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