Estimation of Q-Factors and Resonant Frequencies

Published

March 1, 2003

Author(s)

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

Abstract

We estimate the quality factor Q and resonant frequency f_o 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 f_o 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 F_o. 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 f_o.

Citation

IEEE Transactions on Microwave Theory and Techniques

Volume

51

Issue

No. 3

Pub Type

Journals

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Keywords

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

Citation

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], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=151782 (Accessed October 10, 2025)