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This is my version of explanation. I would suggest you to come up with your own explanation. The best way would be for you to try explain this to somebody else in your own words.

 

Following is my version of explanation, but this is just an example. You may come up with a better version.

 

 

 

Steering a Array Antenna - 8x8

 

 

In this tutorial, you will see the examples of beam steering in horizontal direction (changing the direction of the beam) for 8x8 antenna..

 

Click on Next and Prev button so that some intuitive images forms in your head.

 

For more theoretical explanation related to these slides, I would suggest you to look into another form of my notes listed below.

 

 

 

 

 

Followings are the code that I wrote in Matlab Phased Array System Toolbox  to creates all the plots shown in this page. You may copy these code and play with these codes. Change variables and try yourself until you get your own intuitive understanding.

 

< Code 1 >

 

 

c = 3e8;        % propagation speed

fc = 26e9;      % carrier frequency

lambda = c/fc;  % wavelength

AntArray = [8 8];

 

d_scale = 1.00;

txarray = phased.URA('Size',AntArray,'ElementSpacing',[d_scale*lambda/2 d_scale*lambda/2]);

txarray.Element.BackBaffled = true;

 

a = 0;

e = 0;

startA = 0;

startE = 0;

stepA = 1;

stepE = 1;

steer_ang = [startA + a*stepA; startE - e*stepE];

stv = phased.SteeringVector('SensorArray',txarray);

w = stv(fc,steer_ang);

 

hFig = figure(1);

set(hFig,'Position',[300 100 800 600]);

set(gcf,'color','w');

 

subplot(2,2,1);

pattern(txarray,fc,[-180:180],[-90:90],...

    'PropagationSpeed',c,...

    'CoordinateSystem','polar',...

    'Type','powerdb', ...

    'Weights',w)

view(90,20);

 

sTitle = sprintf("Antenna Array = %d by %d\nSteering Angle=[%d %d]\nd = %0.2f half wavelength",...

                 AntArray(1),AntArray(2),steer_ang(1),steer_ang(2),d_scale);

title(sTitle,'FontWeight','normal');

set(gca,'fontsize',8);

 

subplot(2,2,2);

hold on;

for y = 1:8

  for x = 1:8

     circle(x,y,0.5);

     vx1 = x;

     vy1 = y;

     vx2 = x + 0.5*real(w(8*(x-1)+y));

     vy2 = y + 0.5*imag(w(8*(x-1)+y));

     line([vx1 vx2],[vy1 vy2],'Color','red');

     plot(vx2,vy2,'ro','MarkerFaceColor',[1 0 0],'MarkerSize',3);

  end

end  

axis([0 9 0 9]);

title('Steering Weight','FontWeight','normal');

set(gca,'xticklabel',[]);set(gca,'yticklabel',[]);

set(gca,'xtick',[]);set(gca,'ytick',[]);

set(gca,'fontsize',8);

daspect([1 1 1]);

box on;

hold off;

 

subplot(2,2,3);

 

[pat,azimuth,elevation] = pattern(txarray,fc,0,[-90:90],...

    'PropagationSpeed',c,...

    'CoordinateSystem','polar',...

    'Type','directivity', ...

    'Weights',w ...

    );

pat(isinf(pat)|isnan(pat)) = -40;

pat(pat<=-40) = -40;

polarplot(elevation*pi/180,pat,'r-');

rlim([-40 30]);

rticks([-40 -20 0 10 20 30]);

title('Directivity(dBi)[Elevation @ Azimuth = 0]','FontWeight','normal');

set(gca,'fontsize',8);

 

subplot(2,2,4);

[pat,azimuth,elevation] = pattern(txarray,fc,[-180:180],0,...

    'PropagationSpeed',c,...

    'CoordinateSystem','polar',...

    'Type','directivity', ...

    'Weights',w);

pat(isinf(pat)|isnan(pat)) = -40;

pat(pat<=-40) = -40;

polarplot(azimuth*pi/180,pat,'r-');

rlim([-40 30]);

rticks([-40 -20 0 10 20 30]);

title('Directivity(dBi)[Azimuth @ Elevation = 0]','FontWeight','normal');

set(gca,'fontsize',8);

 

function circle(x,y,r)

    t = linspace(0,2*pi,20);

    plot(x+r*cos(t),y+r*sin(t),'k-');

end