IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 1, JANUARY 2007 99 GO Shaping of Omnidirectional Dual-Reflector Antennas for a Prescribed Equi-Phase Aperture Field Distribution Fernando José da Silva Moreira, Member, IEEE, Aluizio Prata, Jr., Member, IEEE, and José Ricardo Bergmann, Member, IEEE Abstract—A formulation is presented for shaping dual-reflector antennas designed to offer an omnidirectional coverage. The shaping procedure is based on geometrical optics (GO) principles and assumes a uniform phase distribution for the aperture field. Two distinct dual-reflector arrangements, based on the axis-dis- placed Cassegrain (ADC) and ellipse (ADE) configurations, are investigated. The GO shaping results are validated using the accurate analysis provided by the method-of-moments technique. Index Terms—Omnidirectional antennas, reflector antennas, re- flector shaping. I. INTRODUCTION R EFLECTOR antennas are widely used in microwave and millimeter-wave communications and radar systems de- manding large data rates. This is a consequence of their high ef- ficiency capability, relative mechanical simplicity, and inherent broadband characteristics. All these features are ultimately re- lated to their quasi-optical operation behavior. Usually reflector antennas are designed for maximum directivities (as in point-to- point microwave links), but some attention has recently been de- voted to reflector arrangements providing omnidirectional cov- erage [1]–[9]. Among other uses, omnidirectional reflector an- tennas are useful as base-station radiators for point-to-multi- point radio links, such as local multipoint distribution services (LMDS). The work available in the literature covers both classical reflector arrangements (i.e., geometries whose reflectors are generated by conic sections) [2], [7]–[9] and shaped reflectors [1], [3]–[6]. However, no study has yet been devoted to the synthesis of highly-efficient omnidirectional dual-reflector antennas, which are achieved by means of a uniform aperture illumination. On this light, the objective of this work is to present a simple and efficient dual-reflector shaping procedure based on geometrical optics (GO) principles. This procedure can be used to obtain an aperture illumination with uniform Manuscript received October 5, 2005; revised September 5, 2006. This work was supported in part by CNPq, Brazil, under Projects 471750/2004-2 and 302749/2004-7, and in part by FAPERJ, Brazil, under Project E-26/171083/03. F. J. da Silva Moreira is with the Department of Electronics Engineering of the Federal University of Minas Gerais, 30161-970 Belo Horizonte, MG, Brazil (e-mail: fernandomoreira@ufmg.br). A. Prata, Jr., is with the Department of Electrical Engineering—Electro- physics, University of Southern California, Los Angeles, CA 90089-0271 USA. J. R. Bergmann is with the Center for Telecommunications Studies of the Catholic University, 22453-900 Rio de Janeiro, RJ, Brazil. Digital Object Identifier 10.1109/TAP.2006.888396 phase and polarization, and an arbitrary user-specified am- plitude, starting from a prescribed circularly symmetric feed radiation (and some other pertinent geometrical parameters). The arbitrariness of the aperture field amplitude allows the application of the present GO shaping procedure to geometries aiming at maximum antenna directivity (i.e., by choosing a uniform amplitude distribution) or low sidelobe levels (i.e., by implementing a tapered amplitude distribution). In the next section some basic geometrical features of om- nidirectional dual-reflector antennas are briefly discussed. In Section III we derive a GO shaping algorithm, suited for pro- ducing an equi-phase aperture field. In Section IV we present two case studies of omnidirectional dual-reflector configura- tions shaped for uniform aperture illumination and maximum directivity (according to GO principles). Two additional case studies are investigated in the subsequent section, this time with a tapered amplitude distribution imposed over the antenna aper- ture to reduce the radiated sidelobe levels. All case studies dis- cussed here are validated using accurate analyses based on the method of moments (MoM) technique, which accounts for all the electromagnetic effects present on the reflectors and feed structure. This work terminates with some brief conclusions. II. BASIC GEOMETRICAL FEATURES There are four different types of dual-reflector antennas ca- pable of providing omnidirectional coverages, but those based on the classical axis-displaced Cassegrain (ADC) and axis-dis- placed ellipse (ADE) seem to be the most appropriate ones for yielding compact arrangements [8]. Such axially-symmetric ar- rangements are depicted in Figs. 1 and 2, respectively, together with some pertinent geometrical parameters. Inspection of these figures indicate that the most relevant difference between the ADC- and ADE-like configurations is that the principal ray (i.e., the ray leaving the antenna system focus, point , along the symmetry axis and striking the subreflector at its vertex) meets the main reflector at its inner (outer) rim in the ADC (ADE) ar- rangement. The fundamental consequence of this is that, to a first order, the ADE-like reflector system provides a reversal of the feed illumination at the antenna aperture—a feature that can be successfully exploited by the antenna designer. Among the various antenna geometrical parameters, it is useful to single out in Figs. 1 and 2 the width of the antenna conical aperture, the main-reflector outer and inner projected diameters ( and , respectively), the subreflector pro- jected diameter , the distance from the reflector-system 0018-926X/$25.00 © 2007 IEEE