Substantiation of the Use of Profiling Functions for Formulating Effective Problems of Synthesis of Layered Dielectric Filters

In this paper we supplement the problem statement of synthesis of layered dielectric filters considered in our previous studies and based on the ideas of P.L. Chebyshev. Fundamental constraints for such problems on layer materials admissible for synthesis are included. A mathematical apparatus that significantly simplifies the classical approach and computational procedures for such problems while maintaining the mathematical equivalence of the results was developed. For the first time, the broadest approach to the layered media theory is substantiated for the case of piecewise continuous dependence of the dielectric and magnetic permeability. The proposed formulation of the synthesis problem is shown to lead to much more economical computational procedures as compared to the previously known computational procedures, keeping all other important constraints on the synthesis problem unchanged.