Interpolation-based modelling of microwave ring resonators
Date
2006-12
Authors
Schoeman, Marlize
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : University of Stellenbosch
Abstract
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 is
presented. The algorithm models multiple resonance frequencies of a microwave ring resonator
simultaneously by solving an eigenmode problem. To ensure a feasible solution when using the
Method 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 and
requires that the frequency dependence be addressed separately from other physical parameters.
One-dimensional adaptive rational Vector Fitting is used to identify and classify resonance
frequencies into modes. The geometrical parameter space then models the different mode frequencies
using 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 resonance
frequencies are lost during the frequency identification procedure.
A three-point rational interpolant function in the region of resonance is presented for the calculation
of loaded quality factors. The technique utilises the already known interpolant coefficients
of 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 direct
fit 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 model
is experimentally verified and comparative results to measurement predictions are shown. A
disadvantage of the method is that the technique cannot be applied to noisy measurement data
and that results become unreliable under low coupling conditions.
Description
Thesis (PhD (Electical and Electronic Engineering))--University of Stellenbosch, 2006.
Keywords
Adaptive interpolation-based modelling, Vector Fitting, Thiele-type continued fractions, Ring resonators, Resonant frequencies, Q-factors, Theses -- Electrical and electronic engineering, Dissertations -- Electrical and electronic engineering