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