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International Journal of Antennas and Propagation
Volume 2016 (2016), Article ID 4715681, 9 pages
Research Article

Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics

1Department of Electrical Engineering, Federal University of Technology-Paraná, 86300-000 Cornélio Procópio, PR, Brazil
2Center for Telecommunications Studies (CETUC), Catholic University of Rio de Janeiro, 22453-900 Rio de Janeiro, RJ, Brazil
3Department of Electronics Engineering, Federal University of Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil

Received 22 June 2016; Revised 20 November 2016; Accepted 4 December 2016

Academic Editor: Giuseppe Mazzarella

Copyright © 2016 Rafael A. Penchel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.