Hi Roy,

I have read many of your articles, and I have no doubt you are correct.

However, in the ideal case, specifically in the limit as the wire
diameter goes to zero, the current perturbation from mutual inductance
vanishes. (The mutual inductance does not vanish, only its impact on
current distribution.)

I just spent a few minutes playing around with EZNEC 3, and I was able
to achieve a null of -52 dBi (-57 dBmax) for two half-wave elements,
with nominal 90 degree spacing and 90 degree phasing. The wire size was
as small as possible. This null was in the symmetry plane and directly
in the anti-end-fire direction of course. I expect with more
computational precision, and perhaps fine tuning frequencies and
dimensions this null could be driven farther. The reported current
imbalance was a maximum of 0.2%, mid-way between the center and the ends
of the wires. The phase imbalance between the wires was a maximum of 0.2
degrees.

I am not trying to say this is practical. I was just pointing out the
Art's use of polygons and canceling phasors was not particularly unique.

We have since learned that what Art is trying to accomplish is to
eliminate all radiation in the back hemisphere. The cardioid example is
obviously moot for his quest.

73,
Gene
W4SZ

Roy Lewallen wrote:
Gene Fuller wrote:

Art,

Why not?

The cardioid pattern from a two-element array was reported back as
least as far as 1937, by the famous George H. Brown. In the ideal case
(free space, no losses, etc.) the radiation directly to the rear is
precisely zero.

If you add various real world effects then the back lobe is not
precisely zero, and this is shown in the ARRL Antenna Book referenced
by Cecil.
. . .


Actually, this isn't quite true. If you manage to get perfectly phased
and equal magnitude currents in two identical elements where the phase
angle equals 180 degrees minus the element spacing (such as the classic
90-degree fed, 90-degree spaced cardioid), you don't get an infinite
front-back ratio. In the case of the cardioid with typical diameter
quarter wavelength elements, you end up with around a 35 dB front/back
ratio. With longer elements, close to a half wavelength, the front/back
ratio can deteriorate to less than 10 dB when base currents are
identical in magnitude and correctly phased. The reason is that the
mutual coupling between elements alters the current distribution on the
elements. The mutual coupling from element 1 to element 2 isn't the same
as the coupling from element 2 to element 1 (the mutual Z is the same,
but the coupled voltage and coupled impedance aren't). The net result is
that the two elements have different current distributions, so despite
having identical magnitude base currents the two elements don't generate
equal magnitude fields. The overall fields from the two elements end up
being imperfectly phased, also.

This occurs for theoretically perfect and perfectly fed elements, and
isn't due to "real world" effects.

I published some comments about this effect in "Technical
Correspondence" in July 1990 QST ("The Impact of Current Distribution on
Array Patterns"). I'm certainly not the first to have observed it --
some papers published as early as the '40s are referenced in my article.
But I had never seen its effect on front/back ratio of cardioids
mentioned before. Modern versions of the ARRL Antenna Book clearly show
the small reverse lobe of a typical antenna with quarter wavelength
elements.

I stumbled across it when doing some modeling with ELNEC, the
predecessor of EZNEC, and originally thought it was an error in the
program. You'll see it in a plot from the Cardioid.EZ EZNEC example file
(which is also included with the demo program), and a brief explanation
in the corresponding Antenna Notes file.

A theoretically infinite front/back ratio can be achieved by
modification of the base currents. The amount of modification required
depends on the length and diameter of the elements. Only a small
modification is needed if elements are a quarter wavelength high and
small diameter, but in that case, real world effects will probably have
at least as much and likely more of an effect on the front/back than the
current distribution phenomenon. Rather drastic modification is required
of the base currents of elements approaching a half wavelength high,
however, as elaborated in the "Technical Correspondence" piece.

Roy Lewallen, W7EL

Gene,
At a matter of interest during the 80s I tried to get to zero
radiation at 180 degree point
since Lawson stated it was possible. After covering the half acre under the
long boom
with a ground screen, in fraustration, I finally gave up
with the pursuit. On one of my present models the rear radiation never
exceed 40db
for more than 180 degrees but as Roy pointed out earlier you still have to
deal with
the higher angles which was the case with my model in that when the angle
reached
30 degrees elevation we were back to 20 db..
The center "plume" radiation seems difficult to eradicate.
I think I will try your suggetion of radiators with radiators
of 0.01 diameter to see what happens
Regards
Art





"Gene Fuller" wrote in message
...
Hi Roy,

I have read many of your articles, and I have no doubt you are correct.

However, in the ideal case, specifically in the limit as the wire diameter
goes to zero, the current perturbation from mutual inductance vanishes.
(The mutual inductance does not vanish, only its impact on current
distribution.)

I just spent a few minutes playing around with EZNEC 3, and I was able to
achieve a null of -52 dBi (-57 dBmax) for two half-wave elements, with
nominal 90 degree spacing and 90 degree phasing. The wire size was as
small as possible. This null was in the symmetry plane and directly in the
anti-end-fire direction of course. I expect with more computational
precision, and perhaps fine tuning frequencies and dimensions this null
could be driven farther. The reported current imbalance was a maximum of
0.2%, mid-way between the center and the ends of the wires. The phase
imbalance between the wires was a maximum of 0.2 degrees.

I am not trying to say this is practical. I was just pointing out the
Art's use of polygons and canceling phasors was not particularly unique.

We have since learned that what Art is trying to accomplish is to
eliminate all radiation in the back hemisphere. The cardioid example is
obviously moot for his quest.

73,
Gene
W4SZ

Roy Lewallen wrote:
Gene Fuller wrote:

Art,

Why not?

The cardioid pattern from a two-element array was reported back as least
as far as 1937, by the famous George H. Brown. In the ideal case (free
space, no losses, etc.) the radiation directly to the rear is precisely
zero.

If you add various real world effects then the back lobe is not
precisely zero, and this is shown in the ARRL Antenna Book referenced by
Cecil.
. . .


Actually, this isn't quite true. If you manage to get perfectly phased
and equal magnitude currents in two identical elements where the phase
angle equals 180 degrees minus the element spacing (such as the classic
90-degree fed, 90-degree spaced cardioid), you don't get an infinite
front-back ratio. In the case of the cardioid with typical diameter
quarter wavelength elements, you end up with around a 35 dB front/back
ratio. With longer elements, close to a half wavelength, the front/back
ratio can deteriorate to less than 10 dB when base currents are identical
in magnitude and correctly phased. The reason is that the mutual coupling
between elements alters the current distribution on the elements. The
mutual coupling from element 1 to element 2 isn't the same as the
coupling from element 2 to element 1 (the mutual Z is the same, but the
coupled voltage and coupled impedance aren't). The net result is that the
two elements have different current distributions, so despite having
identical magnitude base currents the two elements don't generate equal
magnitude fields. The overall fields from the two elements end up being
imperfectly phased, also.

This occurs for theoretically perfect and perfectly fed elements, and
isn't due to "real world" effects.

I published some comments about this effect in "Technical Correspondence"
in July 1990 QST ("The Impact of Current Distribution on Array
Patterns"). I'm certainly not the first to have observed it --
some papers published as early as the '40s are referenced in my article.
But I had never seen its effect on front/back ratio of cardioids
mentioned before. Modern versions of the ARRL Antenna Book clearly show
the small reverse lobe of a typical antenna with quarter wavelength
elements.

I stumbled across it when doing some modeling with ELNEC, the predecessor
of EZNEC, and originally thought it was an error in the program. You'll
see it in a plot from the Cardioid.EZ EZNEC example file (which is also
included with the demo program), and a brief explanation in the
corresponding Antenna Notes file.

A theoretically infinite front/back ratio can be achieved by modification
of the base currents. The amount of modification required depends on the
length and diameter of the elements. Only a small modification is needed
if elements are a quarter wavelength high and small diameter, but in that
case, real world effects will probably have at least as much and likely
more of an effect on the front/back than the current distribution
phenomenon. Rather drastic modification is required of the base currents
of elements approaching a half wavelength high, however, as elaborated in
the "Technical Correspondence" piece.

Roy Lewallen, W7EL

Yes, as the wire diameter goes to zero, the current distribution
approaches the same on all elements. But in some cases (where the
element height is in the vicinity of a half wavelength) the wires have
to get impossibly thin to achieve good f/b with equal magnitude and
correctly phased base currents. I guess you could categorize needing a
finite diameter wire as a "real world effect" and a zero diameter wire
as "theoretically perfect". As I mentioned, it's not hard to do well at
a quarter wavelength height, but much harder at heights approaching a
half wavelength. For example, I took the EZNEC Cardioid.ez example file
and increased the element heights to 0.4 meter (0.4 wavelength) using 25
segments/element. With wire diameter of 10^-15 mm, the front/back ratio
was still 32 dB. With the original wire diameter of about 0.24 mm, the
front/back was less than 15 dB. And things get worse yet as the elements
get closer to a half wavelength high. But in practice, even at a quarter
wavelength height, people using phased towers might encounter an
unexpectedly low f/b ratio.

For anyone who's interested, I've posted the Technical Correspondence
piece on my web site. You can get it at
http://eznec.com/Amateur/Articles/Current_Dist.pdf.

Roy Lewallen, W7EL

Gene Fuller wrote:
Hi Roy,

I have read many of your articles, and I have no doubt you are correct.

However, in the ideal case, specifically in the limit as the wire
diameter goes to zero, the current perturbation from mutual inductance
vanishes. (The mutual inductance does not vanish, only its impact on
current distribution.)

I just spent a few minutes playing around with EZNEC 3, and I was able
to achieve a null of -52 dBi (-57 dBmax) for two half-wave elements,
with nominal 90 degree spacing and 90 degree phasing. The wire size was
as small as possible. This null was in the symmetry plane and directly
in the anti-end-fire direction of course. I expect with more
computational precision, and perhaps fine tuning frequencies and
dimensions this null could be driven farther. The reported current
imbalance was a maximum of 0.2%, mid-way between the center and the ends
of the wires. The phase imbalance between the wires was a maximum of 0.2
degrees.

I am not trying to say this is practical. I was just pointing out the
Art's use of polygons and canceling phasors was not particularly unique.

We have since learned that what Art is trying to accomplish is to
eliminate all radiation in the back hemisphere. The cardioid example is
obviously moot for his quest.

73,
Gene
W4SZ

Roy Lewallen wrote:

Gene Fuller wrote:

Art,

Why not?

The cardioid pattern from a two-element array was reported back as
least as far as 1937, by the famous George H. Brown. In the ideal
case (free space, no losses, etc.) the radiation directly to the rear
is precisely zero.

If you add various real world effects then the back lobe is not
precisely zero, and this is shown in the ARRL Antenna Book referenced
by Cecil.
. . .



Actually, this isn't quite true. If you manage to get perfectly phased
and equal magnitude currents in two identical elements where the phase
angle equals 180 degrees minus the element spacing (such as the
classic 90-degree fed, 90-degree spaced cardioid), you don't get an
infinite front-back ratio. In the case of the cardioid with typical
diameter quarter wavelength elements, you end up with around a 35 dB
front/back ratio. With longer elements, close to a half wavelength,
the front/back ratio can deteriorate to less than 10 dB when base
currents are identical in magnitude and correctly phased. The reason
is that the mutual coupling between elements alters the current
distribution on the elements. The mutual coupling from element 1 to
element 2 isn't the same as the coupling from element 2 to element 1
(the mutual Z is the same, but the coupled voltage and coupled
impedance aren't). The net result is that the two elements have
different current distributions, so despite having identical magnitude
base currents the two elements don't generate equal magnitude fields.
The overall fields from the two elements end up being imperfectly
phased, also.

This occurs for theoretically perfect and perfectly fed elements, and
isn't due to "real world" effects.

I published some comments about this effect in "Technical
Correspondence" in July 1990 QST ("The Impact of Current Distribution
on Array Patterns"). I'm certainly not the first to have observed it
-- some papers published as early as the '40s are referenced in my
article. But I had never seen its effect on front/back ratio of
cardioids mentioned before. Modern versions of the ARRL Antenna Book
clearly show the small reverse lobe of a typical antenna with quarter
wavelength elements.

I stumbled across it when doing some modeling with ELNEC, the
predecessor of EZNEC, and originally thought it was an error in the
program. You'll see it in a plot from the Cardioid.EZ EZNEC example
file (which is also included with the demo program), and a brief
explanation in the corresponding Antenna Notes file.

A theoretically infinite front/back ratio can be achieved by
modification of the base currents. The amount of modification required
depends on the length and diameter of the elements. Only a small
modification is needed if elements are a quarter wavelength high and
small diameter, but in that case, real world effects will probably
have at least as much and likely more of an effect on the front/back
than the current distribution phenomenon. Rather drastic modification
is required of the base currents of elements approaching a half
wavelength high, however, as elaborated in the "Technical
Correspondence" piece.

Roy Lewallen, W7EL

Art Unwin wrote:
"I have just come to realize that if one drew a polygon of element
phases in an array and all elements were 180 degrees to its companion
element and excluding its driven element, the max gain and max front to
back will occur at the dame frequency!"

I missed a step or two between the polygon`s resultant and coincidence
of maximum gain with maximum front to back ratio.

A vector has both magnitude and direction. A scalar quantity has only
magnitude.

Vectors are represented by arrows whose lengths correspond to their
magnitudes. Directions of the arrows correspond to the directions of the
vectors.

The combined effect of two or more vectors is called a resultant. A
resultant can be found by a geometrical rule called vector addition.
Vectors are placed head to tail while maintaining their magnitudes and
directions. The resultant is a vector drawn from the tail of the first
vector to the head of the final vector. Any number of vectors can be
added by the head to tail method. These can create a polygon of vectors.

If only two vectors are to be added at a time, they can produce a
resultant by the parallelogram method. Two sides of the parallelogram
are formed by the two vectors connected at their tails. Parallel same
length sides are added to form the parallelogram. A diagonal emanating
from the junction of the two vectors forms the resultant

When one vector (call it c) is the resultant of two vectors (call them
and b) we can say that a and b are components of c. Any given vector can
be resolved into an infinite number of pairs. Usually we find it
convenient to resolve a vector into a pair which are at right angles
with each other. Then we can use the Pythagorean theorem (c squared = a
squared + b squared) to find the magnitude of the resultant (c).

In a right triangle in which two sides are perpendicular, all the
trignometric functions are useful in determining the lengths and
directions of its sides.

Best regards, Richard Harrison, KB5WZI

"Richard Harrison" wrote in message
...
Art Unwin wrote:
"I have just come to realize that if one drew a polygon of element
phases in an array and all elements were 180 degrees to its companion
element and excluding its driven element, the max gain and max front to
back will occur at the dame frequency!"

I missed a step or two between the polygon`s resultant and coincidence
of maximum gain with maximum front to back ratio.

snip

What exactly did you miss?
Was it something I missed or an error or a assumption that I made?
What followed the above statement was a treatise regarding the formation
of a polygon that had been described earlier, but I did not see any
relevance or connection
to what you porport that you or I didn't understand or missed!
Regards
Art





..

Best regards, Richard Harrison, KB5WZI

On Sat, 26 Mar 2005 01:48:44 GMT, "
wrote:
I missed a step or two between the polygon`s resultant and coincidence
of maximum gain with maximum front to back ratio.
snip

What exactly did you miss?

Hi Art,

The answer to your question is found in Richard's question you
answered.

73's
Richard Clark, KB7QHC