Beamwidth of antenna array in arbitrary cut

Dear All!

I'm looking for a way to calculate the maximal beamwidth (or beamwidth in an arbitrary cut). The reason for that is, that if I use the beamwidth function, I can only select azimuth and elevation cuts, however, that won't give me the beamwidth I am looking for. In the picture below, the main lobe is pointing towards Az 0, El 0. Nor the azimuth, neither the elevation cut will show the real beamwidth, and selecting the cut and the cut angle will never pass through the widest part of the beam.

I cannot rotate the array towards another direction since setting the element normal the x direction is aligned to the normal, additionally, the pattern is exported from a 3D solver, in which to get a proper phase pattern, I need to ensure, that the antennas are aligned with x axis.

You know about any workaround?

Many thanks in advance!

Answer 1

[Aastha]

Hi Gergely,

I understand that you have a 3D antenna array pattern with an arbitrary cut, and you want to determine the maximal beamwidth.

Kindly refer to the following steps to determine the beamwidth:

1. Define the antenna pattern “r” as a function of azimuth “az” and elevation “el” where “az” and “el” are arrays containing the azimuth and elevation for each point in the antenna pattern. Then, find the location of the maximum power point as illustrated in MATLAB code below:

[maxPower, maxIdx] = max(r(:));%maxPower stores the maximum power, maxIdx is the linear index of this max value 
[elIdx, azIdx] = ind2sub(size(r), maxIdx); 
maxAz = az(azIdx); % Get the azimuth value corresponding to the maximum power 
maxEl = el(elIdx); % Get the elevation value corresponding to the maximum power 

For further information on “ind2sub” functions, kindly refer to the link of MathWorks documentation given below:

https://www.mathworks.com/help/matlab/ref/ind2sub.html?searchHighlight=ind2sub&s_tid=srchtitle_support_results_1_ind2sub

2. Find the value of the half-power point and the locations of all points where the power is greater than or equal to the half-power. You may refer to the MATLAB code given below to do so:

halfPower = maxPower / sqrt(2);%  Find the half-power value (which is maxPower / sqrt(2)) 
halfPowerIdx = find(r >= halfPower); % Get the indices of all points that meet the half-power condition 
[halfElIdx, halfAzIdx] = ind2sub(size(r), halfPowerIdx); % Convert linear indices to subscripts for elevation and azimuth 
halfAzimuthRange = az(halfAzIdx); 
halfElevationRange = el(halfElIdx); 

3. Due to the arbitrary nature of antenna pattern, define a search space around the maximum point of the pattern to look for the half-power points. You can then find the points that lie within this search space and satisfy the half-power condition. This can be done as follows:

azBeamwidth = range(halfAzimuthRange(abs(halfAzimuthRange - maxAz) < pi/10)); % Calculate azimuth beamwidth within the search space 
elBeamwidth = range(halfElevationRange(abs(halfElevationRange - maxEl) < pi/10)); % Calculate elevation beamwidth within the search space 
fprintf('Azimuth Half-Power Beamwidth: %.2f radians\n', azBeamwidth); 
fprintf('Elevation Half-Power Beamwidth: %.2f radians\n', elBeamwidth); 

In this way, you can find the maximal beamwidth for an antenna array with an arbitrary cut. You can experiment with the search space for best results.

Hope this helps!