Parsa Taheri-Tehrani

Hemispherical wineglass resonators fabricated from the microcrystalline diamond

We present the development of millimeter scale 3D hemispherical shell resonators fabricated from the polycrystalline diamond, a material with low thermoelastic damping and very high stiffness. These hemispherical wineglass resonators with 1.1 mm diameter are fabricated through a combination of micro-electro discharge machining (EDM) and silicon micromachining techniques. Using piezoelectric and electrostatic excitation and optical vibration measurement, the elliptical wineglass vibration mode is determined to be at 18.321 kHz, with the two degenerate wineglass modes having a relative frequency mismatch of 0.03%. A study on the effect of the size and misalignment of the anchor and resonator’s radius variation on both the average frequency and frequency mismatch of the 2θ elliptical vibration modes is carried out. It is shown that the absolute frequency of a wineglass resonator will increase with the anchor size. It is also demonstrated that the fourth harmonic of radius variation is linearly related to the frequency mismatch. (Some figures may appear in colour only in the online journal)

Silicon MEMS Disk Resonator Gyroscope With an Integrated CMOS Analog Front-End

We present a 2-mm diameter, 35-μm-thick disk resonator gyro (DRG) fabricated in <;111> silicon with integrated 0.35-μm CMOS analog front-end circuits. The device is fabricated in the commercial InvenSense Fabrication MEMSCMOS integrated platform, which incorporates a wafer-level vacuum seal, yielding a quality factor (Q) of 2800 at the DRGs 78-kHz resonant frequency. After performing electrostatic tuning to enable mode-matched operation, this DRG achieves a 55 μV/°/s sensitivity. Resonator vibration in the sense and drive axes is sensed using capacitive transduction, and amplified using a lownoise, on-chip integrated circuit. This allows the DRG to achieve Brownian noise-limited performance. The angle random walk is measured to be 0.008°/s/√(Hz) and the bias instability is 20°/h.

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

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.

Disk resonator gyroscope with whole-angle mode operation

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

Epitaxially-encapsulated quad mass gyroscope with nonlinearity compensation

We present an epitaxially-encapsulated 2×2 mm2 quad-mass gyroscope (QMG). Relative to the earlier QMG which measured 8×8 mm2 and required an external vacuum package and getter [1], this device is 16x smaller in area and is vacuum-sealed at the wafer-level. Due to the devices small size, high quality factor (Q) and large oscillation amplitude are required to achieve low noise. However, the devices high Q (85,000) makes it highly sensitive to mechanical nonlinearity, resulting in amplitude-frequency dependence and instability of the oscillator loop at large amplitudes. To overcome these problems, we demonstrate electrostatic compensation of the mechanical nonlinearity, enabling 10x greater amplitude and therefore scale factor (SF). Together with closed-loop amplitude control and quadrature compensation, this enables angle-random walk of 0.42 mdeg/s/VHz, comparable to the best QMG published to date. Closed-loop amplitude control and quadrature null are used to achieve a bias instability of 1.6 deg/hr.

Exploiting nonlinear amplitude-frequency dependence for temperature compensation in silicon micromechanical resonators

Resonators used in frequency-reference oscillators must maintain a stable frequency output even when subjected to temperature variations. The traditional solution is to construct the resonator from a material with a low temperature coefficient, such as AT-cut quartz, which can achieve absolute frequency stability on the order of ±25 ppm over commercial temperature ranges. In comparison, Si microresonators suffer from the disadvantage that silicons temperature coefficient of frequency (TCF) is approximately two orders of magnitude greater than that of AT-cut quartz. In this paper, we present an in situ passive temperature compensation scheme for Si microresonators based on nonlinear amplitude-frequency coupling which reduces the TCF to a level comparable with that of an AT-quartz resonator. The implementation of this passive technique is generic to a variety of Si microresonators and can be applied to a number of frequency control and timing applications.

A new electronic feedback compensation method for rate integrating gyroscopes

Towards the objective of a rate integrating gyroscope (RIG) without a minimum rate threshold and performance limited only by electrical and mechanical thermal noise, we present our progress on a new, generalized electronic feedback method for the compensation of resonator damping asymmetry (anisodamping) and stiffness asymmetry (anisoelasticity) with a new method of RIG operation using self-precession. This enables overcoming the precession angle-dependent bias error and minimum rate threshold, two issues identified by Lynch for a MEMS RIG [1]. To correct angle-dependent bias, we augment the electronic feedback force of the amplitude regulator with a non-unity gain output distribution matrix selected to correct for anisodamping. Using this method, we have decreased the angle dependent bias error by a factor of 30, resulting a minimum rate threshold of 3.5 dps. To further improve RIG performance, an electronically-induced self-precession rate is incorporated and successfully demonstrated to lower the rate threshold. The RIGs output noise is also evaluated, demonstrating an ARW of 11 mdps/√Hz, similar to rate gyro operation at same amplitude.

Impact of Synchronization in Micromechanical Gyroscopes

In this paper, we study the occurrence of synchronization between the two degenerate resonance modes of a microdisk resonator gyroscope. Recently, schemes involving the simultaneous actuation of the two vibration modes of the gyroscope have been implemented as a promising new method to increase their performance. However, this strategy might result in synchronization between the two modes, which would maintain frequency mode-matching but also may produce problems, such as degrading stability and sensitivity. Here, we demonstrate for the first time synchronization between the degenerate modes of a microgyroscope and show that synchronization arising from mutual coupling dramatically reduces frequency instability at the cost of increased amplitude instability. We present an alternative synchronization scheme that suppresses this drawback while still taking advantage of a passive frequency mode-match operation. [DOI: 10.1115/1.4036397]

Mutual 3:1 subharmonic synchronization in a micromachined silicon disk resonator

We demonstrate synchronization between two intrinsically coupled oscillators that are created from two distinct vibration modes of a single micromachined disk resonator. The modes have a 3:1 subharmonic frequency relationship and cubic, non-dissipative electromechanical coupling between the modes enables their two frequencies to synchronize. Our experimental implementation allows the frequency of the lower frequency oscillator to be independently controlled from that of the higher frequency oscillator, enabling study of the synchronization dynamics. We find close quantitative agreement between the experimental behavior and an analytical coupled-oscillator model as a function of the energy in the two oscillators. We demonstrate that the synchronization range increases when the lower frequency oscillator is strongly driven and when the higher frequency oscillator is weakly driven. This result suggests that synchronization can be applied to the frequency-selective detection of weak signals and other mechanic...

Synchronization of a micromechanical oscillator in different regimes of electromechanical nonlinearity

In this letter, we investigate the dynamics of injection-locking a nonlinear micromechanical oscillator operating in different regimes of electromechanical nonlinearity to an external tone generated by a secondary oscillator. The micromechanical oscillator exhibits a combination of mechanical and electrostatic nonlinearities that were tuned using a bias voltage to adjust the relative importance of third-order and fifth-order stiffness nonlinearities. While it is well-known that third-order stiffness (Duffing) nonlinearity results in a synchronization range that increases with an oscillators amplitude, little is known about the impact of other nonlinearities. We show that when using Duffing nonlinearity cancellation, higher order nonlinearities dominate, the synchronization range is smaller but has a greater rate-of-increase with oscillation amplitude. When both mechanical stiffness-hardening and electrostatic stiffness-softening nonlinearities are present, the frequency response follows an “s-curve” and,...