Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics
This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential e...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Antennas and Propagation |
| Online Access: | http://dx.doi.org/10.1155/2016/4715681 |
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| author | Rafael A. Penchel José R. Bergmann Fernando J. S. Moreira |
| author_facet | Rafael A. Penchel José R. Bergmann Fernando J. S. Moreira |
| author_sort | Rafael A. Penchel |
| collection | DOAJ |
| description | This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. The investigation explores the interpolating properties of confocal quadrics to locally represent the shaped reflector surface. It allows the partial derivatives involved in the formulation to be analytically expressed. To illustrate the method, two examples of offset single reflectors shaped to radiate a Gaussian power density within a superelliptical contoured beam are presented. The results are validated by Physical Optics analysis with equivalent edge currents. |
| format | Article |
| id | doaj-art-d108fe884dc6451286b85c0751f52105 |
| institution | Kabale University |
| issn | 1687-5869 1687-5877 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Antennas and Propagation |
| spelling | doaj-art-d108fe884dc6451286b85c0751f521052025-02-03T06:07:27ZengWileyInternational Journal of Antennas and Propagation1687-58691687-58772016-01-01201610.1155/2016/47156814715681Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal QuadricsRafael A. Penchel0José R. Bergmann1Fernando J. S. Moreira2Department of Electrical Engineering, Federal University of Technology-Paraná, 86300-000 Cornélio Procópio, PR, BrazilCenter for Telecommunications Studies (CETUC), Catholic University of Rio de Janeiro, 22453-900 Rio de Janeiro, RJ, BrazilDepartment of Electronics Engineering, Federal University of Minas Gerais, 31270-901 Belo Horizonte, MG, BrazilThis work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. The investigation explores the interpolating properties of confocal quadrics to locally represent the shaped reflector surface. It allows the partial derivatives involved in the formulation to be analytically expressed. To illustrate the method, two examples of offset single reflectors shaped to radiate a Gaussian power density within a superelliptical contoured beam are presented. The results are validated by Physical Optics analysis with equivalent edge currents.http://dx.doi.org/10.1155/2016/4715681 |
| spellingShingle | Rafael A. Penchel José R. Bergmann Fernando J. S. Moreira Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics International Journal of Antennas and Propagation |
| title | Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics |
| title_full | Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics |
| title_fullStr | Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics |
| title_full_unstemmed | Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics |
| title_short | Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics |
| title_sort | shaping single offset reflector antennas using local axis displaced confocal quadrics |
| url | http://dx.doi.org/10.1155/2016/4715681 |
| work_keys_str_mv | AT rafaelapenchel shapingsingleoffsetreflectorantennasusinglocalaxisdisplacedconfocalquadrics AT joserbergmann shapingsingleoffsetreflectorantennasusinglocalaxisdisplacedconfocalquadrics AT fernandojsmoreira shapingsingleoffsetreflectorantennasusinglocalaxisdisplacedconfocalquadrics |