We present a 3-D fused-silica micro-scale shell gyroscope, called the birdbath resonator gyroscope (BRG). The BRGs axisymmetric geometry leads to a good frequency and Q symmetry. The birdbath resonator can be fabricated with a good structural symmetry because its anchor is self-aligned to the rest of the structure. The BRG has n=2 wine-glass modes at 10.5 kHz and has a large frequency separation between the n=2 wine-glass modes and the closest parasitic mode (|fparasitic-fn=2|/fn=2=0.3), which will potentially lead to a low vibration sensitivity. The equations of motion for 3-D shell gyroscopes are derived and the effective mass and angular gain of the BRG is estimated using finite element method (FEM). The BRG is fabricated using a 3-D micrometer-blow-torching process and assembly on an electrode substrate made with the silicon-on-glass process. The BRG is operated in the force-rebalance mode at vacuum at room temperature and has a scale factor of 27.9 mV/(deg/s), a full-scale range , an angle random walk of 0.106 deg/√h, and a bias stability of 1 deg/h. A large angular gain (0.317) is measured, which is close to the estimated value of 0.25 obtained via FEM.

Fused-Silica Micro Birdbath Resonator Gyroscope ( $\mu$ -BRG)

This paper presents the architecture and experimental verification of the automatic mode-matching system that uses the phase relationship between the residual quadrature and drive signals in a gyroscope to achieve and maintain matched resonance mode frequencies. The system also allows adjusting the system bandwidth with the aid of the proportional-integral controller parameters of the sense-mode force-feedback controller, independently from the mechanical sensor bandwidth. This paper experimentally examines the bias instability and angle random walk (ARW) performances of the fully decoupled MEMS gyroscopes under mismatched (~ 100 Hz) and mode-matched conditions. In matched-mode operation, the system achieves mode matching with an error frequency separation between the drive and sense modes in this paper. In addition, it has been experimentally demonstrated that the bias instability and ARW performances of the studied MEMS gyroscope are improved up to 2.9 and 1.8 times, respectively, with the adjustable and already wide system bandwidth of 50 Hz under the mode-matched condition. Mode matching allows achieving an exceptional bias instability and ARW performances of 0.54 °/hr and 0.025 °/√hr, respectively. Furthermore, the drive and sense modes of the gyroscope show a different temperature coefficient of frequency (TCF) measured to be -14.1 ppm/°C and -23.2 ppm/°C, respectively, in a temperature range from 0 °C to 100 °C. Finally, the experimental data indicate and verify that the proposed system automatically maintains the frequency matching condition over a wide temperature range, even if TCF values of the drive and sense modes are quite different.

An Automatically Mode-Matched MEMS Gyroscope With Wide and Tunable Bandwidth

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.

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Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope

This paper discusses piezoelectric acoustic devices based on widely used piezoelectric materials. Commonly used piezoelectric thin film deposition techniques and the influence of process parameters on the growth, texture and orientation of the films are discussed. Etching techniques are also outlined. A comparative study of different devices developed previously is given. Also, applications of developed devices in aero-acoustic and medical fields have been briefly discussed. Flow charts of various techniques of deposition along with a combined one for full acoustic device fabrication are given. Various techniques, frequently used for thin film characterization have been discussed. The testing and measurement techniques to determine the responses of acoustic devices such as sensitivity, resonance frequency, frequency response, piezoelectric co-efficient etc. have been briefly illustrated. This paper discusses common failure modes with respect to the field of use of acoustic devices. It also concisely discusses various reliability tests done in industries to assess the quality of the developed devices. This review has also suggested directions for future development of thin film acoustic sensors.

Piezoelectric MEMS based acoustic sensors: A review

This paper presents a bandwidth expansion method for dual-mass microelectromechanical system (MEMS) gyroscopes based on the pole–zero temperature compensation method. When the sense loop operates under open conditions, the mechanical sensitivity of the gyroscope structure conflicts with the bandwidth and is governed by the frequency difference between the drive and the sense modes (min {Δ ω 1, Δ ω 2}), which is proven to change with temperature during the experiment. The pole–zero temperature compensation proportional controller (PZTCPC) is proposed to expand the bandwidth under different temperatures based on the pole–zero compensation method. The force rebalancing combs stimulation method (FRCSM) is used to achieve accurate gyroscope bandwidth characteristics. The mechanical bandwidth of the gyroscope is proven to be approximately 13 Hz when the sense-mode loop is open, and the simulation results show that the PZTCPC method expands the bandwidth to greater than 91.7 Hz after the sense-mode loop is closed. The FRCSM experiments indicate that gyroscope bandwidth is expanded to 95 Hz at –40 °C, 94 Hz at 20 °C and 92 Hz at 60 °C, while the bandwidths at –40, 20, and 60 °C are all 93 Hz with the turntable method. The experimental curves match the simulation curves well and verify the simulation results. The new limiting condition of the closed-loop bandwidth is the trough generated by conjugate zeros, formed by superposition of in-phase and anti-phase sense modes.

Pole-Zero Temperature Compensation Circuit Design and Experiment for Dual-Mass MEMS Gyroscope Bandwidth Expansion

Vascular complications following solid organ transplantation may lead to graft ischemia, dysfunction or loss. Imaging approaches can provide intermittent assessments of graft perfusion, but require highly skilled practitioners and do not directly assess graft oxygenation. Existing systems for monitoring tissue oxygenation are limited by the need for wired connections, the inability to provide real-time data or operation restricted to surface tissues. Here, we present a minimally invasive system to monitor deep-tissue O2 that reports continuous real-time data from centimeter-scale depths in sheep and up to a 10-cm depth in ex vivo porcine tissue. The system is composed of a millimeter-sized, wireless, ultrasound-powered implantable luminescence O2 sensor and an external transceiver for bidirectional data transfer, enabling deep-tissue oxygenation monitoring for surgical or critical care indications. The oxygenation of deep tissues is continuously measured using an ultrasound-powered wireless implant.

/pdf/monitoring-deep-tissue-oxygenation-with-a-millimeter-scale-4uerxc6ud7.pdf

Monitoring deep-tissue oxygenation with a millimeter-scale ultrasonic implant.

In this paper, a Lorentz force magnetometer demonstrates quadrature frequency modulation operation. The Lorentz force magnetometer consists of a conventional 3-port resonator, which is put into oscillation by electrostatic driving and sensing. The bias current flowing through the resonator is proportional to the displacement, and generates Lorentz force in quadrature with the electrostatic force. As a result, the Lorentz force acts as an equivalent spring and the magnetic field can be measured by reading the change in oscillation frequency. The sensor has a sensitivity of 500 Hz/T with a short-term noise floor of 500 nT $\surd $ Hz. The bandwidth of the sensor is increased to 50 Hz, a factor of 12 greater than that of the same resonator operating in amplitude-modulated mode. The short-term noise floor within 50-Hz bandwidth is comparable with CMOS Hall-effect sensors.

Extended Bandwidth Lorentz Force Magnetometer Based on Quadrature Frequency Modulation

This letter presents a micromachined silicon three-axis gyroscope based on a triple tuning-fork structure utilizing a single vibrating element. The mechanical approach proposed in this letter uses a secondary “auxiliary” mass rather than a major “proof” mass to induce motion in the proof mass frame for Coriolis force coupling to the sense mode. These auxiliary masses reduce the unwanted mechanical coupling of force and motion from the drive mode to the three sense modes. The experimental data show that the bias error due to coupling is reduced by a factor up to 10, and the bias instability of each sense axis is reduced by a factor of up to 3 when the gyroscope is actuated using the auxiliary masses rather than the major masses. The gyroscope exhibits a bias instability of 0.016°/s, 0.004°/s, and 0.043°/s for the $x$ -, $y$ -, and $z$ -sense modes, respectively. Furthermore, initial temperature characterization results show that the gyroscope actuated by the auxiliary masses ensures a better bias instability performance in each sense axis over a temperature range from 10 °C to 50 °C in comparison with the gyroscope actuated by the major masses.

Single-Structure Micromachined Three-Axis Gyroscope With Reduced Drive-Force Coupling

This paper presents the architecture and experimental verification of an automatic mode matching system that uses the phase relationship between the residual quadrature and drive signals in a gyroscope to accomplish and maintain the frequency matching condition. The system also allows controlling the system bandwidth by adjusting the closed loop controller parameters of the sense mode. This study experimentally examines the angle random walk (ARW) and bias instability performances of the fully decoupled MEMS gyroscopes under mismatched (∼100Hz) and mode-matched conditions. Moreover, it has been experimentally shown that the performance of the studied MEMS gyroscopes is improved up to 2.4 times in bias instability and 1.7 times in ARW with 50 Hz system bandwidth under the mode-matched condition reaching down to a bias instability of 0.83°/hr and an ARW of 0.026°/√hr.

Soner Sonmezoglu

Papers

An Automatically Mode-Matched MEMS Gyroscope With Wide and Tunable Bandwidth

Monitoring deep-tissue oxygenation with a millimeter-scale ultrasonic implant.

Extended Bandwidth Lorentz Force Magnetometer Based on Quadrature Frequency Modulation

Single-Structure Micromachined Three-Axis Gyroscope With Reduced Drive-Force Coupling

An automatically mode-matched MEMS gyroscope with 50 Hz bandwidth