aperture_effeciency.m

% Ismail Mohamed Ibrahim Elbadawy
% AAST

% This code is designed to plot aperture effeciency Vs subtended angle 
% for parabolic reflector using different values of n (2,4,6,8).
% You can see the same output in "Antenna Theory",Constantine A.Balanis
% Third edition page 914.
% -------------------------------------------------------------------

clc
clear all
close all
fprintf('<< --------- PLEASE BE PATIENT --------- >>')

thetao=0:90;                               % Subtended angle in degrees
syms theta
for j=1:4
    
    n=j*2;
    g=2*(n+1)*((cos(theta))^n);            % Feed Pattern
    h=sqrt(g)*tan(theta/2);
    
    for i=1:length(thetao)
        
        angle=thetao(i)*(pi/180);          % From degree to radian
        
        % Aperture effeciency calculation
        eff(i)=((cot(angle/2))^2)*((abs(eval(int(h,theta,0,angle))))^2);                     
    end

    if j==1
        plot(thetao,eff,'b','linewidth',2)
        hold on
    elseif j==2
        plot(thetao,eff,'k','linewidth',2)
        hold on
    elseif j==3
        plot(thetao,eff,'r','linewidth',2)
        hold on
    else
        plot(thetao,eff,'g','linewidth',2)
        grid on
    end
end

legend('n=2','n=4','n=6','n=8')
xlabel('Reflector half-angle (degrees)')
ylabel('Aperture effeciency')