Dave wrote:
"Cecil Moore" wrote:
Can one reverse the superposition whose result is
zero to recover the original two component waves?
If not, isn't that proof that the two original
component waves interacted?

no, because you have done a non-linear operation on them by converting to
powers. obviously at the start 'a1' and 'a2' are separate.

If V^2/Z0 and I^2*R cannot be reverse superposed
in reality, doesn't that imply than neither can V
and I be reverse superposed in reality?

Doesn't a real world EM wave require ExB joules/sec
for it to exist and to have an associated voltage
and current?
--
73, Cecil http://www.w5dxp.com

Dave wrote:
i should expand a bit more. all your equations above have done is shown
that at the point where you are doing your analysis s11(a1) and s12(a2),
which add up to 0... also produce a net 0 power at that point. this is as
expected for destructive interference AT THAT POINT. as such your s
parameter analysis is insufficient to separate the individual components
after you combine them into a power. however, at the begining they are
obviously separate waves since you have represented them with separate input
values, and given a linear transfer function for your point on the wire, or
in space, they can always be kept separate. it is only your act of
calculating the power at that point that combines them.

True, but we also know that the power is zero at every point
between the Z0-match and the source. That gives us an
infinite number of points with which to work and we still
cannot reverse superpose the two original superposed waves.
--
73, Cecil http://www.w5dxp.com

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

Roy Lewallen wrote:

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

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

Roy Lewallen, W7EL

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

Cheers,
Tom

Tom,

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

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

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

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

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

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

73,
Gene
W4SZ

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

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

Cheers,
Tom

Dave wrote:
"Cecil Moore" wrote in message
. . .

I'm very sorry to see that Cecil has arrived to divert what was an
interesting and informative discussion to yet another one of his endless
argumentative junk science threads. Oh, well, it was nice while it lasted.

Roy Lewallen, W7EL

K7ITM wrote:

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

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

And my thanks to both of you.

Roy Lewallen, W7EL

"Dave" wrote in news:ZPmWh.759$dM1.190@trndny07:


"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

Dave, I was continuing in the assumed context of coherent sources.

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.

Yes, I understand.... Thanks.

Chuck wrote in
:

....
Seems somewhat tautological then that
the probe cannot be designed to
distinguish between the two antennas.

If the assumption so constrains the
probe to fatal infirmities under any
circumstances, then the observance of
failure in a particular circumstance is
void of information.

Chuck, that is emerging from the subsequent discussion.

Owen

On 21 Apr, 15:31, Owen Duffy wrote:
Chuck wrote :

...

Seems somewhat tautological then that
the probe cannot be designed to
distinguish between the two antennas.

If the assumption so constrains the
probe to fatal infirmities under any
circumstances, then the observance of
failure in a particular circumstance is
void of information.

Chuck, that is emerging from the subsequent discussion.

Owen

Waves pass thru each other without interaction!
If intra action occurred then multiple radio conversations at the same
time could not occur.
Why 50 odd posts to state the obvious?

Roy Lewallen wrote:
I'm very sorry to see that Cecil has arrived to divert what was an
interesting and informative discussion to yet another one of his endless
argumentative junk science threads. Oh, well, it was nice while it lasted.

This from the person who used standing-wave current to
measure the phase shift through a loading coil knowing
all the while that standing-wave current has an
unvarying phase. I cannot think of any worse junk
science than trying to hoodwink the uninitiated.
--
73, Cecil http://www.w5dxp.com

Owen,

These examples are quite different. Experiments in one cannot be used to
make an inference in the other. One is electric flow, the other is
photons. The physics are not even close to the same. Which one do you
want to talk about?

- Dan

Owen Duffy wrote:
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