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Re: [TowerTalk] Diffraction Reciprocity

To: towertalk@contesting.com
Subject: Re: [TowerTalk] Diffraction Reciprocity
From: "Ethan Miller K8GU" <ethan@k8gu.com>
Date: Mon, 5 Nov 2007 12:06:40 -0600
List-post: <mailto:towertalk@contesting.com>
I'm not a TT subscriber; but, I read it from time to time.  This may
or may not come through in a timely manner.

If the anechoic chamber experiment is helpful for your understanding
of the physics, do it.  But, the reciprocity of diffraction is a
pretty well-established concept in physics.

You can arrive at this conclusion through a variety of means, whether
it be the Lorentz reciprocity theorem itself or via Huygen's principle
(which is what AI4MI essentially did, wittingly or unwittingly) or
simply the fact that diffraction theory is often used to derive
analytical expressions for antennas.  It's messy; but, fortunately the
proofs have been done.  If you're interested, you might look at
"Principles of Optics" by Born and Wolf or one of the many other
optics and electromagnetics books that cover such topics.  Given what
we know about reciprocal networks, ask yourself, "Why wouldn't
diffraction be reciprocal?"

As N6RK rightfully observed, we must carefully distinguish the
contributions of the ionosphere and the "local" environment.  I've
mentioned this on CQ-Contest at some time in the last year; but, I'll
point it out again here with some further insight:

Check out the book "Radio Waves in the Ionosphere: The Mathematical
Theory of the Reflection of Radio Waves from Stratified Ionised
Layers" by K. G. Budden (Cambridge 1966).  Chapter 23 (of this
edition) is simply titled "Reciprocity."  According to Budden,
Goubau's theorem may be concisely stated the following way:  "For any
aerial system at A it is
always possible to construct at least one aerial system at B so that
there is reciprocity between the terminals of the two aerials."  In
other words, reciprocity between two points is always possible, but
not guaranteed for any given pair of antennas at those points.

There is one curious statement that I don't completely understand
(it's on page 508, the second sentence in 23.5):  "For communication
in two opposite directions there is never complete reciprocity, but
Goubau's reciprocity theorem is always true."  I'll need to digest
that further since I just noticed it while composing this note.
Budden continues this discussion...but, I haven't read it and it
doesn't belong on the reflector.

On the topic of high-band propagation oddities at the bottom of the
cycle:  these paths may exist near the top of the cycle, too; but, no
one notices that they're there because other paths are dominant.
Crazy stuff happens to push the plasma around...sporadic-E, equatorial
spread-F, TID's, and probably a bunch of things we haven't even
discovered yet.

So, what's the moral of the story?  The ionosphere (and indeed the
MF/HF environment) is truly the wiliest of mistresses.  For most of
us, financial, domestic, and practical (eg space and time) constraints
will continue to trump many of physical constraints.  To summarize
N2EA, put up some antennas and have fun.  If you're building a
competitive contest station, know your audience(s) and cater to them.
The models (HFTA, NEC, etc) aren't perfect in every respect; but,
engineering is the art of knowing when and how to make approximations
with science in order to harness it efficiently and effectively.  (By
the way, approximation is a dying art thanks to the
microprocessor...but, this is not a forum for my views on math,
science, and engineering education!)

73,

--Ethan, K8GU/9.
http://www.k8gu.com/
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