A new synthesis algorithm for shaped, double-reflector antennas with complex array feed is presented. The approach presented here aims to improve the efficiency of synthesis techniques without missing the required accuracy. The algorithm is based on a convenient splitting of the original problem into two phases, each one involving a sub-problem significantly simpler than the original one. A double reflector synthesis problem involving only Fourier Transform (FT) operators is of concern during the first phase. The subre- flector surface and a first estimate of the main reflector geometry are obtained in this step. A single reflector synthesis problem is considered during the second phase wherein the final main reflector surface and the excitation coefficients of the primary feed array are obtained. While in the first phase only approximate relationships between the unknowns and the secondary radiated field are exploited, in the second phase accurate radiation operators are involved. Despite this accuracy, the second phase is still numerically effective since it involves a single reflector synthesis problem and exploits, as "good" starting point, the main reflector estimate obtained during the first phase. The effectiveness of the approach is due to the fact that the necessity of dealing simultaneously with two reflector surfaces, the key of the synthesis difficulties, is afforded only during the first phase where efficient computational tools are allowed. A numerical example shows the effectiveness of the proposed approach.
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