A Low-Noise Interface ASIC for MEMS Disk Resonator Gyroscope.

This paper proposes a low-noise interface application-specific integrated circuit (ASIC) for a microelectromechanical systems (MEMS) disk resonator gyroscope (DRG) which operates in force-to-rebalance (FTR) mode. The ASIC employs an analog closed-loop control scheme which incorporates a self-excited drive loop, a rate loop and a quadrature loop. A ΣΔ modulator and a digital filter are also contained in the design to digitize the analog output besides the control loops. The clocks for the modulator and digital circuits are both generated by the self-clocking circuit, which avoids the requirement of additional quartz crystal. A system-level noise model is established to determine the contribution of each noise source in order to reduce the noise at the output. A noise optimization solution suitable for chip integration is proposed based on system-level analysis, which can effectively avoid the effects of the 1/f noise of the PI amplifier and the white noise of the feedback element. A performance of 0.0075°/√h angle random walk (ARW) and 0.038°/h bias instability (BI) is achieved using the proposed noise optimization method. The ASIC is fabricated in a 0.35 µm process with a die area of 4.4 mm × 4.5 mm and power consumption of 50 mW.

Multi-Ring Disk Resonator with Elliptic Spokes for Frequency-Modulated Gyroscope.

In this paper, we report a multi-ring disk resonator with elliptic spokes for compensating the aniso-elasticity of (100) single crystal silicon. The structural coupling between each ring segments can be controlled by replacing the straight beam spokes with the elliptic spokes. The degeneration of two n = 2 wineglass modes could be realized by optimizing the design parameters of the elliptic spokes. The mode-matched resonator could be obtained when the design parameter, aspect ratio of the elliptic spokes was 25/27. The proposed principle was demonstrated by both numerical simulation and experiment. A frequency mismatch as small as 1330 ± 900 ppm could be experimentally demonstrated, which was much smaller than that of the conventional disk resonator, which achieved as high as 30,000 ppm.

Design of a Multiple Folded-Beam Disk Resonator with High Quality Factor.

This paper proposes a new multiple folded-beam disk resonator whose thermoelastic quality factor is significantly improved by appropriately reducing the beam width and introducing integral-designed lumped masses. The quality factor of the fabricated resonator with (100) single crystal silicon reaches 710 k, proving to be a record in silicon disk resonators. Meanwhile, a small initial frequency split of the order-3 working modes endows the resonator with great potential for microelectromechanical systems (MEMS) gyroscopes application. Moreover, the experimental quality factor of resonators with different beam widths and relevant temperature experiment indicate that the dominating damping mechanism of the multiple folded-beam disk resonator is no longer thermoelastic damping.

A Quick Start Method for MEMS Disk Resonant Gyroscope.

High-precision disk resonator gyroscope has a high quality factor in order to improve the performance of the gyroscope, as the high quality factor can lead to a long starting time. In this paper, a control system of the driving loop of the disk MEMS resonant gyroscope with the quick start is designed. The control system has functions of quick frequency locking and fast step response. Coarse-precision mode transition system is designed for quick frequency locking. A large-small mode transition system is designed for fast step response. The correctness of the design is verified by circuit test. The test results show that the start-up time is reduced by over 80% compared with the traditional control loop.

Design of Wideband Bandpass Filter Based on Corrugated Disk Resonator with Multiple Resonant Modes.

A corrugated disk resonator with eight grooves is proposed for wideband bandpass filter (BPF) design. Due to the spoof localized surface plasmons resonances of the corrugated metallic structure, the dipole, quadrupole, hexapole modes, and a fundamental mode excited by the introduced short-circuited via holes are employed to realize four transmission poles (TPs) in the passband. The theoretical analysis is described by the electric field and current distributions on the resonator. The resonant frequencies can be tuned easily by the parameters of the structure, which can be used to adjust the center frequency and bandwidth of the BPF freely. Furthermore, two resonators are cascaded to obtain eight TPs to improve the selectivity performance. Finally, three fabricated filters demonstrate the design method.

Analysis of Parametric and Subharmonic Excitation in Push-Pull Driven Disk Resonator Gyroscopes.

For micro-electromechanical system (MEMS) resonators, once the devices are fabricated and packaged, their intrinsic quality factors (Q) will be fixed and cannot be changed, which seriously limits the further improvement of the resonator's performance. In this paper, parametric excitation is applied in a push-pull driven disk resonator gyroscope (DRG) to improve its sensitivity by an electrical pump, causing an arbitrary increase of the "effective Q". However, due to the differential characteristics of the push-pull driving method, the traditional parametric excitation method is not applicable. As a result, two novel methods are proposed and experimentally carried out to achieve parametric excitation in the push-pull driven DRGs, resulting in a maximum "effective Q" of 2.24 × 106 in the experiment, about a 7.6 times improvement over the intrinsic Q. Besides, subharmonic excitation is also theoretically analyzed and experimentally characterized. The stability boundary of parametric excitation, defined by a threshold voltage, is theoretically predicted and verified by related experiments. It is demonstrated that, when keeping the gyroscope's vibration at a constant amplitude, the fundamental frequency driving voltage will decrease with the increasing of the parametric voltage and will drop to zero at its threshold value. In this case, the gyroscope operates in a generalized parametric resonance condition, which is called subharmonic excitation. The novel parametric and subharmonic excitation theories displayed in this paper are proven to be efficient and tunable dynamical methods with great potential for adjusting the quality factor flexibly, which can be used to further enhance the resonator's performance.

First-Order Linear Mechatronics Model for Closed-Loop MEMS Disk Resonator Gyroscope.

In this paper, a first-order closed-loop mechatronics model of a micro-electromechanical system (MEMS) disk resonator gyroscope (DRG) with a configurable ASIC is established for closed-loop design and performance analysis. There are usually some nonlinear modules in the gyroscope mechatronics model, and it is difficult to design the closed-loop controllers using classical automatic control theory. An order-reduction method (ORM) based on the Laplace transform and inverse Laplace transform is proposed to linearize the nonlinear modules. The linearized model is proved to show good agreement with the original mechatronics model in terms of system response. The experimental verification was conducted to demonstrate the validation of this method.

Study of the Influence of Phase Noise on the MEMS Disk Resonator Gyroscope Interface Circuit.

In this paper, a detailed analysis of the influence of phase noise on the micro-electro-mechanical system (MEMS) disk resonator gyroscope (DRG) is presented. Firstly, a new time-varying phase noise model for the gyroscope is established, which explains how the drive loop circuit noise converts into phase noise. Different from previous works, the time-varying phase noise model in this paper is established in mechanical domain, which gain more physical insight into the origin of the phase noise in gyroscope. Furthermore, the impact of phase noise on DRG is derived, which shows how the phase noise affects angular velocity measurement. The analysis shows that, in MEMS DRG, the phase noise, together with other non-ideal factors such as direct excitation of secondary resonator, may cause a low frequency noise in the output of the gyroscope system and affect the bias stability of the gyroscope. Finally, numerical simulations and experiment tests are designed to prove the theories above.

A Digital Closed-Loop Sense MEMS Disk Resonator Gyroscope Circuit Design Based on Integrated Analog Front-end.

A digital closed-loop system design of a microelectromechanical systems (MEMS) disk resonator gyroscope (DRG) is proposed in this paper. Vibration models with non-ideal factors are provided based on the structure characteristics and operation mode of the sensing element. The DRG operates in force balance mode with four control loops. A closed self-excited loop realizes stable vibration amplitude on the basis of peak detection technology and phase control loop. Force-to-rebalance technology is employed for the closed sense loop. A high-frequency carrier loaded on an anchor weakens the effect of parasitic capacitances coupling. The signal detected by the charge amplifier is demodulated and converted into a digital output for subsequent processing. Considering compatibility with digital circuits and output precision demands, a low passband sigma-delta (ΣΔ) analog-to-digital converter (ADC) is implemented with a 111.8dB signal-to-noise ratio (SNR). The analog front-end and digital closed self-excited loop is manufactured with a standard 0.35 µm complementary metal-oxide-semiconductor (CMOS) technology. The experimental results show a bias instability of 2.1 °/h and a nonlinearity of 0.035% over the ± 400° full-scale range.

Automatic Mode-Matching Method for MEMS Disk Resonator Gyroscopes Based on Virtual Coriolis Force.

An automatic mode-matching method for MEMS (Micro-electromechanical Systems) disk resonator gyroscopes (DRGs) based on virtual Coriolis force is presented in this paper. For this mode-matching method, the additional tuning electrodes are not required to be designed, which simplifies the structure design. By using the quadratic relationship between the driving voltage and the electrostatic force, the virtual Coriolis force is obtained by applying an AC voltage whose frequency is half of the driving mode resonant frequency to the sense electrode. The phase difference between the virtual Coriolis force and the sense output signal is used for mode-matching. The structural characteristics and electrode distribution of the DRG are briefly introduced. Moreover, the mode-matching theories of the DRG are studied in detail. The scheme of the mode-matching control system is proposed. Simultaneously, the feasibility and effectiveness of the mode-matching method are verified by system simulation. The experimental results show that under the control of mode-matching at room temperature, the bias instability is reduced from 30.7575 ° /h to 2.8331 ° /h, and the Angle Random Walk (ARW) decreases from 1.0208 ° / h to 0.0524 ° / h . Compared with the mode mismatch condition, the ARW is improved by 19.48 times.

Design of Microdisk-Shaped Ge on Si Photodetector with Recess Structure for Refractive-Index Sensing.

In this paper, we introduce a disk-shaped Ge-on-Si photodetector for refractive-index difference sensing at an operating wavelength of 1550 nm. For the implementation of a small-scale sensor, a Ge layer was formed on top of a Si layer to increase the absorption coefficient at the expense of the light-detection area. Additionally, the sensor had a ring waveguide structure along the edge of the disk formed by a recess into the inner part of the disk. This increased the interaction between the dominant optical mode traveling along the edge waveguide and the refractive index of the cladding material to be sensed, and conclusively increased detection sensitivity. The simulation results show that the proposed sensor exhibited a detection sensitivity of >50 nm/RIU (Refractive Index Unit), a quality factor of approximately 3000, and a minimum detectable refractive index change of 0.95 × 10-2 RIU with a small disk radius of 3 µm. This corresponds to 1.67 times the sensitivity without a recess (>30 nm/RIU).

Energy Loss in a MEMS Disk Resonator Gyroscope.

Analysing and minimizing energy loss is crucial for high performance disk resonator gyroscopes (DRGs). Generally, the primary energy loss mechanism for high vacuum packaged microelectromechanical system (MEMS) resonators includes thermoelastic damping, anchor loss, and electronic damping. In this paper, the thermoelastic damping, anchor loss, and electronic damping for our DRG design are calculated by combining finite element analysis and theoretical derivation. Thermoelastic damping is the dominant energy loss mechanism and contributes over 90% of the total dissipated energy. Benefiting from a symmetrical structure, the anchor loss is low and can be neglected. However, the electronic damping determined by the testing circuit contributes 2.6%-9.6% when the bias voltage increases from 10 V to 20 V, which has a considerable impact on the total quality factor (Q). For comparison, the gyroscope is fabricated and seal-packaged with a measured maximum Q range of 141k to 132k when the bias voltage varies. In conclusion, thermoelastic damping and electronic damping essentially determine the Q of the DRG. Thus, optimizing the resonance structure and testing the circuit to reduce energy loss is prioritized for a high-performance DRG design.

A New Design of an MOEMS Gyroscope Based on a WGM Microdisk Resonator.

In this paper, we present a new design for a micro-opto-electro-mechanical (MOEMS) gyroscope based on a whispering-gallery mode (WGM) microdisk resonator and MEMS resonator. The mechanical characteristics, frequency split, and quality factor (Q) of the MEMS resonator; the optical characteristics, Q value, and coupling regimes of the WGM resonator; and the coupling between the two resonators were analyzed. Its operation principle-the transformation process from angular velocity to the resonance wavelength of the WGM resonator-is presented at same time. Next, the analysis conclusions were validated with the help of simulations in ANSYS and FDTD (Finite-Difference Time-Domain) Solutions. Afterwards, some key specifications were estimated based on the results of simulations. Lastly, the fabrication process is detailed.

Dynamic Modeling of the Multiring Disk Resonator Gyroscope.

The multiring disk resonator gyroscope (DRG) has been a candidate for high performance gyroscopes, however nowadays the finite element method (FEM) is the main method for its analysis due to its complex structure. In this paper we propose a new method to mathematically model the DRG for its vibrating modes and lumped parameters based on the component mode synthesis (CMS) method. Firstly, the natural frequencies and the associated mode shapes of the DRG are mathematically modeled and a comparison with the FEM results is conducted. It shows that the mode shapes of DRG obtained by FEM and mathematical modeling are identical and in the full ranges of geometrical parameters, natural frequency error of the simulation, and calculation results are limited in ±15%. It demonstrates the effectivity and feasibility of the mathematical modeling method. Then, based on the calculated natural frequencies and mode shapes, the lumped mass-spring model of the DRG and effects of geometry parameters on the lumped mass-spring parameters are investigated, which can be used on the design of the DRG. This mathematical modeling method can effectively improve the analyzing efficiency of the DRG and the method can also be used on the analysis of other complex multiring-type resonators.

Investigation on the Quality Factor Limit of the (111) Silicon Based Disk Resonator.

Quality factor is one of the most important parameters for a MEMS resonator. Most MEMS resonators are dominated by thermoelastic dissipation (TED). This paper demonstrates that the TED in a disk resonator that is made of (111) single-crystal silicon is surpassed by clamping loss. The stiffness-mass decoupling design method, combined with reducing the beam width, was used to engineer high QTED. Experiments show that Q of the (111) disk resonator have an upper boundary that is determined by the clamping loss caused by the unbalanced out-of-plane displacement. The origin of the out-of-plane displacement is explained by theory and simulation.

Biomaterial Disk Lasers by Suppressing the Coffee Ring Effect.

Inspired by the suppression of the coffee ring effect, we developed self-assembled disk lasers that can be formed with a wide variety of biomaterials. For proof of concept, we formed the disks with the natural protein silk fibroin or the synthetic biopolymer polyvinylpyrrolidone, which created a whispering gallery mode resonator that we combined with organic dyes for laser light generation. The lasers were flexible enough to bend around surfaces, physically transient in aqueous environments, and could be directly placed on various substrates. Moreover, the characteristics of laser emission could be modified by altering the size of the disk. Our results therefore highlight a new combination of materials that can be used in the environmentally friendly production of waste-free photonic devices.

Structural Analysis of Disk Resonance Gyroscope.

In this paper, we present two design methods to improve the performance of disk resonator gyroscope (DRG), including decreasing the frequency split and increasing the quality factor (Q). The structure parameters, which can affect the frequency split and Q value were concluded with the help of the FEM software. Meanwhile, devices with different parameters were designed, fabricated, and tested, and the experimental result was in accordance with the simulation. With the proposed methods, the DRG was selected with a high Q value and a low frequency split to satisfy the demand of high performance. The weakness and future works were pointed at last.