Investigation on the Beamwidth of 2-D Sectorial Electric Dipole: Analytical Solutions

The radiation behavior of a horizontal sectorial electric dipole is studied. Azimuthal beamwidth is investigated by employing numerical integrals and approximate analytical expressions. Closed-form formulas for beamwidth calculation are derived by using the Fourier series expansion of the generating functions. In these ways, the beamwidth broadening mechanism of sectorial electric sheet can be quantitatively revealed and mathematically understood. Numerical results on 2-D sectorial electric dipoles with centered angle
$\alpha=240^{\circ}$
under
$\text{TE}_{3/4,1}$
resonance are investigated and compared to the 1-D ones. As can be seen, the sectorial electric dipole exhibits a much wider azimuthal beamwidth of
$110^{\circ}$
, compared to
$78^{\circ}$
and
$47^{\circ}$
of the 1-D counterparts.