Computer aided design of horn radiators for satellite communication by least squares optimization

Computer aided design optimization of corrugated horns became a powerful tool to reduce development costs on the one hand and to improve performance of space antennas on the other. In this paper the physical model is outlined, based on Maxwell's equations, and it is shown how a complete numerical simulation of a circular corrugated horn can be achieved, assuming that the interior geometry of the horn is known. In order to compute the electromagnetic properties of a horn, the so-called scattering matrix is assembled. This matrix is needed to relate mode amplitudes of reflected and transmitted waves in horn sections with different diameters. Envelope functions, determined by a few geometric design parameters, are used to describe the inner geometry of a horn. These parameters are applied to formulate a least squares optimization problem. As a starting point, an amplitude spectrum in the aperture has to be determined which radiates a given far field. The differences between those amplitudes and the amplitudes predicted by the model are to become as small as possible by adapting the design variables. Moreover, the return loss is to be minimized. The resulting least squares optimization problem can be solved by a standard sequential quadratic programming (SQP) code after a suitable transformation into a nonlinear programming problem, by which typical features of Gauss–Newton methods are retained. Some numerical results are included to show the successful application of the introduced advance to design a circular corrugated horn which radiates a given far field.