We present a 2-mm diameter, 35- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> m-thick disk resonator gyro (DRG) fabricated in <111> silicon with integrated 0.35- m CMOS analog front-end circuits. The device is the commercial InvenSense Fabrication MEMS-CMOS platform, which incorporates wafer-level vacuum seal, yielding quality factor ( notation="LaTeX">$Q$ ) of 2800 at...

We present a demonstration of whole-angle mode operation 0.6 mm single-crystal silicon disk resonator gyroscope (DRG). This device has Q factor ~80,000 and resonant frequency ~250 kHz is fabricated in the epi-seal process. Discrete-time control algorithms for rate-integrating gyro were implemented based on Lynch’s algorithm. Despite fact that this DRG over 5 orders magnitude smaller than 58 HRG, device’s error sources are shown to be accurately modeled by basic models developed Lynch.

Toward the objective of direct angle measurement using a rate integrating gyroscope (RIG) without minimum threshold and with performance limited only by electrical mechanical thermal noise, in this paper, we present implementation generalized electronic feedback method for compensation MEMS damping asymmetry (anisodamping) stiffness (anisoelasticity) on stand-alone digital signal processing platform. Using new method, precession angle-dependent bias error threshold, two issues identified...

We present the development of millimeter scale 3D hemispherical shell resonators fabricated from polycrystalline diamond, a material with low thermoelastic damping and very high stiffness. These wineglass 1.1 mm diameter are through combination micro-electro discharge machining (EDM) silicon micromachining techniques. Using piezoelectric electrostatic excitation optical vibration measurement, elliptical mode is determined to be at 18.321 kHz, two degenerate modes having relative frequency...

This letter presents a micromachined silicon three-axis gyroscope based on triple tuning-fork structure utilizing single vibrating element. The mechanical approach proposed in this uses secondary "auxiliary" mass rather than major "proof" to induce motion the proof frame for Coriolis force coupling sense mode. These auxiliary masses reduce unwanted of and from drive mode three modes. experimental data show that bias error due is reduced by factor up 10, instability each axis 3 when actuated...

This paper addresses the impact of cubic nonlinearity on operation a rate-integrating gyroscope (RIG). It is demonstrated that below bifurcation threshold, results in angle-dependent frequency split between two resonant modes gyroscope, which impacts bias, quadrature error, and controller efficacy addition to distorting scale factor due off-resonant excitation. These errors are experimentally using high-Q disk resonator shown be close agreement with theory. A method compensating for error...

Resonators used in frequency-reference oscillators must maintain a stable frequency output even when subjected to temperature variations. The traditional solution is construct the resonator from material with low coefficient, such as AT-cut quartz, which can achieve absolute stability on order of ±25 ppm over commercial ranges. In comparison, Si microresonators suffer disadvantage that silicon's coefficient (TCF) approximately two orders magnitude greater than quartz. this paper, we present...

The hemispherical resonator gyro (HRG) is low loss and high stability, spurring recent interest in micro-scale resonators. To achieve mode-matching high-Q performance a resonator, geometric symmetry combination with thermoelastic damping structural material are critical. In this work, we describe the development of millimeter scale 3D shell resonators fabricated from polycrystalline diamond, very stiffness. relation between fourth harmonic (4θ) Fourier analysis resonator's radius r(θ)...

Towards the objective of a rate integrating gyroscope (RIG) without minimum threshold and performance limited only by electrical mechanical thermal noise, we present our progress on new, generalized electronic feedback method for compensation resonator damping asymmetry (anisodamping) stiffness (anisoelasticity) with new RIG operation using self-precession. This enables overcoming precession angle-dependent bias error threshold, two issues identified Lynch MEMS [1]. To correct bias, augment...

We demonstrate synchronization between two intrinsically coupled oscillators that are created from distinct vibration modes of a single micromachined disk resonator. The have 3:1 subharmonic frequency relationship and cubic, non-dissipative electromechanical coupling the enables their frequencies to synchronize. Our experimental implementation allows lower oscillator be independently controlled higher oscillator, enabling study dynamics. find close quantitative agreement behavior an...

This paper describes the operation of a high quality factor gyroscope in various regimes where electromechanical nonlinearities introduce different forms amplitude–frequency (A–f) dependence. Experiments are conducted using an epitaxially-encapsulated 2 × mm2 quad-mass (QMG) with 85 000. The device exhibits third-order Duffing nonlinearity at low bias voltages (15 V) due to mechanical flexures and (35 electrostatic nonlinearity. At intermediate (~26 V), these cancel dependence is greatly...

We present an epitaxially-encapsulated 2×2 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> quad-mass gyroscope (QMG). Relative to the earlier QMG which measured 8×8 and required external vacuum package getter [1], this device is 16x smaller in area vacuum-sealed at wafer-level. Due device's small size, high quality factor (Q) large oscillation amplitude are achieve low noise. However, Q (85,000) makes it highly sensitive mechanical...

In this letter, we investigate the dynamics of injection-locking a nonlinear micromechanical oscillator operating in different regimes electromechanical nonlinearity to an external tone generated by secondary oscillator. The exhibits combination mechanical and electrostatic nonlinearities that were tuned using bias voltage adjust relative importance third-order fifth-order stiffness nonlinearities. While it is well-known (Duffing) results synchronization range increases with oscillator's...

This paper concerns a micro-scale gyroscope based on 1 mm diameter diamond hemispherical resonator with embedded polysilicon electrodes.Frequency mismatch and quality factor of the wineglass vibration modes are studied.The device has electrodes used for electrostatic transduction mode-matching.The air gap between is small to increase frequency tuning range given supply voltage.The 2θ-mode resonant can be minimized from 2.4% 0.1% by applying low 2.5V voltage.

In this paper, we study the occurrence of synchronization between two degenerate resonance modes a microdisk resonator gyroscope. Recently, schemes involving simultaneous actuation vibration gyroscope have been implemented as promising new method to increase their performance. However, strategy might result in modes, which would maintain frequency mode-matching but also may produce problems, such degrading stability and sensitivity. Here, demonstrate for first time microgyroscope show that...

In this paper, we present observations of the amplitude and frequency noise two self-sustained oscillating modes a single micromechanical resonator under fractional synchronization. The resonant which comprise oscillators have 3:1 ratio frequencies. Increasing low-frequency oscillator increases range frequencies over oscillations synchronize; inversely, increasing high-frequency decreases synchronization range. We show that by either mode, white in higher mode will decrease synchronized...

We present an epitaxially-encapsulated 2×2mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> quad-mass resonator (QMR) with shaped comb fingers for frequency tuning. While electrodes have been used tuning of linear resonators, the device studied here has very high quality factor (g=100,000) resulting in a narrowband resonance which, without electrodes, results undesirable nonlinear behavior such as amplitude-frequency dependence and...

In this paper, we study the occurrence of synchronization between two degenerate resonance modes a micro disk resonator gyroscope.Recently, schemes involving simultaneous actuation vibration gyroscope have been implemented as promising new method to increase their performance.However, strategy might result in modes, which would maintain frequency mode-matching but also may produce problems, such degrading stability and sensitivity.Here, demonstrate for first time micro-gyroscope show that...

We present a 2 mm diameter, 35 μm thick disk resonator gyro (DRG) fabricated in <111> silicon with integrated 0.35 CMOS analog front-end circuits the Invensense NF process. This process incorporates wafer-level vacuum seal, yielding quality factor (Q) of 2800 at DRG's 78 kHz resonance frequency. After performing electrostatic tuning to enable mode-matched operation, this DRG achieves 63 μV/°/s sensitivity. Resonator vibration sense and drive axes is sensed using capacitive transduction,...

In this paper we present our observations of the effect mutual fractional synchronization two oscillators created from distinct resonance modes a single micromechanical resonator on noise oscillators. The have 3:1 frequency ratio and by increasing amplitude lower mode range will increase. We show mode, white in higher decrease. that when synchronized fluctuations reduce 4 times comparison with same oscillator operating at not synchronized. amount reduction is also observed mode.