# Plotting the beamwidth from a matrix

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Aftab Ahmed Khan el 5 de Sept. de 2014
Comentada: Chibuzo Nnonyelu el 23 de Feb. de 2017
Hi everyone, i have this given matrix (Elevation, azimuth & gain) in the attachment. How can i plot the 3db-beamwidth of this antenna pattern ? I just want to see the pattern and want to calculate the 3db-beamwidth. Thank you so much.
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Aftab Ahmed Khan el 5 de Sept. de 2014
Elevation, azimuth and gain.
Chibuzo Nnonyelu el 23 de Feb. de 2017
To calculate beamwidth, you need to have an idea of the mainlobe. In which direction does your mainlobe point in?

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Youssef Khmou el 5 de Sept. de 2014
Another way to compute the beamwidth is to plot the azimuth and Gain :
X=Data.ABS_antenna_gain;
Gain=X(:,3);
Azimuth=X(:,2);
[index,c]=find(Gain>=max(Gain)-3);
figure; plot(Azimuth(index),Gain(index),'*')
figure; plot(Azimuth,Gain,'*')
The beamwidth is 20° .
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Aftab Ahmed Khan el 5 de Sept. de 2014
Thanx.

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### Más respuestas (2)

Star Strider el 5 de Sept. de 2014
Seeing the pattern is relatively easy, at least with the data available:
Az = Ant.ABS_antenna_gain(:,1);
El = Ant.ABS_antenna_gain(:,2);
Gn = Ant.ABS_antenna_gain(:,3);
[X,Y,Z] = sph2cart(Az, El, Gn);
figure(1)
scatter3(X,Y,Z, '.')
grid on
The challenging part would be 3dB beamwidth, and interpolating it as a surface it you want to do that. Is ‘gain’ in dB now? What would you want to plot to look like (examples are helpful).
Before I tackle that, though, I suggest you see if one of the File Exchange contributions on antenna radiation pattern does what you want.
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Aftab Ahmed Khan el 5 de Sept. de 2014
Hi star, The pattern should look like this. And yes the gain is in dB.

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Youssef Khmou el 5 de Sept. de 2014
Editada: Youssef Khmou el 5 de Sept. de 2014
Here is the proposed solution, i suggest that you use the polar coordinates as the following :
X=Data.ABS_antenna_gain;
[x,y,z]=pol2cart(X(:,1),X(:,2),X(:,3));
plot3(x,y,z,'.','MarkerSize',2)
grid on
xlabel('X');
ylabel('Y');
zlabel('Gain [dB]');
The corresponding figure is attached below :
As the vector z is in decibel, you can search for the indexes of z that are above max(z)-3dB :
[index,value]=find(z>=max(z)-3)
Next you plot the matrix with corresponding indexes :
figure; plot3(x(index),y(index),z(index),'.')
grid on
xlabel('X');
ylabel('Y');
zlabel('Gain 3dB');
The result is in the second figure :
The beam width is in the square of 20^2 units of surface, you can deduce the angular value .
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Aftab Ahmed Khan el 5 de Sept. de 2014
Hi Youssef, Thank you for the detailed reply. What do you mean by saying, that beam width is the square of 20^2 units of surface ? Can you explain to me ? Thanks once again.
Youssef Khmou el 5 de Sept. de 2014
in terms of Cartesian coordinates i mean. The final result is part of the ellipsoid , using the x,y, and z values you can calculate the theta beam width .

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