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