For large arrays, the HPBW is approximately taken as half of the BWFN.
For a given array the HPBW is a function of the direction of the main beam. The HPBW is minimum for a broadside direction and maximum for the end-fire direction. The beam width monotonically increases as the main beam tilts towards the axis of the array.
The HPBW for the broad-side array and the end-fire array are approximately given as
The HPBW is inversely related to the array length. Larger the array narrower is the beam i.e., smaller HPBW.
Directivity
The directivity of the uniform array is given by
For a large array, the integral can be approximated by the solid angle of the main beam and the directivities for the broadside and end-fire arrays are given as
Important Observation:
The HPBW of the broadside array is less than that of the end-fire array but the directivity of the end-fire array is larger than the broadside array.
