Numerical synthesis of a single offset reflector with dielectric cone feed

Abstract

This thesis concentrates on the numerical solution of the boundary-value problem arising in the synthesis of a single offset reflector with dielectric cone feed. By employing a complex notation for vectors, under the assumptions of Geometrical Optics, it has been shown that the design problem may be expressed as boundary-value problem in which a second order non-linear partial differential equation of Monge-Ampère form must be solved.

For the circular aperture with Gaussian amplitude distribution, the Monge-Ampère equation is solved by a process of linearisation and finite discretisation. This gives a system of linear equations, which may solved iteratively to give the solution on a grid in the feed domain. From this solution, the reflector and dielectric surfaces may be calculated. Reflection losses together with a GO cross-polarisation calculation, are considered. A number of computed examples are presented.

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