Measurement of Resonant Frequency and Quality Factor of Microwave Resonators: Comparison of Methods

TL;DR

This paper compares seven methods for accurately determining the resonant frequency and quality factor of microwave resonators, finding that nonlinear least-squares fitting techniques perform best under different noise conditions.

Contribution

It systematically evaluates and compares seven methods for measuring resonant frequency and quality factor, identifying the most accurate approaches depending on noise levels.

Findings

Nonlinear least-squares fit to phase vs. frequency is most accurate with high SNR.

Lorentzian fit is better for noisier data.

Results are broadly applicable to various resonant phenomena.

Abstract

Precise microwave measurements of sample conductivity, dielectric, and magnetic properties are routinely performed with cavity perturbation measurements. These methods require the accurate determination of quality factor and resonant frequency of microwave resonators. Seven different methods to determine the resonant frequency and quality factor from complex transmission coefficient data are discussed and compared to find which is most accurate and precise when tested using identical data. We find that the nonlinear least-squares fit to the phase vs. frequency is the most accurate and precise when the signal-to-noise ratio is greater than 65. For noisier data, the nonlinear least squares fit to a Lorentzian curve is more accurate and precise. The results are general and can be applied to the analysis of many kinds of resonant phenomena.