Numerical synthesis of dual reflector antenna systems
Numerical synthesis of dual reflector antenna systems
Research by Westcott and his co-workers at Southampton University has led to the formulation of design equations which may be applied to synthesise a wide range of reflector systems. Using Geometrical Optics principles it has been shown that the design problem may be expressed as a boundary value problem in which a second order non-linear partial differential equation of Monge-Ampere form must be solved subject to non-linear boundary conditions. Numerical solutions to this problem have already been found for point source fed single and dual-reflector systems. To simplify this process, however, it has been found convenient to restrict attention to systems possessing circular symmetry. This thesis concentrates on the numerical solution of the boundary value problem for the case of dual-reflectors. For systems producing uniform phase over a planar output aperture the range of reflector geometries for which solutions have been found is extended to include non-circular apertures. Two different methods are used to achieve this; the first employs conformal transformations of the aperture and the second uses direct aperture deformation. Aperture deformation is shown to be particularly effective in producing elliptical aperture systems. Dual-reflector systems producing a spherical output wave are also considered and it is shown that solutions to the associated boundary value problem may be obtained by using a numerical technique similar to that employed in the aperture deformation scheme.
University of Southampton
1986
Graham, Robert Keith
(1986)
Numerical synthesis of dual reflector antenna systems.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
Research by Westcott and his co-workers at Southampton University has led to the formulation of design equations which may be applied to synthesise a wide range of reflector systems. Using Geometrical Optics principles it has been shown that the design problem may be expressed as a boundary value problem in which a second order non-linear partial differential equation of Monge-Ampere form must be solved subject to non-linear boundary conditions. Numerical solutions to this problem have already been found for point source fed single and dual-reflector systems. To simplify this process, however, it has been found convenient to restrict attention to systems possessing circular symmetry. This thesis concentrates on the numerical solution of the boundary value problem for the case of dual-reflectors. For systems producing uniform phase over a planar output aperture the range of reflector geometries for which solutions have been found is extended to include non-circular apertures. Two different methods are used to achieve this; the first employs conformal transformations of the aperture and the second uses direct aperture deformation. Aperture deformation is shown to be particularly effective in producing elliptical aperture systems. Dual-reflector systems producing a spherical output wave are also considered and it is shown that solutions to the associated boundary value problem may be obtained by using a numerical technique similar to that employed in the aperture deformation scheme.
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Published date: 1986
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Local EPrints ID: 460815
URI: http://eprints.soton.ac.uk/id/eprint/460815
PURE UUID: 99bc5d4e-e168-4401-8b6f-25ac357ea304
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Date deposited: 04 Jul 2022 18:30
Last modified: 04 Jul 2022 18:30
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Author:
Robert Keith Graham
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