The possibility of forming a set of spatially dispersed and mutually orthogonal beams in an array antenna has been known long ago. The method for obtaining a device that forms a fan of beams for arrays with the number of elements and beams equal to N = 2p was suggested by Butler. Realizing a fan of mutually orthogonal beams for arrays with any N, was shown by us in "Synthesis of pattern forming networks" Radio Engineering and Electronic Physics, vol. 27, no. 7, pp. 28-35, 1982. The schemes of the corresponding devices for N = 5, 6 and 8 were also represented, however, the method for building a concrete scheme was described there without details. The present paper is dedicated to the procedure of synthesizing a beam-forming device based on the factorization of its transmission matrix, at this point, each factor represents a matched and decoupling hybrid. As a result, the beam-forming network is represented by a cascade connection of elementary matrices containing one hybrid or several 90° phase shifters. The procedure is illustrated using examples of synthesizing matrices for N = 8 and N = 9 having broadside beams, and also that for N = 6 where the left and right beams are symmetrical as normally assumed for "Butler" matrices. Furthermore, the scheme with N = 8 is compared with the corresponding "Butler" matrix.
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