Drive level dependency in quartz resonators

Patel, Misaal; Yong, Yook‐Kong; Tanaka, Masako; Imai, T.

doi:10.1109/freq.2005.1574036

Cited by 16 publications

(11 citation statements)

References 5 publications

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“…Drive level dependency [7] has been well studied for quartz resonators and is believed to result (ignoring heating effects) from a nonlinearity in the elastic modulus in the crystal. This nonlinearity can be described with an additional term in the standard electrical harmonic oscillator equation: (1) where β describes the degree of third-order nonlinear behavior of the elastic modulus.…”

Section: A Operation Near a Bifurcation Pointmentioning

confidence: 99%

UHF quartz MEMS oscillators for dynamics-based system enhancements

Kubena

Kirby

Yong

et al. 2013

2013 Joint European Frequency and Time Forum &Amp; International Frequency Control Symposium (EFTF/IFC)

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Processes for fabricating full wafers of UHF quartz MEMS oscillators bonded to Si have been developed at HRL over the past several years. These devices have shown state-of-the-art noise and stability along with extremely small vacuum packaged die size of less than 3 mm 2 . An interesting by-product of the high frequency, small size, and wafer-scale fabrication of these devices is that several novel dynamics-based enhancements can be considered. These include the use of nonlinear dynamics for reducing oscillator phase noise at CMOS capable voltages and co-integration with more complex structures for sensing vibration and serving as a local timing reference for reducing thermally-induced sensor drifts. Several of these novel concepts made possible by wafer-scale MEMS-based processing will be reviewed.

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Section: A Operation Near a Bifurcation Pointmentioning

confidence: 99%

UHF quartz MEMS oscillators for dynamics-based system enhancements

Kubena

Kirby

Yong

et al. 2013

2013 Joint European Frequency and Time Forum &Amp; International Frequency Control Symposium (EFTF/IFC)

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“…Consequently we can substitute the first equation of (6) into (8) and assume that boundary conditions are already satisfied. The resulting equation is multiplied respectively by each eigen-mode and integrated through the thickness to obtain two coupled nonlinear ordinary differential equations of motion: …”

Section: B Coupled Nonlinear Equations Of Motionmentioning

confidence: 99%

“…These nonlinearities in quartz resonators are exhibited in well documented phenomena such as their frequency-temperature [2,3], acceleration sensitivity [4,5] and drive level dependency [6,7,8].…”

mentioning

confidence: 99%

Resonator Q increase and noise reduction in third overtone thickness shear resonators

Yong

2012

2012 IEEE International Frequency Control Symposium Proceedings

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Ultra high frequency resonators have higher noise levels due to their greater miniaturization and higher power density. This paper investigates a new method using nonlinear acoustic coupling for improving the resonator Q and hence reducing noise levels in third overtone thickness shear resonators. For trapped energy resonators such as the AT-cut quartz resonators the fundamental and third overtone thickness shear modes are well behaved. At high drive levels, the fundamental mode may be described by a Duffing equation that has a nonlinear cubic term in displacement. This cubic term in displacement has a third overtone thickness shear frequency component that could be used to improve the Q of third overtone thickness shear resonator.The coupling of the Duffing equation for the fundamental thickness shear mode to the third overtone thickness shear mode was solved using a MATLAB Simulink model. At higher drive levels, the mechanical nonlinearities of the fundamental mode will drive the third overtone thickness shear mode if its resonant frequency is sufficiently close to three times the fundamental thickness shear frequency. This nonlinear coupling will improve the Q of the third overtone thickness shear mode by as much as 15-fold. The Q increase is dependent on (1) frequency matching of the third overtone mode to three times the fundamental mode, (2) the drive level of the fundamental mode, and (3) the relative phase of the fundamental drive to the third overtone drive.

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“…Meantime, Wang and Wu studied nonlinear Mindlin plate equations by numerical methods such as finite difference method [14]. Patel and Yong also employed finite element method based on equations of nonlinear three-dimensional piezoelectricity to analyze well-known drive level dependence (DLD) phenomenon in quartz crystal resonators [15]. As earlier efforts in study the nonlinear effect on the vibrations of piezoelectric plates, Yang has established two-dimensional plate equations for the extension and flexure of relatively thin electroelastic plates under strong electric fields [16].…”

Section: Introductionmentioning

confidence: 99%

Solutions of nonlinear thickness-shear vibrations of an infinite isotropic plate with the homotopy analysis method

et al. 2011

Numer Algor

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As a preliminary attempt for the study on nonlinear vibrations of a finite crystal plate, the thickness-shear mode of an infinite and isotropic plate is investigated. By including nonlinear constitutive relations and strain components, we have established nonlinear equations of thickness-shear vibrations. Through further assuming the mode shape of linear vibrations, we utilized the standard Galerkin approximation to obtain a nonlinear ordinary differential equation depending only on time. We solved this nonlinear equation and obtained its amplitude-frequency relation by the homotopy analysis method (HAM). The accuracy of the present results is shown by comparison between our results and the perturbation method. Numerical results show that the homotopy analysis solutions can be adjusted to improve the accuracy. These equations and results are useful in verifying the available methods and improving our further solution strategy for the coupled nonlinear vibrations of finite piezoelectric plates.

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Drive level dependency in quartz resonators

Cited by 16 publications

References 5 publications

UHF quartz MEMS oscillators for dynamics-based system enhancements

UHF quartz MEMS oscillators for dynamics-based system enhancements

Resonator Q increase and noise reduction in third overtone thickness shear resonators

Solutions of nonlinear thickness-shear vibrations of an infinite isotropic plate with the homotopy analysis method

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