Antenna Radiation - Array Size

this models a linear antenna array to show impact of number of elements on beamshape. By varying n, the code demonstrates how having more antenna elements narrows the main beam and reduces sidelobe levels through coherent combining. Element spacing d also impacts beamwidth.

• Key steps:
• Define array factor vectors for each element based on spacing
• Sum array factors coherently
• Plot beam patterns - cartesian, polar, dB
• Parameters:
• n - number of antenna elements
• d - spacing between elements
• phaseShift - weights for coherent combining
• Varying n changes beamwidth and sidelobes
• Varying d impacts main lobe width
• phaseShift steers the beam direction
• Plots:
• Cartesian plot shows narrower main beam with more elements
• Polar plot shows normalized array factor
• dB plot illustrates lower sidelobes with more elements
• Beam steering angle on x-axis

< Code 1 >

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

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

d = 2.0;

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

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

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

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

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

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

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

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

n = 8;

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

a_theta_sum = sum(a_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);

a_theta_sum_abs_dB = a_theta_sum_abs_dB/max(a_theta_sum_abs_dB);

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

subplot(2,2,1);

plot(theta,a_theta_sum_abs);

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(2,2,2);

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');