Omnidirectional pattern directivity in the absence of minor lobes: revisited

The article presents a simple, approximate formula for the directivity of an omnidirectional antenna without minor lobes. This problem has been treated before by Monser (1954), and the results have been cited by Levine and Monser (1961). In this earlier work, an approximate formula, showing antenna directivity as a function of the half-power beamwidth (HPBW), was determined by fitting a curve to data that had been obtained previously by numerically integrating across the half-power beamwidth spectrum: a process involving many integrations. Notwithstanding the evident good agreement between the "exact" and "curve-fitted" data in that instance, it is equally possible to return to the supporting sums and determine directly a very simple, alternative approximation to the defining integral and, hence, to the directivity of such antennas.