Synthesis of plane waveguide arrays taking into account mutual coupling of radiators

Mykhaylo I. Andriychuk; Mykhaylo R. Melnyk

doi:10.3103/S0735272721090028

Authors

Mykhaylo I. Andriychuk Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, Lviv; Lviv Polytechnic National University, Lviv, Ukraine https://orcid.org/0000-0001-9380-8807
Mykhaylo R. Melnyk Lviv Polytechnic National University, Lviv, Ukraine https://orcid.org/0000-0002-8593-8799

DOI:

https://doi.org/10.3103/S0735272721090028

Keywords:

plane rectangular array, analysis (direct) electrodynamic problem, synthesis (inverse) problem, variational statement, mutual coupling of radiators, numerical modeling

Abstract

The variational approach is used for solving the synthesis problem of plane rectangular array with waveguide excitation of its elements. The proposed functional includes three components that allow us to minimize the mean square deviation of the given and synthesized amplitude radiation patterns (RP), the value of the field amplitude in the given near zone regions, and the norm of excitation coefficients of the array elements. The mutual coupling of separate array radiators is taken into account solving the corresponding electrodynamic problem. The Hallen’s integral equation is used to determinate the current distribution in the array radiators. The optimal excitation coefficients of the radiators are determined minimizing the proposed functional, it is reduced to solving the nonlinear Euler integral equations system, since the amplitude radiation characteristics are the input data of the problem. The resulting system of nonlinear integral equations is solved efficiently by the method of successive approximations; the relaxation is its characteristic feature. The calculation results show that the developed approach can be used for arrays with different configurations, in particular with hexagonal placement of radiators.

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