Singly split single ring resonator: Fitting of lumped-element circuit model parameters and some aspects of resonator analysis and design

In this article, a method is proposed to accurately estimate the fundamental resonance frequency of a singly split single resonator based on an equivalent circuit model. A database of several hundred resonators with resonance frequencies from 300 GHz to 1 THz was considered, and their fundamental resonance frequencies were determined using COMSOL software. Dependencies known from the literature that define the parameters of a circuit model of this resonator have been verified, and it has been shown that for planar resonators considered in this paper, these dependencies may lead to large errors. Different relationships defining resonator inductance and gap and surface capacitances were compared. It is shown that the use of Palmer’s formula is necessary for the correct determination of the gap capacitance. A formula for determining the surface capacitance is proposed. It has been optimized by introducing one parameter. As a result, an equation allowing for the precise determination of the resonance frequency of planar resonators was obtained. Next, statistical tests were performed and statistical measures were determined to describe the study sample. For the planar resistors in the considered dataset, the maximum relative percentage error in determining the resonant frequency was 4.25%, and the mean and median errors were about 1%. For the planar resonators not included in the dataset with a fundamental resonant frequency in the 1 GHz–5 THz range, a maximum error of 3.82% and a median error of less than 1.5% were obtained. In addition, the differential sensitivity was found to identify the local effect of changing resonator dimensions on the resonant frequency. A numerical method was also developed to size the resonator to the required resonant frequency.