MODELING OF BANDPASS FILTERS WITH ATTENUATION POLES USING PARALLEL COUPLING CHANNELS
Authors: Shevtsov Kostiantyn , Galitskiy Ilya 
Published: December 2024

Background. Microwave filters are critical components in modern communication systems, playing a fundamental role in signal processing by allowing specific frequency bands to pass while attenuating unwanted frequencies. Over the years, significant advancements have been made in the design and development of various types of microwave filters, including directional, microstrip, and multi-resonator filters. These filters are widely used in radar, satellite communications, and wireless networks, where high performance and precise frequency control are essential. 
Objective. This paper is dedicated to reviewing various microwave filters that were constructed developed or analysed by the team, including directional filters, microstrip filters with attenuation poles, and multi-resonator filters. The studies focus on investigating their unique properties, such as the formation of attenuation poles, metamaterial characteristics, and the effects of resonator coupling on filter performance. New Python-based software realization for modelling different filters six resonators, four resonators, and two resonators were developed and frequently used.
Methods. Electrodynamics simulations using software tools like CST Studio Suite, AWR Microwave Office, and LabVIEW, modelling filters using equivalent circuit models and bridge circuits. Use of microstrip lines, circular resonators, and dielectric resonators to construct and analyse different filter configurations. Analysis of energy propagation paths, resonator coupling, and transmission characteristics to optimize filter design.
Results: Various structures were researched like Microwave Directional Filters, Microstrip Resonator Filters with 2, 4, 6 resonator, their structures and characteristics were analysed, New python-based software that allows modelling resonance curves using corresponding parameters for filters with 2, 4, 6 resonators. The parameters of the scattering matrix of a bridge quadrupole were expressed in an analytical form and were used for Python based program.
Conclusions: the research presented across these publications contributes significantly to the development and understanding of advanced microwave filter designs. The article reveals various resonator-based filters, including directional, microstrip, and multi-resonator filters, these studies have highlighted key performance enhancements achievable through resonator coupling, metamaterial properties, and the introduction of attenuation poles. The use of advanced simulation tools, such as CST Studio Suite, AWR Microwave Office, and LabVIEW, allowed for accurate modelling and validation of theoretical designs. The introduction of Fano resonances and trapped modes in filters demonstrated improvements in selectivity and attenuation characteristics, which are critical for modern communication systems. Trapped modes manifest as attenuation poles, resulting from the interference of even and odd oscillations. This is evidenced by the presence of two independent energy pathways, along which these interfering oscillations propagate. With appropriate design parameters (such as resonator coupling coefficients and resonance frequencies), a complete energy exchange between resonators can occur at a certain frequency, in a direction perpendicular to the primary energy flow from input to output. The design and properties of directional filters based on circular resonators and dielectric resonators were described. These filters have "metamaterial" properties and are widely used in modern microwave technology. The characteristics of bandpass and rejector filters, as well as the characteristics of the filters formed by two microstrip resonators and resonators connected to each other, are given. It is important to emphasize the phenomena of "Fano resonances" observed in these filters, which arise as the interference of oscillations from individual resonators.