Abstract
Thermal noise is a limit to precision measurement in many fields. The relationship of the quality factor of mechanical systems to the thermal noise has compelled many researchers to search for materials with low mechanical losses. Typical measurements of mechanical quality factor involve exciting a mechanical resonator and observing the exponential decay of the amplitude under free oscillations. Estimation of the decay time allows one to infer the quality factor. In this article, we describe an alternative technique in which the resonator is forced to oscillate at constant amplitude, and the quality factor is estimated by measuring the drive amplitude required to maintain constant oscillation amplitude. A straightforward method for calibration of the quality factor is presented, along with an analysis of the propagation of measurement uncertainties. Such a technique allows the quality factor to be measured continuously in real time and at constant signal to noise ratio.
Highlights
Thermal noise is of particular importance in mechanical systems used in precision measurement applications, such as gravitational-wave detection,1 optical clocks,2 and micromechanical resonators
The measurement precision of such systems is often limited by thermal fluctuations of the mechanical components
The quality factor of a mechanical system characterizes the tendency for the system to maintain energy under free oscillations
Summary
Thermal noise is of particular importance in mechanical systems used in precision measurement applications, such as gravitational-wave detection, optical clocks, and micromechanical resonators. The measurement precision of such systems is often limited by thermal fluctuations of the mechanical components. According to the fluctuation-dissipation relationship, the noise spectral density of thermal fluctuations scales inversely with the quality factor.4,5 Researchers in these fields extensively studied the quality factor of various materials used in these experiments.. The energy supplied to the resonator to maintain fixed amplitude oscillation must be equal to the energy dissipated; the drive amplitude provides a measure of the mechanical loss. Using a self resonating circuit in an open-loop configuration has been shown previously.16 This technique is similar to the one used in non-contact atomic force microscopy where a cantilever is set to resonate at constant amplitude, and shifts of the cantilever resonant frequency as the cantilever position is scanned over a structure are used to construct an image of the structure.. Using a self resonating circuit in an open-loop configuration has been shown previously. In addition, this technique is similar to the one used in non-contact atomic force microscopy where a cantilever is set to resonate at constant amplitude, and shifts of the cantilever resonant frequency as the cantilever position is scanned over a structure are used to construct an image of the structure. the analysis of loop response, calibration into physical parameters, and noise characteristics of the dissipation signal have not before been presented in the literature
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