Estimation of Q-factors and resonant frequencies

We estimate the quality factor Q and resonant frequency f₀ of a microwave cavity based on observations of a resonance curve on an equally spaced frequency grid. The observed resonance curve is the squared magnitude of an observed complex scattering parameter. We characterize the variance of the additive noise in the observed resonance curve parametrically. Based on this noise characterization, we estimate Q and f₀ and other associated model parameters using the method of weighted least squares (WLS). Based on asymptotic statistical theory, we also estimate the one-sigma uncertainty of Q and f₀. In a simulation study, the WLS method outperforms the 3-dB method and the Estin method. For the case of measured resonances, we show that the WLS method yields the most precise estimates for the resonant frequency and quality factor, especially for resonances that are undercoupled. Given that the resonance curve is sampled at a fixed number of equally spaced frequencies in the neighborhood of the resonant frequency, we determine the optimal frequency spacing in order to minimize the asymptotic standard deviation of the estimate of either Q or f₀.