Measurement of resonant frequency and quality factor of microwave resonators: Comparison of methods

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 versus 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.