Modelization Methodology for the Quality Factor of Quarter-Wavelength n-Section Coaxial Stepped Impedance Resonators

Abstract

This paper proposes a method to develop an analytical model and/or numerical resolution of the quality factor of quarter-wavelength n-section coaxial stepped impedance resonators (SIRs). The topology is based on cascaded coaxial sections nested within each other. Thanks to the SIR effect, this type of geometrical arrangement offers practical degrees of freedom to modulate the size of the resonator in both longitudinal and transverse dimensions. Moreover, in an air-filled configuration, it provides interesting quality factor, although this depends on its shape factor at any given frequency. In this paper, we show the added value of using an analytical model or numerical resolution for the quality factor, to be able to optimize the topology. To demonstrate the advantages of this model and the numerical method, comparisons of two- and three-section coaxial SIRs at two different frequencies are proposed and discussed. To validate the analytical model and numerical resolution, the values are compared with ones obtained in eigenmodes <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ANSYS HFSS</i> with electromagnetic simulation tool.