Optimized Design of High-efficiency Rectangular Horns for Arrays

A method is described for designing high-efficiency rectangular horns that results in more compact horns than those obtained by using conventional linear tapers or steps. Results are presented for horns suitable for array feed or directly radiating array applications that show an aperture efficiency greater than 90% can be achieved over a 5% bandwidth with horns of aperture size ranging from 1.25 to 3 wavelengths and at the same time have a return loss > 20dB and cross-polar isolation > 22dB. INTRODUCTION Horn antennas are used in directly radiating arrays and also in array feeds for reflector and lens antennas. In directly radiating arrays it is highly desirable that the array elements have high aperture efficiency to maximize the gain for a given number of array elements. Similarly, high efficiency array feeds are important to give good illumination efficiency for shaped beams so as to maximize the edge-of-coverage gain. In this application the feed apertures are usually of small size to fit in the limited space and must have high efficiency over the operating frequency band to give the required illumination taper. Further, for satellite applications, these elements should be also as compact as possible for low ohmic loss and weight. Possible array feed elements include multimode horns (Bird [1], Bhattacharyya & Goyette [2]), partially dielectricloaded horns (Tsandoulas & Fitzgerald [3], Lier et al. [4]), stepped circular horns (eg Kitsuregawa [5]) and circular ‘scrimphorns’ (Wolf [6]). In this paper we concentrate on rectangular horns, which are often used to make the best use of the array aperture real estate. The methodology used to date to design high-efficiency rectangular horns is based on the observation that maximum gain is achieved with uniform aperture phase distribution if the aperture amplitude is also uniform and unidirectional. As a result horns have been designed employing predominantly TEm0 (m=1,3) modes with approximate amplitude of 1/m (Silver [7], Bhattacharyya & Goyette [2]). Efficiencies in excess of 90% can be achieved by this approach, compared with a maximum of about 80% for conventional horns. However, both conventional and dual-mode horns are relatively long due to the linear taper from the waveguide input to the waveguide step that excites the TE30 mode. Dielectric-loaded horns can have efficiencies approaching 100%, but weight and materials selection become additional considerations especially in space-borne applications. The purpose here is to describe a design method for rectangular horns that achieves the highest possible efficiency over a specified frequency band by optimizing the profile of the horn. In addition, the aim is to reduce the length of the taper from the waveguide input. The approach used is an extension of the method we described in [8] for designing corrugated horns. By this method, compact rectangular horns with efficiencies in excess of 90% can be produced. METHODOLOGY The aim is to optimize the profile of a rectangular horn to maximize efficiency over a specified frequency band while simultaneously minimizing input reflection, cross-polarization and length. Aperture efficiency is defined as the ratio of the maximum directivity to the directivity of a uniformly illuminated aperture, which for a rectangular horn is 4πA/λ, where A is the aperture area and λ is the wavelength. Bouwkamp and de Bruijn [9] showed that there is no theoretical limit to the directivity of an aperture of any given size if the aperture distribution is unconstrained. Although it is possible to achieve efficiencies in excess of 100% over a narrow frequency range, ohmic and implementation losses tend to reduce efficiency below this level. A method has been developed for rectangular horns that synthesizes the profile of the horn to meet a specified efficiency and input return loss. The method is based on a simple representation of the horn profile, an optimization technique and a mode-matching method for analyzing the horn. The profile of the smooth-