GO Synthesis of Offset Dual Reflector Antennas Using Local Axis-Displaced Confocal Quadrics

Aline R Assis,José R Bergmann,Fernando J S Moreira

doi:10.1590/2179-10742020v19i2813

Abstract

Abstract This work investigates an alternative numerical scheme for the solution of an exact formulation based on Geometrical Optics (GO) principles to synthesize offset dual reflector antennas. The technique is suited to solve a second-order nonlinear partial differential equation of the Monge-Ampere type as a boundary value problem. An iterative algorithm based on Newton's method was developed, using axis-displaced confocal quadrics to locally represent the subreflector surface, thus enabling an analytical description of the partial derivatives within the formulation. Such approach reduces discretization errors, as exact expressions for the mapping function and its derivatives are analytically determined. To check the robustness of the methodology, an offset dual-reflector Gregorian antenna was shaped to provide a Gaussian aperture field distribution with uniform phase within a superelliptical contour. The shaped surfaces were further interpolated by quintic pseudo-splines and analyzed by Physical Optics (PO) with equivalent edge currents to validate the synthesis procedure at 11,725 GHz.

Highlights

INTRODUCTIONLow sidelobes levels, and low cross-polarization are requirements desired in a wide variety of communication systems, as in satellite communications [1], radio astronomy, and radar [2]
High efficiency, low sidelobes levels, and low cross-polarization are requirements desired in a wide variety of communication systems, as in satellite communications [1], radio astronomy, and radar [2].An efficient way to achieve high performance is by shaping reflector antennas
The Geometrical Optics (GO) synthesis of dual-reflector antennas has been detailed examined by many authors [2], [5]

Summary

INTRODUCTION

Low sidelobes levels, and low cross-polarization are requirements desired in a wide variety of communication systems, as in satellite communications [1], radio astronomy, and radar [2]. Unlike [2], [5] and [6], which adopted iterative numerical procedures with finite differences to linearize the differential operator, [7] used axis displaced confocal quadrics to locally represent the offset reflector surface. Such approach reduced discretization errors associated to partial derivatives, since exact expressions of the mapping function and its derivatives were analytically determined in terms of the computed quadrics’ parameters.

VECTOR DIRECTION IN COMPLEX COORDINATES

GO SYNTHESIS

FORMULATION OF THE GO SHAPING PROCEDURE

NUMERICAL PROCEDURE

CASE STUDY

CONCLUSIONS