves
 

"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.

Independence of waves
 

"Owen Duffy" wrote in message
...
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

yes, superposition is meant to work directly on voltage, current, electric
fields, and magnetic fields. it can be extended by adding appropriate extra
phase terms to power or intensity as cecil prefers to use.

you are at least partially correct. a measurement at a single point at a
single time can only give the sum of the fields at the instant of
measurement. make a series of measurements at a point over time and you can
infer the existance of different frequency waves passing the point, but not
anything about their direction or possibly multiple components. add
measurements at enought other points and you can resolve directional
components, polarization, etc. assuming your points are properly
distributed... this means that a small probe (like a scope probe) can only
make a record of voltages/currents or fields at a single point and can't
tell anything about direction. add a second probe and you could detect the
direction of travel of waves on a wire.

Independence of waves
 

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) + f(y). . .

Now the big question is: Is superposition always reversible?
If not, it implies interaction between f(x) and f(y).
--
73, Cecil http://www.w5dxp.com

Independence of waves
 

Alan Peake wrote:

Owen Duffy wrote:
I can see that we can deal mathematicly with two or more coherent
components thought of as travelling in the same direction on a line
(by adding their voltages or currents algebraicly), but it seems to me
that there is no way to isolate the components, and that questions
whether they actually exist separately.

I reckon that if you can't see them, measure them separate them etc,
then they don't exist.
It's different to being in a null between two antennae. The signals
don't appear to exist where you are, but move directly away from either
antenna, and there they are. So they exist at the null even though you
can't see them there.

So is superposition always reversible? If not, that would
imply interaction between the superposed components.
--
73, Cecil http://www.w5dxp.com