Mode-localized accelerometer in the nonlinear Duffing regime with 75 ng bias instability and 95 ng/√Hz noise floor.

Mode-localized sensors have attracted attention because of their high parametric sensitivity and first-order common-mode rejection to temperature drift. The high-fidelity detection of resonator amplitude is critical to determining the resolution of mode-localized sensors where the measured amplitude ratio in a system of coupled resonators represents the output metric. Operation at specific bifurcation points in a nonlinear regime can potentially improve the amplitude bias stability; however, the amplitude ratio scale factor to the input measurand in a nonlinear regime has not been fully investigated. This paper theoretically and experimentally elucidates the operation of mode-localized sensors with respect to stiffness perturbations (or an external acceleration field) in a nonlinear Duffing regime. The operation of a mode-localized accelerometer is optimized with the benefit of the insights gained from theoretical analysis with operation in the nonlinear regime close to the top critical bifurcation point. The phase portraits of the amplitudes of the two resonators under different drive forces are recorded to support the experimentally observed improvements for velocity random walk. Employing temperature control to suppress the phase and amplitude variations induced by the temperature drift, 1/f noise at the operation frequency is significantly reduced. A prototype accelerometer device demonstrates a noise floor of 95 ng/√Hz and a bias instability of 75 ng, establishing a new benchmark for accelerometers employing vibration mode localization as a sensing paradigm. A mode-localized accelerometer is first employed to record microseismic noise in a university laboratory environment.

On Weakly Coupled Resonant MEMS Transducers Operating in the Modal Overlap Regime.

Miniaturized physical transducers based on weakly coupled resonators have previously demonstrated the twin benefits of high parametric sensitivity and the first-order common-mode rejection of environmental effects. Current approaches to sensing based on coupled resonator transducers employ strong coupling where the modal overlap of the responses is avoided. This strong coupling limits the sensitivity for such mode-localized sensors that utilize an amplitude ratio (AR) output metric as opposed to tracking resonant frequency shifts. In this article, this limitation is broken through by theoretically and experimentally demonstrating the operation of the weakly coupled resonators in the weak-coupling (modal overlap) regime. Especially, a prototype microelectromechanical systems (MEMS) sensor based on this principle is employed to detect shifts in stiffness, with a stiffness bias instability of [Formula: see text]/m (9.5 ppb) and a corresponding noise floor of [Formula: see text]/m/ √ Hz (6.8 ppb/ √ Hz). The linear dynamic range of such AR readout sensors is first explored and found to be defined by the dynamic range of the secondary resonator. The proposed method provides a promising approach for high-performance resonant force and inertial sensors.

A vibrating beam MEMS accelerometer for gravity and seismic measurements.

This paper introduces a differential vibrating beam MEMS accelerometer demonstrating excellent long-term stability for applications in gravimetry and seismology. The MEMS gravimeter module demonstrates an output Allan deviation of 9 µGal for a 1000 s integration time, a noise floor of 100 µGal/√Hz, and measurement over the full ±1 g dynamic range (1 g = 9.81 ms-2). The sensitivity of the device is demonstrated through the tracking of Earth tides and recording of ground motion corresponding to a number of teleseismic events over several months. These results demonstrate that vibrating beam MEMS accelerometers can be employed for measurements requiring high levels of stability and resolution with wider implications for precision measurement employing other resonant-output MEMS devices such as gyroscopes and magnetometers.

Dynamic modulation of modal coupling in microelectromechanical gyroscopic ring resonators.

Understanding and controlling modal coupling in micro/nanomechanical devices is integral to the design of high-accuracy timing references and inertial sensors. However, insight into specific physical mechanisms underlying modal coupling, and the ability to tune such interactions is limited. Here, we demonstrate that tuneable mode coupling can be achieved in capacitive microelectromechanical devices with dynamic electrostatic fields enabling strong coupling between otherwise uncoupled modes. A vacuum-sealed microelectromechanical silicon ring resonator is employed in this work, with relevance to the gyroscopic lateral modes of vibration. It is shown that a parametric pumping scheme can be implemented through capacitive electrodes surrounding the device that allows for the mode coupling strength to be dynamically tuned, as well as allowing greater flexibility in the control of the coupling stiffness. Electrostatic pump based sideband coupling is demonstrated, and compared to conventional strain-mediated sideband operations. Electrostatic coupling is shown to be very efficient, enabling strong, tunable dynamical coupling.

Closed-Loop Characterization of Noise and Stability in a Mode-Localized Resonant MEMS Sensor.

This paper presents results from the closed-loop characterization of an electrically coupled mode-localized sensor topology including measurements of amplitude ratios over a long duration, stability, noise floor, and the bandwidth of operation. The sensitivity of the prototype sensor is estimated to be -5250 in the linear operation regime. An input-referred stability of 84 ppb with respect to normalized stiffness perturbations is achieved at 500 s. When compared to frequency shift sensing within the same device, amplitude ratio sensing provides higher resolution for long-term measurements due to the intrinsic common-mode rejection properties of a mode-localized system. A theoretical framework is established to quantify noise floor associated with measurements validated through numerical simulations and experimental data. In addition, the operating bandwidth of the sensor is found to be 3.5 Hz for 3-dB flatness.

Optimization of the Close-to-Carrier Phase Noise in a CMOS-MEMS Oscillator Using a Phase Tunable Sustaining-Amplifier.

In this paper, the phase noise of a 24-MHz complimentary metal-oxide-semiconductor microelectromechanical systems (CMOS-MEMS) oscillator with zero-level vacuum package is studied. We characterize and analyze the nonlinear regime of each one of the modules that compose the oscillator (CMOS sustaining-amplifier and MEMS resonator). As we show, the presented resonator exhibits a high nonlinear behavior. Such a fact is exploited as a mechanism to stabilize the oscillation amplitude, allowing us to maintain the sustaining-amplifier working in the linear regime. Consequently, the nonlinear resonator becomes the main close-to-carrier phase noise source. The sustaining amplifier, which functions as a phase shifter, was developed such that MEMS operation point optimization could be achieved without an increase in circuitry modules. Therefore, the system saves on area and power, and is able to improve the phase noise 26 dBc/Hz (at 1-kHz carrier frequency offset).

Enhancement of Frequency Stability Using Synchronization of a Cantilever Array for MEMS-Based Sensors.

Micro and nano electromechanical resonators have been widely used as single or multiple-mass detection sensors. Smaller devices with higher resonance frequencies and lower masses offer higher mass responsivities but suffer from lower frequency stability. Synchronization phenomena in multiple MEMS resonators have become an important issue because they allow frequency stability improvement, thereby preserving mass responsivity. The authors present an array of five cantilevers (CMOS-MEMS system) that are forced to vibrate synchronously to enhance their frequency stability. The frequency stability has been determined in closed-loop configuration for long periods of time by calculating the Allan deviation. An Allan deviation of 0.013 ppm (@ 1 s averaging time) for a 1 MHz cantilever array MEMS system was obtained at the synchronized mode, which represents a 23-fold improvement in comparison with the non-synchronized operation mode (0.3 ppm).