Antenna Radiation - Array Size

The code demonstrates basic beamforming of a linear array by computing element factors based on sin of angle and spacing, then coherently combining them. The number of elements n and spacing d impact the pattern.

• Key Aspects:
• Defines array factor for each element based on sin of angle
• Coherently sums array factors
• Plots beam patterns in various forms
• Parameters:
• n - number of antenna elements
• d - spacing between elements
• phaseShift - weights for coherent combining
• Varying n changes beamwidth and sidelobes
• Varying d steers null directions
• phaseShift steers main beam direction
• Plots:
• Array factor magnitude vs angle
• Normalized array factor on polar plot
• Array factor in dB
• Beam steering on x-axis

< Code 1 >

theta = -1.0*pi:pi/100:1.0*pi;

phaseShift = exp(-j*2*pi/8);

d = 1.1;

a_theta = [exp(-j .* 0 .* d .* sin(theta)) ;

           exp(-j .* 1 .* d .* sin(theta));

           exp(-j .* 2 .* d .* sin(theta));

           exp(-j .* 3 .* d .* sin(theta));

           exp(-j .* 4 .* d .* sin(theta));

           exp(-j .* 5 .* d .* sin(theta));

           exp(-j .* 6 .* d .* sin(theta));

           exp(-j .* 7 .* d .* sin(theta))];

n = 8;

a_theta =  a_theta([1:n],:);          

a_theta_sum = sum(a_theta);

%s_theta_sum = sum(s_theta);

a_theta_sum_abs = abs(a_theta_sum);

a_theta_sum_abs = a_theta_sum_abs ./ max(a_theta_sum_abs);

a_theta_sum_abs_dB = 10 .* log(a_theta_sum_abs);

for i = 1:length(a_theta_sum_abs_dB)

    if a_theta_sum_abs_dB(i) <= -30

        a_theta_sum_abs_dB(i) = -30;

    end;    

end;    

a_theta_sum_abs_dB = a_theta_sum_abs_dB - min(a_theta_sum_abs_dB);

if max(a_theta_sum_abs_dB) != 0

   a_theta_sum_abs_dB = a_theta_sum_abs_dB/max(a_theta_sum_abs_dB);

end;

hFig = figure(1,'Position',[300 300 700 600]);

subplot(2,2,1);

plot(theta,a_theta_sum_abs);

xlim([-pi pi]);

ylim([0 1]);

tStr = sprintf("d = %0.2f",d);

title(tStr);

set(gca,'xtick',[-pi -(3/4)*pi  -pi/2 -pi/4 0 pi/4 pi/2 (3/4)*pi pi]);

set(gca,'xticklabel',{'-pi','-3pi/4','-pi/2' '-pi/4' '0' 'pi/4' 'pi/2','-3pi/4','pi'});

subplot(2,2,2);

polar(theta,a_theta_sum_abs,'-r');

t = findall(gcf,'type','text');

%delete(t);

subplot(2,2,3);plot(theta,10 .* log(a_theta_sum_abs));ylim([-30 1]);

xlim([-pi pi]);

tStr = sprintf("d = %0.2f",d);

title(tStr);

set(gca,'xtick',[-pi -(3/4)*pi  -pi/2 -pi/4 0 pi/4 pi/2 (3/4)*pi pi]);

set(gca,'xticklabel',{'-pi','-3pi/4','-pi/2' '-pi/4' '0' 'pi/4' 'pi/2','-3pi/4','pi'});

subplot(2,2,4);

polar(theta,a_theta_sum_abs_dB,'-r');

t = findall(gcf,'type','text');