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