Plotting Radiation Pattern in 3D (in dB)

I am trying to plot the radiation pattern of cos^9(theta) in matlab where theta is the elevation. The code I have so far is the following:

theta = linspace(-pi/2, pi/2);

phi = linspace(0, pi);

[phi, theta] = meshgrid(phi, theta);

rho = 10.*log10((cos(phi)).^9) + 30;

[x,y,z] = sph2cart(phi, theta, rho);

mesh(x,y,z);

The issue is that the log of the cosine creates complex values that cannot be plotted (I do not wish to plot these values either). How should I fix the above code?

I also have access to patternCustom in the antenna toolbox but I am unsure how to use it.

Thank you for your time, help, and advice.

[Jon Ho]

> theta = linspace(-pi/2+0.1,pi/2-0.1);

>> phi = linspace(0,2*pi);

>> rho = 10.*log10((cos(theta)).^9) + 30;

>> patternCustom(rho,theta,phi);

This code also fails to generate any pattern.

[Prahlad Gowtham Katte]

Hello @Jon Ho

I tried the following piece of code in MATLAB R2021b

theta = linspace(-pi/2+0.1,pi/2-0.1);
phi = linspace(0,2*pi);
rho = 10.*log10((cos(theta)).^9) + 30;
patternCustom(rho,theta,phi);

I got the above figure as output.If the problem is not yet solved , please tell the version of MATLAB which you are using currently.

.

[Mathieu NOE]

helo

I simply added an abs to your code to avoid taking the log of negative data but I'm unsure this is making sense...

theta = linspace(-pi/2, pi/2,100);
 phi = linspace(0, pi,100);
 [phi, theta] = meshgrid(phi, theta);
 rho = 10.*log10(abs((cos(phi)).^9)) + 30; % <= here
 [x,y,z] = sph2cart(phi, theta, rho);
 mesh(x,y,z);