Finite difference analysis of electrically large parabolic reflector antennas

Abstract

A reflector antenna is analyzed using the finite-difference method (FD). The induced current densities on an axially symmetric parabolic reflector are rigorously calculated. The measured equation of invariance (MEI) is used to terminate the FD mesh very close to the reflector surface. To take advantage of the axial symmetry, the theory of coupled-azimuthal potentials (CAPs) is employed. Illustrative results are obtained for reflector antennas with different aperture dimensions. Results by physical optics (PO) approximation are also included for comparison. The purpose of this paper is not to replace ray optics (RO) and PO in the design of reflector antennas, but to demonstrate the advancement in the FD method, which hitherto was limited to low-frequency and closed-boundary regime. The calculated surface current densities of a reflector antenna do show that the normal component of the current densities at the edges exhibits high standing waves which are missing in PO, and which we know should be there. The standing wave of current densities may not affect the main beam, but certainly will have an effect on side lobes and have a major impact in estimating the loss of the antenna.