Plot 3D Array Gain of 4x4 Planar Antenna Pattern + Weighting

Hi folks

I created an uniform rectangula antenna array

f=3e9;
c=3e8;
lambda=c/f;
ura = phased.URA('Size',4, 'ElementSpacing',0.5*lambda);

As it is stated in the Help of the Phased Array Toolbox, it generates a 4x4 array in the yz-plane, which means that

 % Azimuthal az
phi=0;
% Elevation el
theta=90;

1. Is this right?

Further, I would like to calculate the Array Gain A(psi), by using the dtft with

   A(psi)= \sum_n a_n*z^n
   z = e^(j*psi)
   psi=(k_x,k_y,k_z)*d= wavefactor: (k*d*sin(theta)*cos(phi), k*d*sin(theta)*sin(phi), k*d*cos(phi))
   k=2*pi/lambda = wavenumber
   d=distance between array elements in (1/lambda)

Taking the values for theta and phi from above, I`ll get as a wavefactor only a value for the k_x direction, that is:

    % psi= k*d = 2*pi/lambda*d = 2pi

Array Gain: I am trying to solve this problem with Z-Transformation but I dont get any reasonable results?

   G = dtft(a_n,psi)

2. Is this right so far? How can I introduce the weights to the coefficients?

Moreover, I really would like to plot the Array Gain G in 3D polar plot.

3. How could I realize this?

I already found the Orfanidis`Toolbox but it does not help me. Looking forward to hearing from you guys.

Cheers, Bryana

Answer 1

[Honglei Chen]

If you mean directivity, you could do the following to generate the 3D plot

f=3e9;
c=3e8;
lambda=c/f;
ura = phased.URA('Size',4, 'ElementSpacing',0.5*lambda);
plotResponse(ura,f,c,'RespCut','3d','Unit','dbi','Format','polar')

[Bryana]

Hi,

thanks for your answer, but I already found this function. I am looking for a 3-D radiation pattern showing the Array Gain in all 3 dimensions.

[Honglei Chen]

What do you mean by 3 dimensions? The syntax does plot a 3D radiation pattern.

[Bryana]

I mean the Radiation Pattern for az (phi 0:2*pi) and el (theta 0:pi) in yxz-dimension like the one in the attachment.

[Honglei Chen]

I'd say that is what you want, just points to a different direction and with a backlobe. You can adjust the element to remove the backlobe and also rotate the axes to get a similar plot

f=3e9;
c=3e8;
lambda=c/f;
ura = phased.URA('Size',4, 'ElementSpacing',0.5*lambda,...
    'Element',phased.CosineAntennaElement);
plotResponse(ura,f,c,'RespCut','3d','Unit','dbi','Format','polar')
set(gca,'CameraUpVector',[1 0 0]);

[Bryana]

Yeah, the diagram looks good. But, doesnt it show the Directivity D? I need to plot the Radiation pattern with its Main/Side/Grating Lobes. Wouldn`t that be in similar fashion something like this?:

    % Gain_total = Element * Array Factor

Or in other words: Wouldn`t that just be the 2-D Antenna Pattern with polar coordinates transformed to 3D meshgrid?

[Honglei Chen]

You can think that way, but the element pattern is 3D, also your example is a 3D polar plot. Everything plotted here is indeed in a 3D mesh grid. If you really want to see the axes, you can simply do

axis on

and you'll see axes. Is that your concern?

[Bryana]

Yeah. That`ll do the trick. Thanks alot!