Where i can get formulas for microstrip patch "element pattern" or "element factor"?

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Where i can get formulas for microstrip patch "element pattern" or "element factor"?

Hello! I used formulas for calculating AF (antenna factor), and after some trial and error get results that match measurements very well. For example, side beams angular position. To calculate approximate radiation pattern i must multiply AF by element pattern. I am unsure how this thing called. When element pattern can cancel out AF side beams, or AF pattern cancels out element side beams. I want to find some approximation formulas of single rectangular patch radiation pattern, or maybe circular patch radiation pattern. Thanks!

p.s. I found similar question without answer here. He explained problem better than me:

Hello everyone,

I would like to know if there's a software/matlab code I could use in order to convert the pattern of an antenna element to a formula that can be plotted in Matlab. For example :

% element pattern of dipole antenna
g(theta) = abs((cos(pi*cos(deg2rad(theta))/2))/sin(deg2rad(theta)));

How is this formula obtained? I already have the array factor, but I need the element pattern in order to multiply and obtain the pattern of the whole array. Since I have no particular background in antenna design (I'm doing a science fair project), help would be very appreciated. My email: fgl_9309@hotmail.com

Thank you!

Thread link: https://www.edaboard.com/threads/171869/

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i found an answer here:
http://www.antenna-theory.com/antennas/patches/antenna.php
and here:
http://valab.det.unifi.it/new/material/UNIFIvallecchi02/Rectangular_patch.pdf