Российский технологический журнал (Oct 2020)
Profiling functions application for layered dielectric filter synthesys problem statement
Abstract
A novel mathematical apparatus allowing formulation and justification of a new approach towards the setting of the mathematical problem of band-pass layered dielectric filters (LDF) synthesis is developed. Аrbitrary layered dielectric systems with piecewise continuous physical media parameters given by the functions of dielectric permittivity and of magnetic permeability, both depending on the coordinate along the normal to the layer pile, with fixed discontinuity points of at least one of the mentioned functions are examined. For such systems, an important conservation law for the difference of the squares of absolute amplitude values of plane waves propagating left and right in given layered medium is stated, which further leads to the traditional energy conservation law in lossless layered media. This new identity law allows turning from synthesis problems in terms of fractional rational energy reflectivity and transmittance of layered systems to equivalent tasks for profiling functions introduced in the work, representing only the numerator or only the denominator of the expressions usually considered in the synthesis. A new concept of the feasible ideal is introduced for the energy coefficients of reflection and transmission of layered systems. It is shown that the feasibility of the energy coefficients of reflection and transmission of layered systems is equivalent to the feasibility of the profiling functions of such systems, which together with the main identity allows a significant change of the existing LDF synthesis approach. The rule for converting the ideal of the reflection or transmission coefficient into the ideal of the profiling function is given. The proposed synthesis problem statement leads to considerably less intensive computational procedures.
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