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Formula for Mean and Extreme Values of Profiling Functions in Synthesis Problems

  • TO THE 75th ANNIVERSARY OF MIREA—RUSSIAN TECHNOLOGICAL UNIVERSITY
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Abstract

In this paper, we propose a new approach different from the traditional for the problems of synthesizing layered dielectric filters (LDFs) and antireflection systems, which is based on the concept of using ideals for the profiling functions of layered homogeneous dielectric systems (LDSs) obtained from ideals for energy reflection or transmission coefficients of the required filter. We substantiate a significant development of our previously proposed mathematical apparatus, taking into account the fundamental restrictions on the permissible values of the impedances of the layer materials, which are common for setting and solving synthesis problems. For the first time, formulas for calculating the average and extreme values of the numerator and denominator of the energy reflection coefficient, which characterize the spectral indicators of the designed systems, are substantiated. In addition, attention is, for the first time, drawn to the qualitative “heterogeneity” of the parameters of the parallelepiped of constraints in the impedance space, which is of fundamental importance in solving optimization problems of synthesis.

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Notes

  1. As in [1], functions \(\tilde {R}\left( \kappa \right)\) and \(\tilde {T}\left( \kappa \right)\) are called ideals for the corresponding spectral characteristics physically realized by a specific filter.

  2. The name of computational parameters is motivated by the fact that the most important properties of the LDS generating functions are analytically expressed through them.

  3. The exponential representation of the numerator and denominator of the LDS reflection coefficient was guessed in [5] and changed and substantiated in [3].

  4. We are dealing with two families of computational parameters: for the numerator \(\left( {{{j}_{0}} = 1} \right)\) and denominator \(\left( {{{j}_{0}} = 0} \right)\) in the representation of the \({\mathbf{J}}\) vector for Fourier coefficients \(C_{s}^{{\left( 0 \right)}}\), where \({{j}_{0}} = s\). Families differ in sign \({{( - 1)}^{{{{j}_{0}}}}}\) in their expressions. We will point to this.

  5. As in [3], the \(\left( {ijkl} \right)\) and \(\left( {\overline {ijkl} } \right)~\) substitution symbols are used to shorthand the inequalities: \(\alpha _{i}^{2} < \alpha _{j}^{2} < \alpha _{k}^{2} < \alpha _{l}^{2}\) valid for interior points of 𝒫2 faces.

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Authors and Affiliations

  1. Russian Technological University (MIREA), 119454, Moscow, Russia

    Yu. I. Khudak, D. V. Parfenov & A. I. Starikovskii

Authors
  1. Yu. I. Khudak
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  2. D. V. Parfenov
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  3. A. I. Starikovskii
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Correspondence to Yu. I. Khudak.

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Translated by A. Ivanov

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Khudak, Y.I., Parfenov, D.V. & Starikovskii, A.I. Formula for Mean and Extreme Values of Profiling Functions in Synthesis Problems. J. Commun. Technol. Electron. 67, 1327–1336 (2022). https://doi.org/10.1134/S1064226922110043

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