Quality Factor Maximization Through Dynamic Balancing of Tuning Fork Resonator

Zotov, Sergei A.; Simon, Brenton R.; Prikhodko, Igor P.; Trusov, Alexander A.; Shkel, Andrei M.

doi:10.1109/jsen.2014.2314614

Cited by 53 publications

(20 citation statements)

References 22 publications

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“…The quality factor is a dimensionless parameter that indicates the energy losses within a resonant element. In general, energy dissipation in vibratory MEMS is governed by several mechanisms, including viscous damping, dissipation through the substrate, thermo-elastic dissipation, and resonator surface effects [14]. The quality factor indicates energy loss relative to the amount of energy stored within the system.…”

Section: Governing Equationsmentioning

confidence: 99%

Stochastic Stability of a Class of MEMS-Based Vibratory Gyroscopes under Input Rate Fluctuations

Bognash

Asokanthan

2018

Vibration

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The influence of stochastic fluctuations in the input angular rate of a class of single axis mass-spring microelectromechanical (MEM) gyroscopes on the system stability is investigated. A white noise fluctuation is introduced in the coupled 2-DOF model that represents the system dynamics for the purposes of stability prediction. Numerical simulations are performed employing the resulting set of stochastic differential equations (SDEs) that govern the system dynamics. The SDEs are discretized using the higher-order Milstein scheme for numerical computations. Simulations via the Euler scheme, as well as the measure of the largest Lyapunov exponent are employed for validation purposes due to a lack of similar analytical solutions or experimental data. Responses have been predicted under different noise fluctuation magnitudes and different input angular rates for stability investigations. A parametric study is performed to estimate the noise intensity stability threshold for a range of quality factor values at different input angular rates. The predicted results show a nonlinear dependence of the threshold on the quality factors for different input rates. Under typical gyroscope operating conditions, a realistic frequency mismatch appears to have insignificant influence on system stability. It is envisaged that the present quantitative predictions will aid improvements in performance, reliability, and the design process for this class of devices.

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Section: Governing Equationsmentioning

confidence: 99%

Stochastic Stability of a Class of MEMS-Based Vibratory Gyroscopes under Input Rate Fluctuations

Bognash

Asokanthan

2018

Vibration

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“…In the experimental results presented in this paper, an identical tuning voltage magnitude was applied to both proof masses simultaneously. Alternatively, an asymmetric tuning voltage could be used for the purpose of dynamically balancing the structure, as described in [19]. Thermal compensation by differential FM also applies to the scale factor.…”

Section: Thermal Compensation Against Temperaturementioning

confidence: 99%

High Quality Factor Resonant MEMS Accelerometer With Continuous Thermal Compensation

et al. 2015

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We report a new silicon MEMS accelerometer based on differential Frequency Modulation (FM) with experimentally demonstrated thermal compensation over a dynamic temperature environment and µg-level Allan deviation of bias. The sensor architecture is based on resonant frequency tracking in a vacuum packaged SOI tuning fork oscillator. To address drift over temperature, the MEMS sensor die incorporates two identical tuning forks with opposing axes of sensitivity. Demodulation of the differential FM output from the two simultaneously operated oscillators eliminates common mode errors and provides an FM output with continuous thermal compensation. The first SOI prototype with quality factor of 350,000 was built and characterized over a temperature range between 30 • C and 75 • C. Temperature characterization of the FM accelerometer showed less than a 0.5 % scale-factor change throughout a temperature range from 30 • C to 75 • C, without any external compensation. This is enabled by an inherently differential frequency output, which cancels common-mode influences, such as those due to temperature. Allan deviation of the differential FM accelerometer revealed a bias instability of 6 µg at 20 s, along with an elimination of any temperature drift due to increases in averaging time. After comparing the measured bias instability with the designed linear range of 20 g, the sensor demonstrates a wide dynamic range of 130 dB. A second design iteration of the FM accelerometer, vacuum-sealed with getter material, was created to maximize Q-factor, and thereby frequency resolution. A Q-factor of 2.4 million was experimentally demonstrated, with a time constant of greater than 20 minutes. have achieved this level of performance for targeting and inertial applications, through the use of temperature post-compensation algorithms. A few examples include Northrop Grumman Corporation's NGC (USA) SiAc [1], Colibrys' (Switzerland) RS9010 [2], [3], Georgia Institute of Technology (USA) [4], University of Southampton, (UK) [5], and Institute for Nanostructures (Portugal), Univ. of the British Columbia (Canada), Delft University of Technology (The Netherlands) [6]. Conventional micromachined pendulous accelerometers rely on Amplitude Modulation (AM) of the input stimulus, where the inertial input produces a proportional change in the sensor output voltage. In other words, the inertial input is amplitude modulated. In this approach, the final output signal of the sensor is proportional to the true input, as well as a number of device parameters, including the stiffness of the springs, pick-up electronics gain, and so on. These additional factors contribute to the bias and scale factor of the sensor and require calibration to eliminate their influence. Variation of these internal parameters with time and environment also produce unpredictable drifts in the sensor output, and as such, these analogue devices typically show poor long term and environmental stability. These types of accelerometers are typically limited in terms of in-run bias stab...

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“…There are also researchers investigating the effect of electrostatic forces on Q factors, but mostly for tuning fork resonators. For example, Zotov et al electrostatically tuning the reaction force at the anchors caused by fabrication imperfection to increase the Q factor of anti-phase driven tuning fork Micro-electromechanical Systems (MEMS) [35,36]. Cheng et al investigated the effect of polarization voltage on the measured Q factor of a multiple-beam tuning-fork gyroscope [37].…”

Section: Introductionmentioning

confidence: 99%

Influence of Electrostatic Forces on the Vibrational Characteristics of Resonators for Coriolis Vibratory Gyroscopes

Peng

Qiu

Pan

et al. 2020

Sensors

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The Coriolis Vibratory Gyroscopes are a type of sensors that measure angular velocities through the Coriolis effect. The resonator is the critical component of the CVGs, the vibrational characteristics of which, including the resonant frequency, frequency mismatch, Q factor, and Q factor asymmetry, have a great influence on the performance of CVG. The frequency mismatch and Q factor of the resonator, in particular, directly determine the precision and drift characteristics of the gyroscope. Although the frequency mismatch and Q factor are natural properties of the resonator, they can change with external conditions, such as temperature, pressure, and external forces. In this paper, the influence of electrostatic forces on the vibrational characteristics of the fused silica cylindrical resonator is investigated. Experiments were performed on a fused silica cylindrical resonator coated with Cr/Au films. It was shown that the resonant frequency, frequency mismatch, and the decay time slightly decreased with electrostatic forces, while the decay time split increased. Lower capacitive gaps and larger applied voltages resulted in lower frequency mismatch and lower decay time. This phenomenon was theoretically analyzed, and the variation trends of results were consistent with the theoretical analysis. This study indicates that, for fused silica cylindrical resonator with electrostatic transduction, the electrostatic influence on the Q factor and frequency, although small, should be considered when designing the capacitive gap and choosing bias voltages.

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Quality Factor Maximization Through Dynamic Balancing of Tuning Fork Resonator

Cited by 53 publications

References 22 publications

Stochastic Stability of a Class of MEMS-Based Vibratory Gyroscopes under Input Rate Fluctuations

Stochastic Stability of a Class of MEMS-Based Vibratory Gyroscopes under Input Rate Fluctuations

High Quality Factor Resonant MEMS Accelerometer With Continuous Thermal Compensation

Influence of Electrostatic Forces on the Vibrational Characteristics of Resonators for Coriolis Vibratory Gyroscopes

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