Timo Nieminen wrote:
On Thu, 10 Jul 2003, W5DXP wrote:
The devil is in the details. Here's what I have said over on
rec.radio.amateur.antenna that has stirred up a hornet's nest.

In a system where all reflections toward the source are eliminated at an impedance
discontinuity by wave cancellation (destructive interference), the two rearward-
traveling reflected voltages are equal in magnitude and 180 degrees out of phase
with each other. Same for the two rearward-traveling reflected currents. Therefore,
on the source side of the impedance discontinuity, the rearward-traveling
voltage and current both go to zero in the direction of the source. Waves can be
destroyed but the energy in those waves cannot be destroyed.

The destructive interference in the direction of the source supports constructive
interference in the direction of the load and satisfies the (V1+V2)^2/Z0 power
requirements of the two in-phase superposed voltages on the load side. The
destructive interference becoming constructive interference in the opposite
direction can be thought of as an energy reflection from the wave cancellation
event.

In other words, the disappearance of two waves during a wave cancellation event
can result in reflected energy coherent with those two canceled waves. I don't
find that in the literature anywhere. Do you know of a reference?

I'm curious as to what kind of objections people had. It all makes perfect
sense to me.

As for references, Stratton "Electromagnetic theory" covers transmission
through and reflection by a dielectric layer, and points out that it is
exactly the same for transmission lines, but just lets the math do the
talking, so doesn't go into the detail that you do above. Don't know of
any other book that goes into more detail, but I expect that a lot of EE
books must.

In any case, it's a simple enough exercise to calculate the reflection,
transmission, and phase change due to an impedance discontinuity, either
for plane waves incident on a dielectric interface, or for signals in a
transmission line. Then just look at two waves incident from opposite
directions. It's nice that, just using the boundary conditions for the
amplitudes of the waves, one gets conservation of energy as a result. It
might be an interesting exercise to derive the boundary conditions for the
reflection/transmission starting with conservation of energy.

Thanks Timo, I guess I may not be crazy after all. I hope you won't mind
me cross-posting your wisdom to rec.radio.amateur.antenna.
--
73, Cecil http://www.qsl.net/w5dxp



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