how to draw a 5x5 three-dimensional planar array with isotropic elements using the formula AF_(n ) (θ,ϕ)= {1/M sin⁡(M/2 ψ_x )/sin⁡(ψ_x/2) }{1/N sin⁡(N/2 ψ_y )/sin⁡(ψ_y/2) }

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Answer 1

[Divyam]

Hi @Moch Dwi Putra Maulana,

Here is the code for plotting a 5x5 3D planar array

% Defining the size of the array
M = 5; 
N = 5; 

theta = linspace(0, pi, 180); % Taking sample values for theta
phi = linspace(0, 2*pi, 360); % Taking sample values for phi

% Creating a meshgrid for theta and phi
[Theta, Phi] = meshgrid(theta, phi);

% Defining the wave number and element spacing
k = (2 * pi) / 30; % Assuming wavelength lambda = 30
d_x = 7.5; % Given lambda/4
d_y = 7.5; % Given d_x = d_y

% Calculating the phase shifts
psi_x = k * d_x * sin(Theta) .* cos(Phi);
psi_y = k * d_y * sin(Theta) .* sin(Phi);

% Calculating the array factor
AF_x = (1/M) * (sin(M/2 * psi_x) ./ sin(psi_x/2));
AF_y = (1/N) * (sin(N/2 * psi_y) ./ sin(psi_y/2));
AF = abs(AF_x .* AF_y); 

figure;
surf(psi_x, psi_y, AF, 'EdgeColor', 'none');
xlabel('$\psi_x$','Interpreter', 'latex');
ylabel('$\psi_y$', 'Interpreter', 'latex');
zlabel('Array Factor');
title('3D Planar Array Factor');
colorbar;