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Re: [TowerTalk] Takeoff Angles and Non-Reciprocal Propagation

To: towertalk@contesting.com
Subject: Re: [TowerTalk] Takeoff Angles and Non-Reciprocal Propagation
From: "Dan Zimmerman N3OX" <n3ox@n3ox.net>
Date: Sat, 3 Nov 2007 15:15:26 -0400
List-post: <mailto:towertalk@contesting.com>
> It simply
>occurred to me that my suggestion for what might be happening to signals
>over asymmetric terrain might be similar to what happens with a
>circulator, where energy going in one direction takes one path while
>energy coming back takes another, keeping in mind I'm only talking about
>the portion of the path between the originating station and the
>significant terrain in front of it.

I've had my breakfast and coffee and plenty of time after to think
about it and I'm still left muttering "time reversal symmetry"

The best I can do right now is this:
http://uw.physics.wisc.edu/~walker/phys325/TimeReversal.pdf

The demonstration of reciprocity ends in equation 9, showing that the
wave coming in from the left (1) and exiting the right (t) gives the
same fraction of transmission across the barrier the as the wave
entering the right (1) and leaving the left (t').  If you transmit 1
and the DX station gets t, reciprocity says that if the DX station
transmits 1, you get t.  You transmit 100W they get, say, 20
microwatts... they transmit 100W, you get 20 microwatts.

We can extend it to more complicated diffraction/interference
structures than a thin film, but the result will be the same.

If you have polarization rotation that always rotates the wave
clockwise independent of the direction of propagation, this breaks the
time reversal symmetry  and you CAN get nonreciprocal propagation, but
the equations of simple DIFFRACTION have time reversal symmetry.

Maybe not fully satisfying...  I'll keep thinking while I do some car work.



73,
Dan
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