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has been cited by the following article:

• TITLE: Non-Linear Synthesis Problems for Plane Radiating Systems According to the Prescribed Power Directivity Pattern

  AUTHORS: Mykhaylo Andriychuk, Petro Savenko, Myroslava Tkach

  KEYWORDS: Power Radiation Pattern; Synthesis Problem; Non-Linear Equation; Bifurcation of Solutions; Numerical Modeling

  JOURNAL NAME: Open Journal of Antennas and Propagation, Vol.1 No.2, September 24, 2013

  ABSTRACT: A variational formulation of the synthesis problem for plane radiating systems according to the prescribed power directivity pattern (DP) is considered. The function representing the mean-square deviation of the prescribed and synthesized power DPs and containing the additional term with squared norm of the current or field in the antenna aperture is considered as the criterion of optimization. Freedom to choose the phase DP is used to improve the proximity of the prescribed and synthesized DPs. In such formulation, the classes of non-linear problems, for which the non-uniqueness of solutions, their branching and bifurcation are characteristic, arise. The properties of solutions depend on the electric size of radiating system and prescribed power DP. From a practical point of view, the existence of different solutions creating the same or similar DPs, gives the opportunity to choose the solution that has a simpler implementation. The synthesis problems for plane radiating systems and plane arrays are considered.