Hello, Richard.

Well, you certainly got the gist, without seeing the book, of the underlying
problem I was having with phase, time, and distance. That was a helpful
paradigm shift for me. I leanred a new word in the process, fungible. It was
well used. I had thought about the sense of all this with respect to
direction finding, but you added some extras.

Ultimately, I'm trying to comprehend, via a proof, that two receivers
separated by a distance D can act as though they are a single receiver of
size D. Perhaps it can be done by simply considering the Young double slit
experiment. It bothers me that the idea is passed along without ever proving
it. Maybe the proof is trivial.

Richard Clark wrote:

On Fri, 24 Mar 2006 18:48:28 GMT, "W. Watson"
wrote:


There are several cases, which
involve fixed or differences in phase and amplitude he considers, Chap. 4,
sect. 4.2. Can anyone make the idea of phase dependency for an antenna,
particularly an isotropic antenna (or whatever), a little more practical or
real? Early on he talks about the phase delta being a function of (theta,
phi) according to a typical Kraus 3-D view of this material. A nice
abstraction, but I need something a little more concrete*.


Hi Wayne,

Not having that reference in front of me, I will wing what appears to
be the topic at hand.

When you have two detectors that are resolving one source, or when you
have two sources that are impinging on one detector; then you have the
makings of triangulation. I hope that much of the 3-nature of this
problem reduced to its simplest terms is apparent.

For the sake of discussion, we can call them X, Y, and A; where the
pairing of the X-Y are the two that are similar and A is the odd one
out.

The distance XA can be expressed in meters, phase, or time. Similarly
the distance YA can be expressed in meters, phase, or time. Going
further, the distance XY can be expressed in meters, phase, or time.
The units of meters, phase, and time are all fungible. That means
they substitute equally as long as you take care to use the same units
throughout. Whenever you read distance, think phase instead, or
convert to phase. Even though they are the same, meters or seconds
just aren't as useful in our discussion.

When you mathematically combine these distances, you can precisely
described the signal strength at any point (including those points not
described as A, X, or Y).

Take a simple DC example of X being a positive charge of 1, and Y
being a negative charge of 1. If A lies on a line that is between the
two, and is perpendicular to their axis, then A will sense a
difference of 0. If you move A out of this perpendicular plane, it
will encounter non-zero fields because the contribution of the two
charges do not cancel fully. This moving of A throughout space will
map out what is called "the dipole moment" which looks like a figure
8.

Extend this analogy to the RF by simply stating that X and Y are 180°
out of phase. In the first position of A, it will still resolve a 0
difference (the two paths XA and YA are equal by definition and the
phase is bucking - net 0 signal). Move A out of its perpendicular
plane and the two path distances will be non equal. A small signal
will emerge from the combination of the two XY signals.

Push this analogy a little more by slightly changing the phase of
either X or Y. A at its original position will now perceive two out
of phase signals, but their phase difference will yield a small signal
response.

If you move A to the correct spot (out of the plane of
perpendicularity), you may find that null again. Thus THAT null
occupies a region that satisfies the combination of a resultant phase
of 180°. This is accomplished by shifting the
XA distance - YA distance
expressed in terms of phase such that when added to the XY phase
yields 180°.

This last operation is called Beam Steering, you moved the null in
3-space using only phase shift at one X or Y. You could have as
easily moved X or Y too to accomplish nearly the same result. You can
also steer the point of maximum (the anti-null) - and did. If you
flip the roles of the source and detector, you have source location.

You can also achieve some steering through amplitude shifts of XY, but
this is bringing more complexity to the topic. Suffice it to say that
this math of combining amplitudes and phases for Beam Steering or
source triangulation applies equally to source/detectors as it does to
detector/sources.

With two sources/detectors XY, there are ambiguous results. The nulls
occupy two regions, not one. If you add a non co-planar third
source/detector XYZ, then you can resolve without ambiguity (or
perhaps less). This is still a matter of combining distances to A in
terms of meters, time, or phase.

The Method of Moments used by NEC is simply (ironically, more complex)
the substitution of many, many sources in the place of segments of an
antenna's structure. That is, a MOM dipole is composed of perhaps a
dozen infinitesimal radiators in a line, with each having a phase
shifted signal of a different amplitude. Their combination at a
distance gives us that "Dipole Moment" (figure 8 field) that is so
familiar. The utility of the MOM is you can shape up to several
hundred or thousand sources into a complex geometry to present a more
complex field resultant. NEC is merely a phase/distance/time
combining engine that moves A throughout space to build a response
map.

To this last point, it reveals a truism:
The entire radiator emits, not just a portion of it.

The "entire" radiator consists of the antenna, its counterpoise, its
loading, and sometimes its feedline.

Another truism arises:
The entire radiator emits in all directions (think spherically).

Remote detectors are illuminated by a radiator no matter where they
might lie. That they may not sense this illumination is merely the
consequence of overlapping, bucking phases.

One might be tempted to say that for the classic dipole, there is no
radiation off the ends. The second truism negates that. You need
only flip the phase of one half of the dipole to make it endfire (yes,
easier said than done). In the first, classic sense both sides
illuminate far colinear objects destructively. In the second sense
both sides illuminate far colinear objects constructively.

73's
Richard Clark, KB7QHC



Wayne T. Watson (Watson Adventures, Prop., Nevada City, CA)
(121.015 Deg. W, 39.262 Deg. N) GMT-8 hr std. time)
Obz Site: 39° 15' 7" N, 121° 2' 32" W, 2700 feet
--
"Nature invented space so that everything didn't
have to happen at Princeton." -- Martin Rees,
Britain's Royal Astronomer, in a lecture at Princeton

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