Directivity from Array Factor - Suggestions?

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:
h**p://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!

Your definition of Directivity from the Array Factor looks correct. Inefficient, but it should give a decent value. I don't know how you determined the array factor as there are undefined variables.

I would take a known array factor, e.g. for a circular array of dipoles, and see if you get the correct directivity. Most antennas books, like Stutzman and Thiele or Balanis, will have simple array factors.

Try this attach. It will help you.
and look at the soft to calculate what you need.
https://www.edaboard.com/viewtopic.p...hlight=balanis


pl

Thanks for the reply...I do get a decent value but I wasn't sure when I posted...and now I'm positive its wrong because theta,phi used for directivity and fx,fy used for the AF generation aren't...umm...the same coordinate system...not related...anyways wrong Directivity calculation for this particular array factor =)...got to work on that by maybe generating the AF in spehrical cordinates instead of the way I did using spatial fx, fy (exp(fx.x+fy.y))

And undefined variables? I guess it would be clearer if I provided the full code...let me know if you want to see it.

Added after 3 minutes:

Thanks for the link...I dont have enough points to download it though...but could you tell me if it is the same program as the one Balanis provides for his Chapter on Arrays...Chapter 6 to be exact?

yes its from 3 edition
also presentation.

pl