Numerical method for solving of synthesis problems of radiating systems on a prescribed power directivity pattern

A numerical solution method is presented for nonlinear problems in radiator synthesis, based on a prescribed power directivity pattern (DP). A variational problem is considered in which both mean square deviation between the prescribed and synthesized DPs and constraints imposed on the norm of excitation sources are taken into account. An existence theorem is proved for quasi-solutions, and the corresponding Euler-Lagrange equation is derived to determine them. Convergence criteria are found, and the convergence of the iterative processes employed in computing the problem is proved. For a linear radiator, the theory of branching of solutions to nonlinear equations is invoked to determine the general solution structure used in the numerical analysis of the problem.