3D radiation pattern / array factor of planar array in cylindrical coordinates

Dear MatLab Central Community,

I would like to plot the 3D array factor of a planar (2D) antenna array in cylindrical coordinates. I have calculated the array factor in spherical coordinates AF(theta, phi) and I can easily plot it in spherical coordinates (using

[x,y,z] = sph2cart(THETA,PHI,R)

for coordinate conversion and then "surf(x,y,z)" or "mesh(x,y,z)" for 3D plotting), but I do not know how to do that in cylindrical coordinates. In other words, I want the domain of the 2D function on the xy plane to be a grid in RHO, THETA and for each point plot the Z = AF value. I tried to use other coordinate transformations but I did not manage to do that.

Thank you very much for any help.

Answer 1

[Himanshu]

Hi Maurizio,

To plot the 3D array factor of a planar antenna array in cylindrical coordinates, you need to convert your spherical coordinates ((\theta, \phi, R)) to cylindrical coordinates ((\rho, \theta, z)).

Here is a MATLAB code snippet to help you with the conversion and plotting:

% Assume THETA, PHI, and AF are your spherical coordinates and array factor
% THETA and PHI are 2D matrices, and AF is the array factor corresponding to these angles

% Convert spherical to cylindrical
R = abs(AF); % Assuming R is the magnitude of the array factor
RHO = R .* sin(THETA);
Z = R .* cos(THETA);

% Plot in cylindrical coordinates
figure;
surf(RHO .* cos(PHI), RHO .* sin(PHI), Z, abs(AF)); % Use abs(AF) for coloring
xlabel('X (Cylindrical)');
ylabel('Y (Cylindrical)');
zlabel('Z (Cylindrical)');
title('3D Array Factor in Cylindrical Coordinates');
colormap jet; % Optional: Change the colormap
colorbar; % Optional: Add a colorbar
axis equal; % Optional: Ensure equal scaling for all axes

The provided MATLAB code snippet calculates (\rho) and (z) using the relationships (\rho = R \sin(\theta)) and (z = R \cos(\theta)), where (R) is the magnitude of the array factor. The 'surf' function is then used to create a 3D surface plot, with the surface color mapped to the magnitude of the array factor for enhanced visualization.