Rapid Processing of a Shaped Reflector by Complex Source Point and Gaussian Beams

The rapid development of telecommunications and multimedia applications has resulted in the emergence of a number of projects related to geostationary satellites. The performance of these satellites can be optimised by the use of aerials with shaped reflectors. To this effect, it was decided to develop a rapid and accurate analysis tool, capable of predicting the characteristics of both the radiation and the aerials. However, for current techniques, the time required for simulation becomes a prohibitive factor. This study has focused on the development of a more rapid method and which would enable good result accuracy to be maintained. There are three stages to the technique: 1) decomposition of the incident radiation on the basis of Gaussian beams - Elliptical Gaussian Beams (EGB) if the reflector is concave, Complex Source Point (CSP) if it is convex; 2) Gaussian beams enable the radiated field to be determined for any point in space using vectorial superposition to sum the reflected beams arising from the local interactions; 3) the uniform theory of diffraction uses C³ rather than R³. The complex source points require determination of the specular reflection points before calculation of the sum of all the contributions. The solution is exact because the CSP is a solution of the Helmholtz propagation equation.