# Scattering of Electromagnetic Waves by Frequency-Detuned Systems of Dielectric Resonators

## DOI:

https://doi.org/10.20535/RADAP.2024.96.5-13## Keywords:

scattering, detuned dielectric resonator, scattering matrix, bandpass filter, bandstop filter, elliptical filter, demultiplexer## Abstract

The general problem of scattering on a system of frequency-detuned coupled Dielectric Resonators (DRs) located in one or several transmission lines is considered. The field describing the natural oscillations of the system of detuned DRs is decomposed over the field of partial resonators. A system of equations is derived, the solution of which allows one to determine the frequencies and amplitudes of the system’s natural oscillations. It is shown that the resulting system of equations, by means of algebraic transformations, can be reduced to the problem of determining the eigenfunctions and eigenvalues of a finite-dimensional operator, determined through the elements of the coupling operator of frequency-detuned DRs. The limitations of the proposed calculation method are noted. The solution to the scattering problem is expanded in terms of the natural oscillation field of the system of detuned DRs. A system of linear equations for the amplitudes of forced oscillations is obtained. It is shown that in the particular case of identical resonator frequencies, the found system exactly coincides with the equations obtained previously for various types of DR. General solutions are found for the scattered field on frequency-detuned resonators located in different transmission lines. Several examples are given of calculating the frequency dependences of the scattering matrix for the most interesting structures consisting of coupled dielectric resonators detuned in natural oscillation frequencies. The frequency characteristics of the scattering of two bandstop filters with different stop bands, made on detuned DRs in the same transmission line, are calculated. The frequency dependences of the scattering matrix on two bandpass filters located parallel between regular lines are calculated. The scattering characteristics of bandpass filters of complex designs containing various DRs are calculated: a bandpass filter built on a system of coupled DRs in a transmission line break and several DRs in a regular line, as well as an elliptical bandpass filter. The capabilities of the proposed method are demonstrated by the example of optimizing the scattering characteristics of a demultiplexer built on the basis of two bandpass filters with different passband frequencies. The proposed method also makes it possible to calculate the scattering characteristics of bandpass and bandstop filters with several operating frequency bands used in modern communication systems.

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*Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia*, (96), pp. 5-13. doi: 10.20535/RADAP.2024.96.5-13.

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