Directivity calculation in Matlab for circular array-suggestions?

[Gattstheberserker]

Hi everyone,

Could someone help me out in calculating the Directivity of my circular array. I'm using Matlab and I'm pretty certain my method is not correct (explained a little below).

Very Briefly, this is how I generate the Array factor:

a1=-50;b1=50;c1=.2;
[fx,fy]=meshgrid(a1:c1:b1,a1:c1:b1);
t=linspace(0,2*pi,250)

And inside a loop:

for k=1:length(t)
x=cos((t)+offset); y=sin((t)+offset);

ArrF=exp(-i*2*pi*(fx*(rad(j)*x(k))+fy*(rad(j)*y(k))));
plot(rad(j)*x(k),rad(j)*y(k),'.b');
AF1=AF1+ArrF;

And I plot it with:

dbaf=20*log10(abs(AF1));
mesh(fx,fy,dbaf);

And this is how the Array and the Array factor looks if that helps:

http://img110.imageshack.us/img110/5355/af7rq.jpg

So now I have my Array factor AF1 which is a 501x501 array and here is where I could use some help in calculating the directivity.

I tried calculating the directivity this way:

theta=linspace(0,180*pi/180,501);
phi=linspace(0,360*pi/180,501);
[thtmesh,phimesh]=meshgrid(theta,phi);

dth=theta(2)-theta(1);
dph=phi(2)-phi(1);

Prad=sum(sum(abs(AF1).^2.*sin(thtmesh)*dth*dph));
Directivity=4*pi*max(max(abs(AF1).^2))/Prad;

But as I mentioned...I doubt this gives a correct value...I used linspace to set theta and phi to 501 so that the matrix dimensions match AF1...and I have no clue if the value I get is right.


Could someone help me out with the Directivity here?
Sorry if my query is too long but I thought it would help if I was as descriptive as possible.

Thanks!

 

[VEBill]

Average directivity should be 0 dBi (assuming that the mass is constant *).

* subtle joke.

 

[Higgler]

Directivity for most antennas is pretty accurate (in dB) as 10* log [41,000/[(beamwidth 1)*(beamwidth 2)]]. beamwidth 1&2 are principal planes in orthogonal (perpindicular) directions.
compare that to your results as a quick check, it should be within 1 dB unless those sidelobes in your chart are very high.

kch