Analysis of rotationally symmetric arrays of apertures on conducting spherical surfaces

Rotationally symmetric arrays of circular waveguide fed apertures on conducting spherical surfaces have been analyzed. Representation of the outside electromagnetic fields in terms of spherical transmission line modes permits the array analysis to be viewed as a spherical waveguide junction discontinuity problem. The apertures, in general, carry dual polarized circular waveguide TE₁₁ modes. Two independent formulations-the unit cell method and the eigen excitation method, which take rotational symmetry into account-are developed and are checked against each other numerically for computational accuracy. These two formulations are analytically linked as discrete Fourier series pairs. It is seen that mutual coupling along the array decays more rapidly when the polarization of excitation is perpendicular to the array plane than when it is parallel to it. This analysis has been applied in the performance analysis of the dome lens phased array radar antenna