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This paper reports a precision mode-localized accelerometer operating in a higher-order flexural mode. The accelerometer consists of two symmetric resonators coupled by a central rigid coupler to generate an ultra-weak coupling factor. A reduced noise floor is observed when the resonators operate in the higher-order flexural mode compared to the basic lower-order mode. The mode-localized accelerometer working in the fifth-order mode demonstrates an input-referred bias instability of 130 ng and noise floor of 85 ng/ $\surd $ Hz, which are the best results obtained for accelerometers employing the mode localization paradigm to date. These results indicate that the performance of the mode-localized sensors can be improved by operating at a higher working frequency if the coupling factor and quality factor do not drop significantly. [2020-0365]

Bulk acoustic wave gyroscopes have been researched for potential benefits such as immunity to shock and vibration and the high Q factors achievable with the bulk modes. This paper outlines an approach to address mode matching in bulk acoustic wave (BAW) disk gyroscopes using electrostatic frequency tuning. Electrostatic frequency tuning is achieved by varying the potential difference between the body of the resonator and electrodes surrounding the disk resonator. Tuning of the frequencies of both drive and sense modes is demonstrated in this work as a means to achieving mode matching. The experimental results are also compared to COMSOL simulations reporting mode matching.

This paper reports on the experimental characterization of a vacuum packaged bulk acoustic wave disk gyroscope with T-shape anchors fabricated on a (100) single-crystal silicon substrate. Improvements in key device performance parameters are achieved by implementing mode matching using electrostatic frequency tuning to decrease the frequency split between two near-degenerate bulk acoustic modes from 4 Hz to 0.4 Hz. Gyroscopic operation is demonstrated by driving one of the secondary degenerate elliptical modes while sensing the response in the other elliptical mode, both demonstrating quality factors exceeding 1 million at an operating frequency of ~976 kHz. As a result, the mechanical sensitivity of the gyroscope is improved by a factor of 7.76 times for near mode-matched operation relative to the case with no tuning of the frequency spacing between the modes. Additionally, the angle random walk and bias instability were improved from 0.042 °/√h to 0.037 °/√h and 1.65 °/h to 0.95 °/h respectively, benchmarking favorably with respect to the state-of-the-art of BAW disk gyroscopes. [2021-0151]

This paper reports experimental results demonstrating excellent short-term frequency stability of 45.6 µLHz (36 ppt@0.4 s integration time) for a bulk acoustic wave (BAW) silicon disk resonator oscillator. The n=4 radial mode of a BAW disk resonator demonstrates an extremely high-quality factor of 1.8*10^6 at 1.25 MHz. The disk is designed with anchors aligned with nodal locations to minimize anchor damping. The results on the measured short-term frequency stability reported here benchmark favourably relative to the state-of-the-art.

The principle of vibration mode localization has been been researched in recent years as an approach towards the high accuracy transduction of inertial forces. This transduction scheme comprises of two or more weakly coupled resonators and a low coupling factor is critical in order to enhance parametric sensitivity and consequently resolution. In this paper, we report a new mode-localized accelerometer topology which enables a high amplitude ratio scale factor using a differential acceleration perturbation method. Further, by employing a parametric pump, an adjustable ultra-weak virtual coupling factor is realized where the coupled resonators can operate in the weak coupling regime. In this regime, modal overlap is apparent and the amplitude ratio sensitivity is much improved, by decreasing the pump strength. The experiments show that the amplitude ratio sensitivity of the proposed accelerometer is 9.2/g, and it can be enlarged to as high as 6300/g by employing a parametric pump signal with 100 mV strength, indicating a scale-factor improvement factor of 684. Consequently, the input-referred bias instability is improved from 6.7 µg for the case of no parametric pump to 420 ng while employing a parametric pump for operation in the modal-overlap regime, showing an improvement by a factor of ~16.

This paper reports experimental results demonstrating significant gains in frequency stability for bulk acoustic wave (BAW) silicon disk resonator oscillators due to the locking of degenerate modes. The results show that when two degenerate modes are locked, the minimum Allan deviation is improved by a factor of more than two times in comparison with the minimum Allan deviation for oscillators locked to the individual degenerate modes. A shortterm stability of 48.3 μHz (51 ppt @ 0.27 s integration time) is recorded for a MEMS oscillator with an output of ~1 MHz which benchmarks favourably relative to the MEMS oscillator state-of-the-art and commercial crystal oscillators. The approach is applicable to the locking of oscillators based on degenerate modes generally and can be scaled to higher frequency axisymmetric resonators with the higher-order bulk modes also providing inherent immunity to shock and vibration.

Mode-localized sensors have attracted great attention due to the high parametric sensitivity and common mode rejection to temperature drift. The reported results from such sensors has largely relied on operation in the linear regime. However, operation at specific bifurcation points in the nonlinear regime can enable improvements in relevant performance metrics. This paper theoretically and experimentally reveals the operation of mode-localized sensors with respect to applied stiffness perturbations while operating in the nonlinear Duffing regime. The operation of a mode-localized accelerometer is optimized with benefit of the insights gained from theoretical analysis with operation at the top bifurcation point in the nonlinear regime. A prototype accelerometer device demonstrates a noise floor of 85 ng/√Hz and a bias instability of 130 ng, establishing a new benchmark for sensors employing vibration mode localization as a sensing paradigm.