Analysis of an arbitrary profile reflector antenna having resistive-type surface — H-polarization case

Abstract

A regularization-based numerical solution is obtained for arbitrary-shape conic section profile reflector antenna in 2-D, for the H-polarization case. New point is that the reflector surface is assumed a resistive-type material. The problem is treated by reducing the singular integral equation obtained from the boundary condition to the dual series equations and application of the Riemann Hilbert Problem (RHP) technique. The resulting matrix equation has regularized form. Sample numerical results are obtained for various values of the eccentricity of the conic section contour of reflector and the resistivity of its surface. INTRODUCTION:Reflector antennas have originally 3-D geometry but sometimes nearly 2-D cylindrical reflectors are also used in practice; besides, these 2-D reflectors can be considered as canonical shapes to validate the numerical analysis methods. In real applications large dishes are mostly used and can be simulated by high-frequency ray-tracing techniques like GTD, UTD, PO and PTD. However, these techniques do not produce a single solution valid in all directions. Still they are erroneous in the caustic and transition regions. In the simulations of 2-D reflectors, Wiener-Hopf method based analytical treatment has been applied and certain asymptotic results have been obtained in [1], however they have a limited validity. On the other hand purely numerical techniques can also be applied to the reflector antenna problems. Method-of-Moments (MoM) with local basis functions is a standard tool in electromagnetics, however it is efficient only for small or medium size single-reflector geometries. Moreover, MoM does not guarantee the accuracy and the convergence of the performed numerical solution.An alternative for the same 2-D reflector antenna problem is the method of analytical regularization (MAR) [2]. With MAR, a part of the full-wave operator is inverted analytically and the resulting operator equation having favorable features is solved numerically. RHP based solutions are examples of the MAR. In [3], RHP based solutions were built for the analysis of the circular-strip 2-D reflector antenna problems for the both polarizations. These RHP based solutions provide fast convergence and easily controlled accuracy. In [4] and [5], the conic-section-profile reflectors excited by complex-source-point (CSP) feeds were analyzed and the regularized solutions were obtained. Similar MAR-type algorithms have been also proposed based on different techniques. For example, projection on Chebyshev polynomials and Jacobi polynomials was suggested in [6] and [7], respectively. However these papers did not present reliable numerical data for arbitrary profiles; nor they attacked electrically larger geometries. A different numerical approach is based on the Nystrom-type interpolation techniques, which are efficient for large reflectors up to quasioptical size and multi-reflector configurations [8][9][10]. In all above mentioned studies the solutions have been performed only for perfectly electric cond...