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

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

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

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

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

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

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

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

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

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