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Within the context of elementary mathematical model a nonlinear synthesis problem of flat equidistant antenna array at the given requirements to the amplitude directivity pattern is investigated. It is shown, that for the problems of this class the nonuniqueness and branching of solutions, dependent on physical parameters of the array is characteristic. The justified algorithms of finding the branching lines of solutions and optimum synthesized amplitude directivity pattern are stated. A numerical example of synthesis of two-beam amplitude directivity pattern is given.

flat antenna array; synthesis; amplitude directivity pattern; non-uniqueness and branching of solutions; lines of branching