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Estimation of Q-Factors and Resonant Frequencies



Kevin J. Coakley, Jolene D. Splett, Michael D. Janezic, R F. Kaiser


We estimate the quality factor Q and resonant frequency fo of a microwave cavity based on resonance curve observations 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 fo and other associated model parameters by the method of weighted least squares (WLS). Based on asymptotic statistical theory, we also estimate the one-sigma uncertainty of Q and Fo. In a simulation study, the WLS method outperforms the 3-dB method and the Estin method. For real data, we show that the WLS method yields the most precise estimates. 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 and fo.
IEEE Transactions on Microwave Theory and Techniques
No. 3


cavity, experimental design, microwave, noise characterization, optimal frequency spacing, quality factor, resonance curve, resonant frequency


Coakley, K. , Splett, J. , Janezic, M. and Kaiser, R. (2003), Estimation of Q-Factors and Resonant Frequencies, IEEE Transactions on Microwave Theory and Techniques, [online], (Accessed April 16, 2024)
Created March 1, 2003, Updated February 17, 2017