Synthesis of antenna arrays with regard to the radiators mutual coupling and vector characteristics of electromagnetic fields


  • L. M. Pasnak Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, Ukraine
  • P. O. Savenko Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of National Academy of Sciences of Ukraine, Ukraine



The nonlinear synthesis problems of antenna arrays according to the given amplitude radiation pattern (RP) are solved by the method which regards the mutual coupling of radiators. The mutual coupling is taken into account by solving the boundary problem of the high-frequency electrodynamics on the multi-connected areas. The variational formulation of problems is considered. It is reduced to solving the nonlinear integral or matrix equations – the Euler equations. The numerical algorithm of solving for optimum generation minimization sequence, which weakly convergences to the point of the local minimum is developed. The branching of solutions in the case of linear vibrators synthesis, is investigated by the methods of nonlinear analysis [1]. The number of solutions to these problems and their qualitative characteristics are dependent on both the electrical size of the array and the properties of the given RP.


Chaplin, A.F. Analysis and Synthesis of the Antenna Arrays. Lvov 1987, 179 p.

Dmitriev, V.I.; Sereda, P.P. Mathematical models and method of the integral equation in the theory of the spiral antenna. Numerical Methods and Programming. Moscow: MGU, 1980.

Savenko, P.O. About existence solutions of the synthesis problem of the radiating system for the given amplitude RP. Mathematics Methods and Phys.-Mech. Fields, 1995, Vol. 38, p. 72-78.

Andriychuk, M.I.; Voitovich, N.N.; Savenko, P.A.; Tkachuk, V.P. The antenna synthesis according to the amplitude radiation pattern. Numerical Methods and Algorithms. Kiev: Naukova Dumka, 1993 [in Russian].