Independence of waves
 

There has been much discussion about wave cancellation, anihalation,
interaction etc. The discussion was initially about waves confined to a
transmission line (but would apply also to a waveguide in a sense) and
then progressed to radiation in free space.

Let me initially explore the case of radiation in free space. I am
talking about radio waves and the radiation far field.

If we have two widely separated antennas radiating coherent radio waves
don't they each radiate waves that travel independently through space. (I
have specified wide separation so as to make the effect of one antenna on
the other insignificant.

If we were to place a receiving antenna at a point in space to couple
energy from the waves, the amount of energy available from the antenna is
the superposition of the response of the antenna to the wave from each
source. This is quite different to saying that the electric field (or the
magnetic field) at that point is the superposition of the field resulting
from each antenna as is demonstrated by considering the response of
another recieving antenna with different directivity (relative to the two
sources) to the first receiving antenna.

A practical example of this is that an omni directional receiving antenna
may be located at a point where a direct wave and a reflected wave result
in very low received power at the antenna, whereas a directional antenna
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.

Though we frequently visualise nodes and antinodes in space, or talk of
nulls in space (eg have you ever noticed that when you stop a car at
traffic lights, you are smack in the middle of a null), whereas it seems
to me that the realisation of a null involves the response of the
receiving antenna.

This explanation IMHO is more consistent with the way antennas behave
than the concept that waves superpose in space, it allows waves to
radiate outwards from a source, passing through each other without
affecting each other. Whilst we routinely look at plots of the
directivity of an antenna, and assume that the plotted directivity is
merely a function of polar angle, we overlook that the plotted pattern
assumes an isotropic probe at a distance very large compared to the
dimensions of the antenna (array). Tracing the position of a pattern
minimum in towards the array may well yield a curved path rather than a
straight line, and a curved path is inconsistent with waves anihalating
each other or redistributing energy near the antenna and radiating
outwards in true radial direction from some virtual antenna centre.

So, it seems to me that coherent waves from separated sources travel
independently, and the response of the probe used to observe the waves is
the superposition of the probe's response to each wave. (A further
complication is that the probe (a receiving antenna) will "re-radiate"
energy based on its (net) response to the incoming waves.)

Now, considering transmission lines, do the same principles apply?

A significant difference with uniform TEM transmission lines is that
waves are constrained to travel in only two different directions.

Considering the steady state:

If at some point two or more coherent waves travelling a one direction,
those waves will undergo the same phase change and attenuation with
distance as each other and they must continue in the same direction
(relative to the line), and the combined response in some circuit element
on which they are incident where superposition is valid (eg a circuit
node) will always be as if the two waves had been superposed... but the
response is not due to wave superposition but superposition of the
responses of the circuit element to the waves. It is however convenient,
if not strictly correct to think of the waves as having superposed.

That convenience extends to ignoring independent coherent waves that
would net to a zero response. For example, if we were to consider a
single stub matching scheme, though one there might consider that
multiple reflected waves arrive at the source, if they net to zero
response, then it is convenient to regard that in the steady state there
are no reflected waves, the source response is as if there were no
reflected waves. An alternative view of that configuration is that
superposition in the circuit node that joins the stub, the line to the
load and the line to the source results in conditions at that end of the
source line that do not require a reflected wave to satisfy boundary
conditions at that point, and there really is no reflected wave.

Steady state analysis is sufficiently accurate and appropriate to
analysis of many scenarios, and the convenience extends to simplified
mathematics. It seems that the loose superposition of waves is part of
that convenience, but it is important to remember the underlying
principles and to consciously assess the validity of model
approximations.

Comments?

Owen

Independence of waves
 

"Owen Duffy" wrote in message
...

There has been much discussion about wave cancellation, anihalation,
interaction etc. The discussion was initially about waves confined to a
transmission line (but would apply also to a waveguide in a sense) and
then progressed to radiation in free space.

Let me initially explore the case of radiation in free space. I am
talking about radio waves and the radiation far field.

If we have two widely separated antennas radiating coherent radio waves
don't they each radiate waves that travel independently through space. (I
have specified wide separation so as to make the effect of one antenna on
the other insignificant.

If we were to place a receiving antenna at a point in space to couple
energy from the waves, the amount of energy available from the antenna is
the superposition of the response of the antenna to the wave from each
source. This is quite different to saying that the electric field (or the
magnetic field) at that point is the superposition of the field resulting
from each antenna as is demonstrated by considering the response of
another recieving antenna with different directivity (relative to the two
sources) to the first receiving antenna.

A practical example of this is that an omni directional receiving antenna
may be located at a point where a direct wave and a reflected wave result
in very low received power at the antenna, whereas a directional antenna
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.

Though we frequently visualise nodes and antinodes in space, or talk of
nulls in space (eg have you ever noticed that when you stop a car at
traffic lights, you are smack in the middle of a null), whereas it seems
to me that the realisation of a null involves the response of the
receiving antenna.

This explanation IMHO is more consistent with the way antennas behave
than the concept that waves superpose in space, it allows waves to
radiate outwards from a source, passing through each other without
affecting each other. Whilst we routinely look at plots of the
directivity of an antenna, and assume that the plotted directivity is
merely a function of polar angle, we overlook that the plotted pattern
assumes an isotropic probe at a distance very large compared to the
dimensions of the antenna (array). Tracing the position of a pattern
minimum in towards the array may well yield a curved path rather than a
straight line, and a curved path is inconsistent with waves anihalating
each other or redistributing energy near the antenna and radiating
outwards in true radial direction from some virtual antenna centre.

So, it seems to me that coherent waves from separated sources travel
independently, and the response of the probe used to observe the waves is
the superposition of the probe's response to each wave. (A further
complication is that the probe (a receiving antenna) will "re-radiate"
energy based on its (net) response to the incoming waves.)

Now, considering transmission lines, do the same principles apply?

A significant difference with uniform TEM transmission lines is that
waves are constrained to travel in only two different directions.

Considering the steady state:

If at some point two or more coherent waves travelling a one direction,
those waves will undergo the same phase change and attenuation with
distance as each other and they must continue in the same direction
(relative to the line), and the combined response in some circuit element
on which they are incident where superposition is valid (eg a circuit
node) will always be as if the two waves had been superposed... but the
response is not due to wave superposition but superposition of the
responses of the circuit element to the waves. It is however convenient,
if not strictly correct to think of the waves as having superposed.

That convenience extends to ignoring independent coherent waves that
would net to a zero response. For example, if we were to consider a
single stub matching scheme, though one there might consider that
multiple reflected waves arrive at the source, if they net to zero
response, then it is convenient to regard that in the steady state there
are no reflected waves, the source response is as if there were no
reflected waves. An alternative view of that configuration is that
superposition in the circuit node that joins the stub, the line to the
load and the line to the source results in conditions at that end of the
source line that do not require a reflected wave to satisfy boundary
conditions at that point, and there really is no reflected wave.

Steady state analysis is sufficiently accurate and appropriate to
analysis of many scenarios, and the convenience extends to simplified
mathematics. It seems that the loose superposition of waves is part of
that convenience, but it is important to remember the underlying
principles and to consciously assess the validity of model
approximations.

Comments?

Owen


its too well considered and sensible... i predict this thread will die a
quick and quiet death, there is no fodder for arguments.

Independence of waves
 

I believe there's at least one basic fallacy in your development.

The problem is that a directional antenna can't be made to take up zero
space. Let's consider a situation where we can have complete
cancellation of waves from two sources. There surely are many others,
but let's look at this one for starters.

Consider two identical vertical omnidirectional antennas radiating
equal, out of phase fields. There will be a plane of zero field passing
directly between them, where their fields sum to zero. My challenge is
this: Devise a directional antenna which lies entirely in this plane and
which has a response that's different for the two antennas. That is, an
antenna which has a stronger response to the field from one antenna than
the other. I maintain that you can't do it. Your directional antenna
must extend beyond the plane, where the cancellation isn't complete. And
it's there where it gets its signal to deliver to the load, and where it
can distinguish between the two fields.

Also, any antenna placed in a field in a way that it delivers a
detectable signal to a load alters the field. That's a second potential
problem with your development. However, I believe that the first problem
is enough to invalidate it. If the initial analysis of fields in space
is invalid, and I believe it is, then the extension to transmission
lines is based on a false premise and is questionable.

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. This is a very important and
fundamental point, and I'm glad you brought it up. If you or anyone can
devise an example where a directional antenna can be placed entirely in
a region of zero field and yet detect that the field is made up of
multiple fields, please present it.

I am, of course, assuming that everything in this discussion takes place
in a linear medium.

Roy Lewallen, W7EL

Independence of waves
 

Owen Duffy wrote:

If we were to place a receiving antenna at a point in space to couple
energy from the waves, the amount of energy available from the antenna is
the superposition of the response of the antenna to the wave from each
source. This is quite different to saying that the electric field (or the
magnetic field) at that point is the superposition of the field resulting
from each antenna as is demonstrated by considering the response of
another recieving antenna with different directivity (relative to the two
sources) to the first receiving antenna.

A practical example of this is that an omni directional receiving antenna
may be located at a point where a direct wave and a reflected wave result
in very low received power at the antenna, whereas a directional antenna
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.

Well, sort of. Waves superpose everywhere, including presumably, the
space that an antenna might happen to occupy. But an antenna that
approaches a wavelength in physical length will not see a uniform
pattern along its length. The net effect will certainly be a function
of the orientation of the antenna.

Considering the steady state:

If at some point two or more coherent waves travelling a one direction,
those waves will undergo the same phase change and attenuation with
distance as each other and they must continue in the same direction
(relative to the line), and the combined response in some circuit element
on which they are incident where superposition is valid (eg a circuit
node) will always be as if the two waves had been superposed... but the
response is not due to wave superposition but superposition of the
responses of the circuit element to the waves. It is however convenient,
if not strictly correct to think of the waves as having superposed.

It is certainly true that a probe can perturb the nature of the
environment it is investigating. But it is not accurate to describe
the probe as determining the nature of that environment. If it is
effective, it will simply observe and report nature.

Steady state analysis is sufficiently accurate and appropriate to
analysis of many scenarios, and the convenience extends to simplified
mathematics. It seems that the loose superposition of waves is part of
that convenience, but it is important to remember the underlying
principles and to consciously assess the validity of model
approximations.

Superposition as a convenient model approximation. Of what, I wonder?

A well reasoned and interesting article, Owen. Thank you.

73, Jim AC6XG

Independence of waves
 

Roy Lewallen wrote in news:132fvs4qvp5je04
@corp.supernews.com:

I believe there's at least one basic fallacy in your development.

The problem is that a directional antenna can't be made to take up zero
space. Let's consider a situation where we can have complete

Roy, the type of probe I was considering does take up space, and I
understand your point that therein lies a possible / likely explanation
for its behaviour.

I was thinking along the lines of the superposition occuring within the
directional antenna where segment currents would each be dependent on the
field from each of the sources (and to some extent field from other
segments of itself), and the antenna was where the superposition mainly
occurred. But you are correct that the antenna is of non zero size, and
the segments that I refer to are not all located at a point where the
field strength from each source is equal and opposite.

....

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. This is a very important and
fundamental point, and I'm glad you brought it up. If you or anyone can

I understand the second point.

Extended to transmission lines, I think it means that although we can
make an observation at a single point of V and I, and knowing Zo we can
state whether there are standing waves or not, we cannot tell if that is
the result of more than two travelling waves (unless you take the view
that there is only one wave travelling in each direction, the resultant
of interactions at the ends of the line).

I will think some more about the "actual zero field", but that cannot
suggest that one wave modified the other, they must both pass beyond that
point, each unchanged, mustn't they? If that is so, the waves must be
independent, but the resultant at a point is something separate to each
of the components and doesn't of itself alter the propagation of either
wave.

Owen

Independence of waves
 

On Fri, 20 Apr 2007 00:52:32 GMT, Owen Duffy wrote:

Roy Lewallen wrote in news:132fvs4qvp5je04
:

I believe there's at least one basic fallacy in your development.

The problem is that a directional antenna can't be made to take up zero
space. Let's consider a situation where we can have complete

Roy, the type of probe I was considering does take up space, and I
understand your point that therein lies a possible / likely explanation
for its behaviour.

I was thinking along the lines of the superposition occuring within the
directional antenna where segment currents would each be dependent on the
field from each of the sources (and to some extent field from other
segments of itself), and the antenna was where the superposition mainly
occurred. But you are correct that the antenna is of non zero size, and
the segments that I refer to are not all located at a point where the
field strength from each source is equal and opposite.

Hi Owen,

Why would you think that superposition fails for this?

73's
Richard Clark, KB7QHC

Independence of waves
 

Owen,

It's a pleasure to have a rational discussion. We will both learn from
this, and perhaps some of the readers will also.

Owen Duffy wrote:
Roy Lewallen wrote in news:132fvs4qvp5je04
@corp.supernews.com:

I believe there's at least one basic fallacy in your development.

The problem is that a directional antenna can't be made to take up zero
space. Let's consider a situation where we can have complete

Roy, the type of probe I was considering does take up space, and I
understand your point that therein lies a possible / likely explanation
for its behaviour.

I was thinking along the lines of the superposition occuring within the
directional antenna where segment currents would each be dependent on the
field from each of the sources (and to some extent field from other
segments of itself), and the antenna was where the superposition mainly
occurred. But you are correct that the antenna is of non zero size, and
the segments that I refer to are not all located at a point where the
field strength from each source is equal and opposite.

Yes, each element is seeing a different field from the other. Those
induce different currents in the elements. The sum of those is what
ultimately gives you the output from the antenna. If the two elements
both were at a point of complete wave cancellation, both would produce zero.

. . .

Extended to transmission lines, I think it means that although we can
make an observation at a single point of V and I, and knowing Zo we can
state whether there are standing waves or not, we cannot tell if that is
the result of more than two travelling waves (unless you take the view
that there is only one wave travelling in each direction, the resultant
of interactions at the ends of the line).

Hm, let's think about this a little. In my free space example, we had
two radiators whose fields went through the same point, and those two
radiators were equal in magnitude and out of phase. The sum of the two E
fields was zero and the sum of the H fields was zero, so there was no
field at all where they crossed.

But now let's look at a transmission line with waves created by
reflections from a single source. I believe that there is no point along
the line where both the E and H fields are zero, or where both the
current and the voltage are zero. (Please correct me if I'm wrong about
this.) That's a different situation from the free space, two-radiator
situation I proposed. So in a transmission line, we can find a point of
zero voltage (a "virtual short"), say, but discover that there's current
there. There will be an H field but no E field. And conversely for a
"virtual open". So there is a difference between those points and a
point of no field at all. And there is energy in the E or H field. (This
also occurs in free space where a wave interferes with its reflection or
when waves traveling in opposite directions cross.) Now, if you could
feed two equal canceling waves into a transmission line, going in the
same direction, then you would have truly zero E and H fields, and zero
voltage and current, like the plane bisecting the two free space
antennas. You couldn't tell the difference between that and no waves at
all. But as Keith recently pointed out, superposition of two parallel
equal voltage batteries would show large currents in both directions.
But they would sum to zero, which is what we observe. And as long as the
batteries remain connected, we can never detect those supposed currents.
The two-wave scenario I described is in the same category, I believe.

We can readily concede that there is no field, voltage, current, or
energy beyond the point at which the two canceling waves meet, without
having to invoke any interaction or seeing any violation of energy
conservation. Show me the whole circuit which produces this overlaying
of canceling waves, and I'll show you where every erg of energy from
your source(s) has gone. None of it will be beyond that canceling point.

I will think some more about the "actual zero field", but that cannot
suggest that one wave modified the other, they must both pass beyond that
point, each unchanged, mustn't they?

Absolutely!

If that is so, the waves must be
independent

Absolutely!

, but the resultant at a point is something separate to each
of the components and doesn't of itself alter the propagation of either
wave.

Sorry, I don't fully understand what you've said. But it is true that
the propagation of neither wave is affected in any way by the presence
of the other.

Roy Lewallen, W7EL

Independence of waves
 

On Apr 19, 5:52 pm, Owen Duffy wrote:

....

I will think some more about the "actual zero field", but that cannot
suggest that one wave modified the other, they must both pass beyond that
point, each unchanged, mustn't they? If that is so, the waves must be
independent, but the resultant at a point is something separate to each
of the components and doesn't of itself alter the propagation of either
wave.

Owen

Hi Owen,

I've seen it written, by a well-respected expert on antennas, that
electromagnetic fields may be viewed in either of two different ways.
Are there more than two, other than minor variations on the theme?
I'm not sure. The two I know from that author are that (1) fields are
real physical entities, and (2) that fields are merely mathematical
abstractions to help explain our observations: in the case of
electromagnetic fields, that acceleration of a electron results in
sympathetic motion of free electrons throughout the universe. It
seems to me that in either of those cases, the result of fields from
multiple sources, in a linear medium, is always the sum of the fields
from each of the sources independently. That is practically the
definition of linearity, is it not? It does not depend on us putting
something there to detect the field, or to test if the mathematical
model is correct. Certainly if we were watching waves in water, we
could see lines along which there was cancellation, where the water
would not be moving. But even if the fields are merely a mathematical
abstraction, then I still know where they sum to zero. The utility of
a mathematical abstraction to practical folk, of course, is that it
can accurately predict the behaviour in the physical world. So if
fields are just an abstraction, I can still use them to predict where
I can place a wire that's in the sphere of influence of two or more
radiating sources, and have the electrons in that wire unaffected by
the sources (because those theoretical fields canceled there). On the
other hand, if my field theory is describing something physical, if
fields are entities apart from (but inexorably linked to) the motion
of electrons, then it seems that whether we are able to observe those
fields directly or not, their cancellation is real. That does assume
that we've correctly deduced the nature of those fields, I suppose, so
that our model does say what's going on in that physical medium we can
only probe with our free electrons.


Cheers,
Tom

Independence of waves
 

K7ITM wrote:
. . .
I've seen it written, by a well-respected expert on antennas, that
electromagnetic fields may be viewed in either of two different ways.
Are there more than two, other than minor variations on the theme?
I'm not sure. The two I know from that author are that (1) fields are
real physical entities, and (2) that fields are merely mathematical
abstractions to help explain our observations: in the case of
electromagnetic fields, that acceleration of a electron results in
sympathetic motion of free electrons throughout the universe. . .
. . .

Throughout my time at the USAF technical school, I was frustrated by the
hand-waving of the instructors when the topic was electromagnetic fields
(and many other topics, for that matter). It was obvious that they
really had a very poor grasp of the subject(s). So on the very first day
of my first college semester of fields, I asked the professor, "What is
an electromagnetic field?" His response: "Electromagnetic fields are
mathematical models we use to help us understand phenomena we observe."
The professor was Carl T.A. Johnk. I have his textbook _Engineering
Electromagnetic Fields and Waves_, which was in draft manuscript form at
the time I took the course. The first sentence in section 1-1 on page 1
is "A field is taken to mean a mathematical function of space and time."

Roy Lewallen, W7EL

Independence of waves
 

Roy Lewallen wrote in
:

Owen,

It's a pleasure to have a rational discussion. We will both learn from
this, and perhaps some of the readers will also.

Thanks Roy.


Owen Duffy wrote:
....

Extended to transmission lines, I think it means that although we can
make an observation at a single point of V and I, and knowing Zo we
can state whether there are standing waves or not, we cannot tell if
that is the result of more than two travelling waves (unless you take
the view that there is only one wave travelling in each direction,
the resultant of interactions at the ends of the line).

Hm, let's think about this a little. In my free space example, we had
two radiators whose fields went through the same point, and those two
radiators were equal in magnitude and out of phase. The sum of the two
E fields was zero and the sum of the H fields was zero, so there was
no field at all where they crossed.

But now let's look at a transmission line with waves created by
reflections from a single source. I believe that there is no point
along the line where both the E and H fields are zero, or where both
the current and the voltage are zero. (Please correct me if I'm wrong
about this.) That's a different situation from the free space,

Yes, I agree with you, and I think the key factor is that waves are only
free to travel in two directions, and if multiple coherent waves can
travel in the same direction, they are colinear.

two-radiator situation I proposed. So in a transmission line, we can
find a point of zero voltage (a "virtual short"), say, but discover
that there's current there. There will be an H field but no E field.
And conversely for a "virtual open". So there is a difference between
those points and a point of no field at all. And there is energy in
the E or H field. (This also occurs in free space where a wave
interferes with its reflection or when waves traveling in opposite
directions cross.) Now, if you could feed two equal canceling waves
into a transmission line, going in the same direction, then you would
have truly zero E and H fields, and zero voltage and current, like the
plane bisecting the two free space antennas. You couldn't tell the

But is it possible to inject two coherent waves travelling independently
in the same direction? Could I not legitimately resolve the attempt at a
circuit node (line end node) of two coherent sources to drive the line to
be the superposition of the voltages and curents of each to effectively
resolve to a single phasor voltage and associated phasor current at that
node, and then the conditions on the line would be such as to comply with
the boundary conditions at that line end node. Though I have mentioned
phasors which implies the steady state, this should be true in general
using v(t) and i(t), just the maths is more complex.

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.

So, whilst it may be held by some that there is re-reflected energy at
the source end of a transmission line in certain scenarios, a second
independent forward wave component to track, has not the forward wave
just changed to a new value to comply with boundary conditions in
response to a change in the source V/I characteristic when the reflection
arrived at the source end of the line? I know that analysis of either
scenario will yield the same result, but one may be more complex, and it
is questionable whether the two (or more) forward wave components really
exist independently.

....
I will think some more about the "actual zero field", but that cannot
suggest that one wave modified the other, they must both pass beyond
that point, each unchanged, mustn't they?

Absolutely!

If that is so, the waves must be
independent

Absolutely!

, but the resultant at a point is something separate to each
of the components and doesn't of itself alter the propagation of
either wave.

Sorry, I don't fully understand what you've said. But it is true that
the propagation of neither wave is affected in any way by the presence
of the other.

I am saying that resolution of the fields of two independent waves at a
point in free space to a resultant is not a wave itself, it cannot be
represented as a wave, and it does not of itself alter the propagation of
either wave. It may be useful in predicting the influence of the two
waves on something at that point, but nowhere else.

Having thought through to the last sentence, I think I am agreeing with
your statement about free space interference "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."

And we haven't mentioned power, not once!

Owen

Independence of waves
 

Richard Clark wrote in
:
....
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.

Owen

Independence of waves
 

K7ITM wrote in
oups.com:

On Apr 19, 5:52 pm, Owen Duffy wrote:

...

I will think some more about the "actual zero field", but that cannot
suggest that one wave modified the other, they must both pass beyond
that point, each unchanged, mustn't they? If that is so, the waves
must be independent, but the resultant at a point is something
separate to each of the components and doesn't of itself alter the
propagation of either wave.

Owen

Hi Owen,

I've seen it written, by a well-respected expert on antennas, that
electromagnetic fields may be viewed in either of two different ways.
Are there more than two, other than minor variations on the theme?
I'm not sure. The two I know from that author are that (1) fields are
real physical entities, and (2) that fields are merely mathematical
abstractions to help explain our observations: in the case of
electromagnetic fields, that acceleration of a electron results in
sympathetic motion of free electrons throughout the universe. It
seems to me that in either of those cases, the result of fields from
multiple sources, in a linear medium, is always the sum of the fields
from each of the sources independently. That is practically the
definition of linearity, is it not? It does not depend on us putting
something there to detect the field, or to test if the mathematical
model is correct. Certainly if we were watching waves in water, we
could see lines along which there was cancellation, where the water
would not be moving. But even if the fields are merely a mathematical
abstraction, then I still know where they sum to zero. The utility of
a mathematical abstraction to practical folk, of course, is that it
can accurately predict the behaviour in the physical world. So if
fields are just an abstraction, I can still use them to predict where
I can place a wire that's in the sphere of influence of two or more
radiating sources, and have the electrons in that wire unaffected by
the sources (because those theoretical fields canceled there). On the
other hand, if my field theory is describing something physical, if
fields are entities apart from (but inexorably linked to) the motion
of electrons, then it seems that whether we are able to observe those
fields directly or not, their cancellation is real. That does assume
that we've correctly deduced the nature of those fields, I suppose, so
that our model does say what's going on in that physical medium we can
only probe with our free electrons.


Thanks Tom.

All noted, and it seems of all wave types, EM waves are most difficult to
prove the link between mathematical models and the real world.

To some extent, some of the muddy water is about whether waves superpose
(whatever that means), or whether the fields of a wave superpose at a point
and those superposed fields do not imply anything about fields or waves at
any other points.

If that is the case, it comes back to defining what waves means.

Owen

Independence of waves
 

On Fri, 20 Apr 2007 05:40:13 GMT, Owen Duffy wrote:

Richard Clark wrote in
:
...
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.

Hi Owen,

I presume all of this flows from your statement:
A practical example of this is that an omni directional receiving antenna
may be located at a point where a direct wave and a reflected wave result
in very low received power at the antenna, whereas a directional antenna
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.

As Roy did not quote any of your material, I must presume this. Am I
correct?

73's
Richard Clark, KB7QHC

Independence of waves
 

Richard Clark wrote in
:

On Fri, 20 Apr 2007 05:40:13 GMT, Owen Duffy wrote:

Richard Clark wrote in
m:
...
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.

Hi Owen,

I presume all of this flows from your statement:
A practical example of this is that an omni directional receiving
antenna may be located at a point where a direct wave and a
reflected wave result in very low received power at the antenna,
whereas a directional antenna 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.

As Roy did not quote any of your material, I must presume this. Am I
correct?

Yes

Independence of waves
 

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.

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).

73's
Richard Clark, KB7QHC

Independence of waves
 

On Fri, 20 Apr 2007 06:49:46 GMT, Owen Duffy wrote:

Richard Clark wrote in
A practical example of this is that an omni directional receiving
antenna may be located at a point where a direct wave and a
reflected wave result in very low received power at the antenna,
whereas a directional antenna 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.

As Roy did not quote any of your material, I must presume this. Am I
correct?

Yes

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?

73's
Richard Clark, KB7QHC

Independence of waves
 

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?
Alan

Independence of waves
 

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. That is, use
any number of elements you want, oriented and phased any way you want,
and as long as all elements lie entirely on the plane, I don't think you
can make it favor the signal from one of the radiators over the other. I
believe you'll find this same problem with any region of total wave
cancellation. I don't have any rigorous proof of this, just intuition
from observing the symmetry, and would be glad to see an example which
would prove me wrong. (It might reveal a whole new class of directional
antennas! Maybe one of Art's Gaussian marvels would do it?) 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.

Roy Lewallen, W7EL

Independence of waves
 

Owen Duffy wrote:

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

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. 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. The wave going down the third line is exactly
like before, but reversed in phase.

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. 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. There's no problem in accounting for all the power
leaving the generators and being, in this case, completely dissipated in
their source resistances, without the need for assuming any wave
interaction, any waves of power or energy, or assigning some amount of
power or energy to each of the two supposed waves.

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.

Could I not legitimately resolve the attempt at a
circuit node (line end node) of two coherent sources to drive the line to
be the superposition of the voltages and curents of each to effectively
resolve to a single phasor voltage and associated phasor current at that
node, and then the conditions on the line would be such as to comply with
the boundary conditions at that line end node. Though I have mentioned
phasors which implies the steady state, this should be true in general
using v(t) and i(t), just the maths is more complex.

I'm afraid you've lost me again, but I think maybe you're describing
something similar to the example I just presented.

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.

Yes, as in the example, there is no difference between no waves at all
and two overlaid canceling traveling waves. They are the same thing.

So, whilst it may be held by some that there is re-reflected energy at
the source end of a transmission line in certain scenarios, a second
independent forward wave component to track, has not the forward wave
just changed to a new value to comply with boundary conditions in
response to a change in the source V/I characteristic when the reflection
arrived at the source end of the line?

I maintain that no wave (that is, V or I wave) changes due to another.
While alternative approaches might give correct answers in some cases or
perhaps even every case, the approach I use has proved to adequately
explain all observed phenomena for over a century. So I'll stick with it.

I know that analysis of either
scenario will yield the same result, but one may be more complex, and it
is questionable whether the two (or more) forward wave components really
exist independently.

They either exist independently or not at all.

I am saying that resolution of the fields of two independent waves at a
point in free space to a resultant is not a wave itself, it cannot be
represented as a wave, and it does not of itself alter the propagation of
either wave. It may be useful in predicting the influence of the two
waves on something at that point, but nowhere else.

I agree with that.

Having thought through to the last sentence, I think I am agreeing with
your statement about free space interference "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."

And we haven't mentioned power, not once!

I did cringe at your mention of "re-reflected energy", which would be
energy in motion. But at least we don't have power in motion. As soon as
that comes into a discussion, it invariably quickly enters the realm of
junk science in a desperate attempt to get the numbers to add up -- or
subtract, as need be. And I've learned to run, not walk, away from
those. (They kinda remind me of overheard conversations at the UFO
museum in Roswell. But that's another story.)

Roy Lewallen, W7EL

Independence of waves
 

Owen Duffy wrote:
But is it possible to inject two coherent waves travelling independently
in the same direction? Could I not legitimately resolve the attempt at a
circuit node (line end node) of two coherent sources to drive the line to
be the superposition of the voltages and curents of each to effectively
resolve to a single phasor voltage and associated phasor current at that
node, and then the conditions on the line would be such as to comply with
the boundary conditions at that line end node. Though I have mentioned
phasors which implies the steady state, this should be true in general
using v(t) and i(t), just the maths is more complex.

Two coherent waves traveling independently in the same
direction in a transmission line are collinear and
interfere in a permanent manner, i.e. they interact. Why
this is so is easy to understand when one superposes the
two E-fields and the two H-fields. The total E-field changes
by the same percentage as does the H-field. In an EM wave,
ExB is proportional to the joules/sec associated with the
wave.

When two coherent EM
waves are superposed while traveling in the same direction
in a transmission line, the total ExB magnitude decreases
if the interference is destructive and increases if the
interference is constructive. A destructive interference
event gives up energy to a constructive interference event
somewhere else. That is what changes the direction and
magnitude of the reflected wave at a Z0-match point. If
the interference is destructive toward the source, the
"extra" energy will be redistributed in the direction of
the load as constructive interference energy.

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.

Thanks Owen, you have just described coherent wave interaction
in a transmission line.

So, whilst it may be held by some that there is re-reflected energy at
the source end of a transmission line in certain scenarios, a second
independent forward wave component to track, has not the forward wave
just changed to a new value to comply with boundary conditions in
response to a change in the source V/I characteristic when the reflection
arrived at the source end of the line?

Yes, wave interaction is permanent. Canceled waves cease to
exist in their original direction of travel in the transmission
line.

And we haven't mentioned power, not once!

Every EM wave possesses an E-field and an H-field. The cross
product of the RMS value of those fields is proportional to
average power. One can avoid mentioning power, but one cannot
run away from the fact that the power associated with each EM
wave is ExB. If Vref and Iref exist, then the joules/sec in
Eref x Href has to exist. The fields cannot be separated from
the energy necessary for them to exist. Such is the basic
nature of EM waves.
--
73, Cecil http://www.w5dxp.com

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

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