Delta models of oscillatory structures and passband filters

Abstract

Introduction. Oscillatory circuits and resonant sections of transmission line (TL) are the basic signals frequency filtering structures. Oscillatory circuits belong to lumped oscillatory structures with one resonant frequency. A set of connected one-resonant oscillatory structures forms a structure with several resonant frequencies used in band-filtering. In various scientific and technical areas the approach based on $\delta$-functions is widely used for simulation. In the presented paper the approach based on $\delta$-models expand on oscillatory structures and bandpass filters.
Delta-models of oscillatory structures. Models of oscillatory circuits and resonant TL sections as impedance resonant δ -inhomogeneities are proposed. These models are called δ-models. It is shown that resonant δ-barrier is equivalent to series oscillatory circuit and resonant δ-well - to parallel oscillatory circuit. Resonance δ-inhomogeneities are characterized by three parameters - direction determining the resonance nature (series or parallel), its own resonant frequency and parameter directly proportional to the quality factor.
Comparison of TL resonant section and δ-model characteristics. TL section and δ-model frequency characteristics are compared. It is shown that with increasing of the difference between transmission line and section impedances section characteristic approaching δ-model characteristic.
Delta models of coupled resonant structures. Delta-models of coupled oscillatory circuits are presented. Comparison of transmission coefficient of two coupled δ-models with frequency response of two identical coupled circuits illustrate their accordance.
Delta models of bandpass filters. Delta-models of bandpass filter formed by series and parallel oscillatory circuits are presented. Delta models simplify filter analysis and for the filter with quarter-wave links between oscillatory structures allow finding a solution with fewer quality factor values and lower quality factor maximum, which simplifies filter design.
Conclusion. The proposed δ-models of oscillatory structures in the form of resonant impedance δ-heterogeneities allows to simulate single lumped and distributed oscillatory structures, coupled oscillatory structures, and also filters on their basis. Delta models simplify the analysis of oscillatory structures and filters and, as in the case of reactive elements δ-models, "prompt" new filter solutions; in the case considered with improved constructive parameters.