On the relationship between the directivity and the half-power beamwidth in quasi-symmetric pencil-beam radiation patterns

In antenna theory, the formulae relating the directivity and the half-power beamwidth are reexamined in the case of pencil-beam radiation patterns from large grounded apertures, both square and circular. It is shown that the differences among them can be reconciled by taking into account, for example, effects due to sidelobes. Effects due to an aperture-edge taper are also addressed.