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

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

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