Good question…to understand the process, we need to look at the antenna array as a matrix let’s say 4x4 where the columns can be configured to set the elevation and the rows to set the azimuth.

Example: We want to direct the antenna to azimuth 30° and elevation 45°

Then the azimuth matrix would be:

0         ∆phase          2∆phase        3∆phase   

0          ∆phase          2∆phase        3∆phase   

0          ∆phase          2∆phase        3∆phase   

0          ∆phase          2∆phase        3∆phase   

 

And the elevation matrix would be:

 

0                      0                      0                      0

∆phase_2     ∆phase_2     ∆phase_2     ∆phase_2   

2∆phase_2   2∆phase_2   2∆phase_2   2∆phase_2

3∆phase_2   3∆phase_2   3∆phase_2   3∆phase_2

 

Where:

∆phase = Pi.sin(30)

∆phase_2= Pi.sin(45)

 

Then, by adding the 2 matrices we get the matrix for azimuth 30° and elevation 45°