An iterative curve fitting method for accurate calculation of quality factors in resonators

A new method for eliminating the noise effect in interpreting the measured magnitude transfer characteristic of a resonator, in particular in extracting the Q-factor, is proposed and successfully tested. In this method the noise contribution to the measured power spectral density of resonator is iteratively excluded through a sequence of least-square curve fittings. The advantage of the presented method becomes more tangible when the signal to noise power ratio (SNR) is close to unity. A set of experiments for a resonant cantilever vibrating at different amplitudes has shown that when SNR is less than 10, the calculation results of conventional methods in extracting the Q-factor, i.e., the 3 dB bandwidth and single least-square curve fit, exhibit significant deviations from the actual Q-factor, while the result of the proposed iterative method remains in 5% margin of error even for a SNR of unity. This method is especially useful when no specific data is available about the measurement noise, except the assumption that the noise spectral density is constant over the measured bandwidth.