I was browsing through Antennas by Kraus, second ed., looking for something
that might explain how two antennas separated by a distance D would have a
resolution as the same as an antenna of size D, and hit upon some methods
for computing radiation patterns. I'm not all that familiar with the
methodology, but think it might be worthwhile exploring.

I'm not all that knowledgeable about antenna theory, but was stumped by the
introduction of antenna phase. He computes the patterns for several pairs of
isotropic antennas separated by a distance d. 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*.

Of course, maybe my statement above about D is simpler to *prove* (not hand
wave) than wading through this material.

* I just noticed section 3-17 has some material on phase. Maybe that'll work.

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

Web Page: home.earthlink.net/~mtnviews

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

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

Web Page: home.earthlink.net/~mtnviews

On Sat, 25 Mar 2006 01:53:24 GMT, "W. Watson"
wrote:

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.

Hi Wayne,

The two receivers/antennas is called "synthetic aperture." You can
observe the same thing with one antenna that is moving, we commonly
call it "picket fencing." This effect is due to reflections and
direct signals interfering constructively and destructively as you
move through the interference field. The math for that alone is found
in "Fresnel loss."

The Young double slit IS the proof in that it contains all the math
you need. It contains two transcendental operations (sin or cos) as
many thetas as there are phases and distances, some magnitude
information, and the result pops out at you.

In fact, the math is all the same for all of these effects.

73's
Richard Clark, KB7QHC

On Fri, 24 Mar 2006 12:07:31 -0800, Richard Clark
wrote:


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.



S N I P



73's
Richard Clark, KB7QHC


What's frightening is I think I understood all that....

Thanks for the explanation.


--
73 for now
Buck
N4PGW

Richard Clark wrote:

On Sat, 25 Mar 2006 01:53:24 GMT, "W. Watson"
wrote:


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.


Hi Wayne,

The two receivers/antennas is called "synthetic aperture." You can
observe the same thing with one antenna that is moving, we commonly
call it "picket fencing." This effect is due to reflections and
direct signals interfering constructively and destructively as you
move through the interference field. The math for that alone is found
in "Fresnel loss."

The Young double slit IS the proof in that it contains all the math
you need. It contains two transcendental operations (sin or cos) as
many thetas as there are phases and distances, some magnitude
information, and the result pops out at you.

In fact, the math is all the same for all of these effects.

73's
Richard Clark, KB7QHC
My *old* physics book doesn't give the proof, but Hecht's Optics does.
Whoops. It's in Waves by Crawford. No mention though that is the proof of
this particular fact. Hecht mentions the experiment, and it may be proven in
subsequent sections using Fourier methods. Waves does it the old fashioned
way. Accepting your comment then, I can read through it with a little more
attention. Thanks.


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
--
"No, Groucho is not my real name. I am only
breaking it in fora friend." -- Groucho Marx

Web Page: home.earthlink.net/~mtnviews

Richard Clark wrote in
:

On Sat, 25 Mar 2006 01:53:24 GMT, "W. Watson"
wrote:

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.

Hi Wayne,

The two receivers/antennas is called "synthetic aperture." You can
observe the same thing with one antenna that is moving, we commonly
call it "picket fencing." This effect is due to reflections and
direct signals interfering constructively and destructively as you
move through the interference field. The math for that alone is found
in "Fresnel loss."

The Young double slit IS the proof in that it contains all the math
you need. It contains two transcendental operations (sin or cos) as
many thetas as there are phases and distances, some magnitude
information, and the result pops out at you.

In fact, the math is all the same for all of these effects.

It gets a bit interesting to implement, though, if the antennas are 2000
miles apart!

--
Dave Oldridge+
ICQ 1800667

On Sun, 26 Mar 2006 03:48:19 GMT, Dave Oldridge
wrote:

It gets a bit interesting to implement, though, if the antennas are 2000
miles apart!

Hi Dave,

If you mean by interesting, SETI.

73's
Richard Clark, KB7QHC

Dear Dave Oldridge (no call sign given):

Interesting? Yes, but it has been done in radio astronomy and many years
ago. Receivers were well over 10 Mm apart and signals were recorded along
with time signals.

73 Mac N8TT

--
J. Mc Laughlin; Michigan U.S.A.
Home:

"Dave Oldridge" wrote in message

snip
It gets a bit interesting to implement, though, if the antennas are 2000
miles apart!

--
Dave Oldridge

Wayne,

I don't know if the others answered your question, but be careful. Your
original post says:
"...two antennas separated by a distance D would have a resolution as
the same as an antenna of size D,..."

*Resolution* is key here, not, as you state later,: "..can act as though
they are a single receiver of size D"

"Resolution" vs. "act" may be ambiguous.

I'll take a stab.

Think of water waves. Picture some very nice, regular waves. All the same
size, shape and wavelength. This is a good analogy for RF.
Now, put two *vertical* antennas in the pool (come-on in the water's fine).
From the top they just look like dots right?

First, position them so they are in the same line with the wave front -- so
each wave hits both at precisely the same time. (a broad-side array)

When like this, each antenna is receiving the same *PHASE* signal. The
voltage goes up and it goes down at the same time in both antennas.

Now, slightly rotate this array so one of the antennas gets its waves a bit
earlier. It will receive an *advanced * phase. The further apart these two
antennas are, the more sensitive it will be to a small angle of rotation.
Making your "D" bigger will make the antenna array "see" more phase shift
for the same small angle (hat it is turned, right?

Also, if the signal comes from a slightly different direction, the same
thing happens and therefore it can *RESOLVE* direction better with a larger
"D".

Help any?

73, Steve, K9DCI














"W. Watson" wrote in message
nk.net...
Richard Clark wrote:

On Sat, 25 Mar 2006 01:53:24 GMT, "W. Watson"
wrote:


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.


Hi Wayne,

The two receivers/antennas is called "synthetic aperture." You can
observe the same thing with one antenna that is moving, we commonly
call it "picket fencing." This effect is due to reflections and
direct signals interfering constructively and destructively as you
move through the interference field. The math for that alone is found
in "Fresnel loss."

The Young double slit IS the proof in that it contains all the math
you need. It contains two transcendental operations (sin or cos) as
many thetas as there are phases and distances, some magnitude
information, and the result pops out at you.

In fact, the math is all the same for all of these effects.

73's
Richard Clark, KB7QHC
My *old* physics book doesn't give the proof, but Hecht's Optics does.
Whoops. It's in Waves by Crawford. No mention though that is the proof of
this particular fact. Hecht mentions the experiment, and it may be proven
in
subsequent sections using Fourier methods. Waves does it the old fashioned
way. Accepting your comment then, I can read through it with a little more
attention. Thanks.


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
--
"No, Groucho is not my real name. I am only
breaking it in fora friend." -- Groucho Marx

Web Page: home.earthlink.net/~mtnviews