The formula for z which you gave would give me nightmares.
Are you absolutely sure that what you have written is correct?
Perhaps first principles was overstated n my posting

Art

"Richard Clark" wrote in message
...
On Fri, 11 Mar 2005 23:05:28 GMT, "
wrote:

A cardioid pattern has radiation in the 180 degree portion behind the feed
point
first described by Johann Castillon made a Fellow of the Royal Society
of London in 1753:
r = 2a(1 + cos(theta))
where theta = 180 such that:
r = 2a(1 + cos(180))
r = 2a(1 + -1)
r = 0

Hi Art,

Understandably, the term you are so unfamiliar with, insofar as no
rearward radiation (not the same as no radiation to 180 degrees) is
Lambertian. As may be expected, the term is derived from the work of
mathematician Johann Heinrich Lambert (1728-1777).

It is a distribution curve derived from reflections off of a "diffuse
surface" (note, not the same thing as reflections off of a specular
antenna element):
(x²+y²+z²)² = z

At 300 years+ both are pretty old works that each easily qualify
within the purview of "first principles" if one is serious about
radiation.

73's
Richard Clark, KB7QHC

I wrote:
"However, there is a measured by D.C. Glockner of Ohio State University
pattern of the 3-element Yagi-Uda with more than 7 dB gain and almost
zero radiation from the direction of 180-degrees from the maximum. It is
on page 246."

No correction required but I should add that the book is the 3rd edition
(2002) of "Antennas" by John D. Kraus et al.

Best regards, Richard Harrison, KB5WZI

I did rotate it and placed it on the ground, the gain dropped
by 4db and the circular lobe
pointed straight up. Some time I will look at same at 1 WL
Art
"Cecil Moore" wrote in message
...
wrote:
If the phases and and magnitudes of the paired elements
are exactly the same, then radiation to the rear is zero.

If you rotate the elements by 90 degrees, can you make the
radiation toward the ground zero?
--
73, Cecil http://www.qsl.net/w5dxp


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On Sat, 12 Mar 2005 00:38:31 GMT, "
wrote:
The formula for z which you gave would give me nightmares.

Hi Art,

That is the Cartesian form. A 2D polar form would follow:

I = I0 · A · cos (phi) · cos (theta) / Pi
where
I is the intensity at a point with elevation theta
A is the area of the surface
I0 is the radiation directed normal to a diffuse surface
phi is the angle of incidence (all angles being considered)

A variant for conforming radiators is found in:

I = I0 · cos (theta)

Observation will reveal why this is called Lambert's Cosine Law.
Simple draughting techniques will reveal the circular distribution
curve.

A simple example of the last equation is found in the common, unlensed
LED. Insofar as radios go, I expect the same response would follow
from placing an isotropic source above a diffuse reflector (you would
then have to use the first equation).

73's
Richard Clark, KB7QHC

wrote:
A cardioid pattern has radiation in the 180 degree portion behind the feed
point

You want zero radiation in an entire hemisphere?
Arecibo probably meets that specification. :-)
--
73, Cecil http://www.qsl.net/w5dxp


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Yup.
They have now upgraded the mountain road so you don't have to take a spare
rear axle with you now.
Art
"Cecil Moore" wrote in message
...
wrote:
A cardioid pattern has radiation in the 180 degree portion behind the
feed point

You want zero radiation in an entire hemisphere?
Arecibo probably meets that specification. :-)
--
73, Cecil http://www.qsl.net/w5dxp


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But that formula for z does not appear to be correct!
Art
"Richard Clark" wrote in message
...
On Sat, 12 Mar 2005 00:38:31 GMT, "
wrote:
The formula for z which you gave would give me nightmares.

Hi Art,

That is the Cartesian form. A 2D polar form would follow:

I = I0 · A · cos (phi) · cos (theta) / Pi
where
I is the intensity at a point with elevation theta
A is the area of the surface
I0 is the radiation directed normal to a diffuse surface
phi is the angle of incidence (all angles being considered)

A variant for conforming radiators is found in:

I = I0 · cos (theta)

Observation will reveal why this is called Lambert's Cosine Law.
Simple draughting techniques will reveal the circular distribution
curve.

A simple example of the last equation is found in the common, unlensed
LED. Insofar as radios go, I expect the same response would follow
from placing an isotropic source above a diffuse reflector (you would
then have to use the first equation).

73's
Richard Clark, KB7QHC

On Sat, 12 Mar 2005 03:15:42 GMT, "
wrote:
But that formula for z does not appear to be correct!

Hi Art,

As I said, you are not working in Cartesians in the first place with
"polygons." It is a formula for computer generation of the surface.

If you absolutely need to understand the formula, read through the
code that is used to construct the distribution curve:
#define sz 2000000
#define bc 19
static double fr() {return rand()/(double)~(131);}
static double sq(double x){return x*x;}
int hi[bc]; int out=0;
int main(){
{int j=bc; while(j--) hi[j]=0;}
{int j=sz; while(j--) {
double x = fr()*1.4-.7, y=fr()*1.4-.7, z=fr();
if(sq(x*x+y*y+z*z) z) {
++hi[(int)(z/sqrt(x*x+y*y+z*z)*bc)];}
else ++out;}}
{int j; for(j=0; jbc; ++j) printf("%d %d %8.2f\n",
j, hi[j], (sz-out)*(j+.5)/(bc*bc/2));}
printf ("%d out of box.\n", out);
}

If you still don't understand, the polar coordinate formulas are just
as useful, simpler, and take very little work to construct a "polygon"
that obtains complete closure. It is, after all, a construction much
like any of a number of classic curves. You need only conform to the
requirements of a Lambertian surface or emitter to obtain the curve
you describe.

73's
Richard Clark, KB7QHC

Put the antenna half way up and a small part broke!
Have put the antenna to one side
and I will pick it up again during the summer
Regards
Art

" wrote in message
news:dySVd.30807$r55.174@attbi_s52...
I have just come to realise that if one drew a polygon of element phases in
a array
and all elements were 180 degrees to its companion element and excluding
the
driven element, the max gain and max front to back will occur at the SAME
frequency!
Until now I was of the understanding that these two max figures could not
occur at
the same frequency. Is there anything written about this possibility?
Regards
Art

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