Polar plot draw line at -3dB opening

I am drawing a radiation diagram for an antenna but I need to draw what we call the 3dB opening which is the region where the antenna receives 3dB less than it's maximum. Below is the code I have and as you will see, the maximum is -18.2 so the 3dB opening would be where the polar plot intersects the -21.2dB 'line'.

angl = 0:10:360; 
pow = [-18.2 -18.5 -19.7 -21 -22.3 -23 -24.1 -28.1 -33 -37.8 -34 -32.4 -33.1 -32.8 -34.2 -36 -37.9 -39.2 -40 -40 -39.2 -36 -34.2 -32.8 -33.1 -32.4 -34 -37.8 -33 -28.1 -24.1 -23 -22.3 -21 -19.7 -18.5 -18.2];
R = deg2rad(angl);
powc = pow - max(pow);
powc(powc<-40) = -40;
h = polarplot(R, pow + 40, 'Linewidth', 1, 'color', [.21 .81 .94]);
haxes = get(h, 'Parent');
haxes.RTickLabel = {'-40 dB', '-30 dB', '-20 dB'};
title('Diagramme de rayonnement antenne TP-LINK TL-AN2409A');

I'm not sure how I could get two lines from the center to the edge of the plot which interesect the plot line at -21.2dB.

Any help is appreciated.

EDIT:

If there is a way to smooth the plot, I'd love to know how to do that also.

Answer 1

[Star Strider]

From your description, this seems to work:

angl = 0:10:360; 
pow = [-18.2 -18.5 -19.7 -21 -22.3 -23 -24.1 -28.1 -33 -37.8 -34 -32.4 -33.1 -32.8 -34.2 -36 -37.9 -39.2 -40 -40 -39.2 -36 -34.2 -32.8 -33.1 -32.4 -34 -37.8 -33 -28.1 -24.1 -23 -22.3 -21 -19.7 -18.5 -18.2];

R = deg2rad(angl);
powc = pow - max(pow);
powc(powc<-40) = -40;

hpp = -21.2;
db3(1) = interp1(pow(1:5), R(1:5), hpp);                        % Half-Power Angle 1
db3(2) = interp1(pow(end-4:end), R(end-4:end), hpp);            % Half-Power Angle 2

figure
h = polarplot(R, pow + 40, 'Linewidth', 1, 'color', [.21 .81 .94]);
hold on
polarplot([0 0; db3(1) db3(2)], [-40 -40; hpp hpp]+40, '-r')    % -3dB Opening’ Lines
hold off
haxes = get(h, 'Parent');
haxes.RTickLabel = {'-40 dB', '-30 dB', '-20 dB'};
title('Diagramme de rayonnement antenne TP-LINK TL-AN2409A');

producing:

If you want the lines to go to the edge of the plot, replace ‘hpp’ here:

polarplot([0 0; db3(1) db3(2)], [-40 -40; hpp hpp]+40, '-r')    % -3dB Opening’ Lines

with the radius of the edge of the plot, that being ‘max(rlim)’.

You could smoothe the plot with a cubic or similar interpolation, using the interp1 function, first using the linspace function to define ‘R’ with a larger number of grid points.

Experiment to get the result you want.

Answer 2

[Da Huang]

if you have antenna toolbox or phase array toolbox, you can use polarpattern function to plot your own pattern. it also provide the measurement tools in it, right click on the figure, you will see a lot of options there.

the command will be:

polarpattern(angl,pow)

then right click in the plot to discover the tools.