Interpolation-based modelling of microwave ring resonators

[摘要] Resonant frequencies and Q-factors of microwave ring resonators are predicted using interpolation-based modelling.A robust and efficient multivariate adaptive rational-multinomial combination interpolant ispresented. The algorithm models multiple resonance frequencies of a microwave ring resonatorsimultaneously by solving an eigenmode problem. To ensure a feasible solution when using theMethod of Moments, a frequency dependent scaling constant is applied to the output model.This, however, also induces a discontinuous solution space across the specific geometry andrequires that the frequency dependence be addressed separately from other physical parameters.One-dimensional adaptive rational Vector Fitting is used to identify and classify resonancefrequencies into modes. The geometrical parameter space then models the different mode frequenciesusing multivariate adaptive multinomial interpolation.The technique is illustrated and evaluated on both two- and three-dimensional input models.Statistical analysis results suggest that models are of a high accuracy even when some resonancefrequencies are lost during the frequency identification procedure.A three-point rational interpolant function in the region of resonance is presented for the calculationof loaded quality factors. The technique utilises the already known interpolant coefficientsof a Thiele-type continued fraction interpolant, modelling the S-parameter response of a resonator.By using only three of the interpolant coefficients at a time, the technique provides a directfit and solution to the Q-factors without any additional computational electromagnetic effort.The modelling algorithm is tested and verified for both high- and low-Q resonators. The modelis experimentally verified and comparative results to measurement predictions are shown. Adisadvantage of the method is that the technique cannot be applied to noisy measurement dataand that results become unreliable under low coupling conditions.

[发布机构] Stellenbosch University