Electrical interconnect loss degrades the intrinsic high Q-factor of MEMS gyroscopic resonators and alters their phase response. This article proposes, for the first time, a loss cancellation approach utilizing an in situ integrated negative impedance converter (NIC), which requires no additional tuning structures or electrodes. Controllable positive feedback is embedded into the conventional transimpedance amplifier (TIA), yielding a virtual negative resistance (NR) that cancels the interconnect loss or even the intrinsic loss of the resonator itself. We further demonstrate that through proper zero-pole arrangement of the Opam and its feedback network, the NIC can be degenerated into a single-pole system, thereby eliminating stability risk. Serving as the front-end of a split-mode MEMS gyroscope, this scheme recovers the sense Q-factor from a damped value of 2.8 k to its intrinsic value of 42 k and passively reduces its thermal variation from 52% to 2.1%. Furthermore, it corrects the gyro's phase shift from 1.25 degrees to 0.06 degrees, corresponding to a reduction in the quadrature leakage coefficient from 2.2% to 0.1% and maintaining a variation of 40 ppm over a 100 degrees C-temperature range, even without the use of a high-accuracy active stabilization loop.

This article proposes an active probe card (APC) equipment for MEMS gyroscopes offering multiparameter capabilities that address the concerns of manufacturers and end users. An efficient and reliable frequency and Q-factor (f&Q) measurement method, enabled by a negative impedance converter (NIC), is first applied to the one-port sense resonator of the gyroscope. While the gyroscope's drive loop oscillates continuously, the f&Q measurement periods for drive/sense resonators and the fully operational gyroscope characterization periods are merged. It eliminates the time overhead associated with high-Q mode ring-down, restart-up waiting, and connection reconfiguration. Furthermore, the system incorporates a variable polarization voltage . The true process-related monitoring parameters and predictions of gyroscope operating behaviors with a specific frequency split are automatically extracted from two sequential tests with different Vp loads. The time cost per DUT is < 5 s. The probe's carrier card and active electronics card are interconnected with pluggable shielded cables, facilitating easy upgrading and adaptation to gyroscopes with different pin definitions. Using the proposed APC equipment, we demonstrate that it can: 1) realize the extraction and monitoring of true dimension and encapsulated pressure parameters in both the same and different process stages, and 2) perform system-level gyroscope operating behaviors prevalidation and grading at the wafer level.

This work analyses and improves the impact of parasitic resistances and capacitances, which are present in MEMS gyro fabrication process, on angle random walk (ARW). An electromechanical noise model with parasitics of MEMS gyros is presented to quantitatively analyze the role of parasitics on ARW. The parasitic capacitances affect the frontend interface current noise and the parasitic resistance affects the mechanical thermal noise due to quality factor loading effects. We analyze their contributions to the ARW of mode-split and mode-matched gyros. The gyro design criterions to limit the impact of parasitics are proposed, which has been validated via four specially designed gyros. The ARW is improved by a factor of 2.9 with optimized wires, parasitic and static sensing capacitances.

This work proposes a rectifier with adjustable temperature coefficient based on different the tail current ratio. In order to obtain better accuracy of MEMS resonator vibration amplitude control, this paper problem of rectifier tail current mismatch in our previous work, and realizes a rectifier with low temperature coefficient output amplitude. Then, based on this scheme, a rectifier with different temperature coefficient output amplitudes is realized by adjusting the current ratio of the tail current source of the rectifier to compensate the temperature coefficient of other modules in the MEMS resonator circuit, so as to reduce the temperature coefficient of the MEMS resonator amplitude. The design is realized by 0.35 mu m BCD process. The simulation results show that the temperature coefficient of MEMS resonator amplitude decreases from +716.6 ppm/C-circle to less than +/- 70ppm/C-circle under different type of process corner in the working temperature range of -40(circle)C to +60(circle)C

We propose a novel Q-factor measurement method utilizing a negative impedance converter (NIC) in the MEMS gyros for the first time. It can be regarded as a variant of the commonly used closed-loop counterpart but with only one mandatory port. It facilitates a more reliable Q-factor measurement of the sense resonator in an open-loop MEMS gyro, where the force electrode is unavailable. Its build-up time can be shortened to 0.16s with a Q-factor of 15.4k by increasing the value of negative impedance. Alternatively, the build-up time can also be improved by adding noise excitation during its drive phase. This approach also applies to the drive resonator, and two pairs of drive and detection caps can both be utilized to provide 2x extra gain factor.

In this paper, bias instability (BIS) and angle random walk (ARW) noise sources of quadrature correction for mode-split MEMS gyroscopes are first investigated. We propose a general noise model based on coupling stiffness correction that reveals the transfer mechanism of 1/f and white noise sources. The BIS with a small frequency split is mainly dominated by the electrostatic frequency-tuning voltage noise and that with a large frequency split is determined by the voltage reference noise in the quadrature loop. Due to the electrostatic frequency-tuning voltage noise, the quadrature correction system is unable to compensate for the quadrature error to zero. The BIS with quadrature correction is related to the initial quadrature error and frequency split. We find a good match between the presented model and measurements with an error of less than 15.1%. The simulation and experimental results have indicated that ARW will not be deteriorated by the quadrature compensation system. A MEMS mode-split gyroscope has achieved an ARW of 0.029 degrees/root h and a BIS of 0.08 degrees/h under the initial quadrature of 130 degrees/s and the frequency split of 85 Hz with quadrature error compensation. [2025-0014]

Compared to optical gyroscopes, MEMS gyroscopes still have gaps in long-term stability and accuracy, especially in terms of output drift under complex environmental loads. This paper proposes a co-simulation and experimental analytical approach to investigate the effects of assembly non-idealities on quadrature errors in MEMS gyroscopes. First, the material properties of the PCB are determined through topographical measurements to establish a model of PCB deformation and anchor displacement. Second, a diagonal screw loading experiment is designed to separate quadrature errors and validate the model through voltage modulation. Finally, systematic simulations and experiments are conducted to quantify assembly non-idealities and propose optimization strategies. Through experimental validation, it is found that PCB positioning non-idealities (±300 micrometers) can cause quadrature errors of 0.59°/s at 25.5V (with a simulated result of 0.42°/s), confirming the correlation between positioning non-idealities and the sensitivity of quadrature errors. By intentionally reducing the preload by 30% on one screw, the experimentally measured quadrature error reaches 0.51°/s (with a simulated result of 0.43°/s), confirming that asymmetric preload significantly exacerbates quadrature errors.

The performance of high-precision MEMS SRA is seriously affected by the mounting deformation of PCB. In this paper, the PCB deformation under different mounting conditions and its effect on the accelerometer output are systematically investigated and verified by finite element simulations. The results show that the PCB deformation gradually decreases with the increase of screw spacing, and the relative relationship between the screw installation direction and the sensitive direction of the accelerometer will affect the positive or negative change of the addition frequency under screw installation. Notably, four-hole screw mounting reduces PCB deformation by 91% compared to two-hole mounting, thereby minimizing frequency alterations. The purpose of the paper is to show the fundamental relationships on which all further considerations regarding MEMS SRA under PCB deformation are built.

A double mass MEMS gyroscope (DMG) with a large drive amplitude for north-finding is proposed, which is robust to fabrication imperfections and 1/f noise in its polarization voltage. Its drive amplitude is increased to 18 mu m to compensate for the gain loss in split mode, and we prove it's superior to narrow the frequency split for low 1/f noise consideration. The gyro's drive and sense motions are decoupled via specifically designed coupling beams. Fabricated in a 6-inch SOI process with a wafer-level vacuum package, the number of dies with a quadrature error <80 degrees/s is up to 70%. Even without a quadrature nulling loop, the proposed MEMS gyro could realize a bias-instability (BIS) <0.1 degrees/h with high yield interfaced with a customized ASIC. Utilizing "short-term but repeated" Maytagging, the proposed gyro realizes 0.23 degrees (4 milliradians) azimuth accuracy (1 sigma) within 5min.

This paper proposes a versatile and efficient tool for MEMS gyros offering multi-parameter concerned by both manufacturer and customer at the wafer-level. Two active probe cards (APCs) measure the gyros' static (capacitance and resistance) and dynamic parameters (frequencies, Q-factors, etc) as well as predicted system-level performance (zero-rate-output (ZRO), zero-quadrature-output (ZQO), etc). The process monitoring parameters and customer-concerned device operating parameters and behaviors under diverse applications with specific.f are automatically extracted from two sequential tests with different voltage loads within 10s per die. System-level characteristic parameters are revalidated, and the gyro's bias-instability (BIS) is also tested after dicing and packaging. The experimental results suggest the proposed APCs could facilitate the best working die selection and system-level performance pre-validation for different application scenarios (e.g., northfinding), at the wafer level.

To monitor the MEMS process stability and pre-characterize the fabricated errors of MEMS gyro at the wafer level, an identification system is proposed that can efficiently and non-destructively characterize the beam width and the comb gap errors on the scale of hundreds of nm. Based on the static negative stiffness effect of the resonant mode of MEMS gyro, a multi-function active probe card with variable bias voltage excitation capacity and multi-parameter automatic acquisition and calculation program are designed. The proposed identification system facilitates the in situ non-destructive identification of beam width and comb gap size errors, and large data acquisition of parameters such as resistance and capacitance characteristics, resonance frequency and Q-factor characteristics, and closed-loop quadrature coupling error. The experimental results show that the etching error distributions of the drive beam widths, the sense beam widths, and the gap of the combs are −80~160 nm, −100~140 nm, and 10~310 nm. Moreover, the above dimension errors' distributions are strongly correlated with the quadrature error of MEMS gyros. The test time per die is 6 s, and the overall 6-inch wafer test time is less than 1 hour.

This paper proposed an in-situ electrical method that can identify the drive beam width and the sense beam width of the MEMS gyroscope at the wafer level. The mechanical frequencies of two special modes were selected to characterize the beam width. Ten chips distributed on a wafer was selected for experiments. The experimental results indicate that the etching error increasing from the wafer center to the edge, and the dispersion on a wafer with a radius of 75 mm is about 300 nm. Optical microscopy was used to prove the reliability of the method and the wafer-level data verified the distribution of the etching error. This work is aimed at providing a method for fabless designers to explore the fabrication imperfections during the MEMS wafer processing.

This work analyzes the influence of different temperature compensation strategies on the bias instability (BI) of MEMS gyro for north-finding. Three temperature sources are involved, namely, conventional CMOS sensor and two virtual sensors based on the gyro's drive frequency and gain control voltage. We show that virtual measurement based on drive frequency is immune to the 1/f noise in CMOS readout circuit, and the measurement instability improved from 20m degrees C to 1.2m degrees C. Although virtual measurement based on gain control voltage still suffers from 1/f noise disturbance, its larger temperature sensitivity results in a better instability of 7m degrees C. The selection criteria of temperature sensor for mass-produced MEMS gyro with different temperature coefficients (TCOs) is proposed. Applying the virtual compensation strategies to a 4-position Maytagging procedure, the azimuth accuracy is increased from 0.47 degrees to 0.26 degrees and 0.35 degrees within 5min.

Quality factor tuning is attractive in degenerate and nondegenerate (NDE) MEMS gyros for drift suppression or shock and vibration immunity. This article proposes three resistance-based Q -factor tuning approaches without dedicated electrodes for NDE gyro. The inherent sensing capacitance is utilized as a Q -tuning mechanism for low cost, size, weight, and power (C-SWaP). Routing traces on MEMS or application-specified integrated circuit chips as well as the input impedance of charge sensitive amplifier (CSA) are utilized as damping sources. The theoretical and experimental results indicate Q -tuning utilizing the CSA's input impedance does not deteriorate the gyro's noise floor (angle random walk = 0.01°/√h, bias instability = 0.12°/h). Large-scale Q -tuning using the regulation of polarization voltage reduces the sensing Q -factor from 38 to 3 k. The gyro's settling time after shock is also reduced from 1.4 to 0.13 s after Q -tuning. Besides, a frequency-independent fine Q -tuning using tail current regulation in Opam is proposed to correct the thermal variation of the sensing Q -factor. It improves the gyro's bias drift from 1.5°/s to 0.2°/s. This work presents a low C-SWaP Q -tuning solution for high-end industrial MEMS gyro.

In this article, bias instability induced by phase noise via electrostatic frequency tuning is first investigated. We propose a noise model that reveals the transfer mechanism of electrostatic frequency tuning on scale factor (SF) instability noise and demodulated phase noise in an open-loop sense system of gyroscopes to analyze the relationship between frequency split and noise performances. The 1/f noise sources are the electrostatic frequency-tuning voltage noise and drive amplitude noise. By varying the frequency split and monitoring the instability of gyro's quadrature output and rate output, it is possible to identify these noise sources and contributions to bias instability (BIS) of zero-rate output. This identification also indicates the low bias-instability design criteria from both mechanical and circuit aspects, for example, the needed quadrature coupling rate, Q-factor, and frequency split. According to the proposed noise model, including amplitude and phase conversion processes, the lower limit of frequency split can be determined considering the bias-instability deterioration effect. A frequency-tuning criterion of open-loop MEMS mode-split gyroscopes for different noise requirement is hence established. Angle random walk (ARW) and BIS together define the adjustable range of frequency split in MEMS gyroscopes. The upper limit of frequency split is set by suppression of the white noise from the interface circuit. The experimental result indicates that an MEMS mode-split gyroscope has achieved an ARW of 0.009 degrees/root h and a BIS of 0.17 degrees/h under the quadrature of 40. /s and the frequency split of critical value (110 Hz).

For highly accurate micro-electromechanical systems (MEMS) gyroscopes, comb gap errors influence mechanical coupling errors and limit performance. In this study, an in situ method was proposed to identify the gaps of drive combs, drive-sense combs, and sense combs in MEMS gyroscopes that can be applied at the wafer level. Negative electrostatic stiffness of combs was considered in the model construction of the sense mode and the ${Y}$ -axis in-phase mode, and the frequency change caused by this was applied to characterize the comb gaps. Eight chips in different positions of a wafer were selected for verification of this method. The results shows that errors of drive comb gaps, drive-sense comb gaps, and sense comb gaps in the chip near the wafer center were 0.67, 0.60, and $0.53 \mu \text{m}$ , respectively, and those in the chip at the wafer edge were 0.96, 0.95, and $0.71 \mu \text{m}$ , respectively. The variation of comb gaps was $0.08 \mu \text{m}$ in a single chip near the wafer center and $0.03 \mu \text{m}$ in a single chip at the wafer edge. This work provides a method for fabless designers to explore the effect of the wafer process on the structures and reduce it through careful design.

Vibrating beam accelerometers (VBAs) have significant application potential in navigation guidance. This article proposed a novel high-precision frequency readout method and integrated CMOS circuit implementation for VBAs, and technologies, including sigma-delta modulation, up-sample and split, data synchronization, and nonlinearity correction, are employed in the method, which is analyzed in detail in this article. The method offers the advantages of low quantization noise, enough range, fixed output rate, and high linearity. Other force-frequency sensors could also benefit from this method but note that its noise suppression is most effective when the output rate is much lower than the frequency under test. The method is implemented by a CMOS circuit and integrated with an oscillator circuit, which makes a full-function single-package VBA possible. Static, shock, random vibration, and centrifugal tests of the frequency readout circuit and VBA were performed. Test results show that the frequency quantization noise is less than $10 \mu $ Hz/ $\surd $ Hz at 1 Hz, and can support $0.1 \mu \text{g}$ noise output. They also show that the vibration rectification error (VRE) is lower than 0.5 mg at 8 $\text{g}_{\text {rms}}$ and that the 20 g full range nonlinearity is 16 ppm.

This paper reports an active Q-factor stabilization approach utilizing electrical dissipation regulation for the first time. A bias current regulation loop is proposed to adjust the input impedance of the charge-sensitive-amplifier (CSA) automatically and stabilize the Q-factor of the MEMS resonator without altering its resonant frequency. After adopting the proposed stabilization loop, the Q-factor is stable at a relatively high point of 29.5k and its variation from -40℃ to +60℃ is reduced from 86.5% to 0.5%. The proposed approach requires no additional tuning structures or electrodes and applies to all MEMS resonators.

为了避免相敏解调引入的1/f噪声,同时进一步提高集成度、降低功耗,实现高精度硅微陀螺仪的全数字输出,设计了一种硅微陀螺仪数模单片集成电路.首先,针对已有的∑-△模数转换器(ADC)交流量化方案,设计了一种基于数字滤波系统的信号链预处理电路;其次,研究了数字滤波系统和乘法解调方案在有限版图面积中低功耗的硬件电路的实现方法,在IC设计平台上完成了包括前端信号链预处理电路、乘法解调模块、实时温度测量模块及串行接口(SPI)通信模块的设计与验证,并采用TSMC 0.35 μm工艺进行了流片.实验结果表明,硅微陀螺仪输出零偏不稳定性为0.38°/h,角度随机游走为0.05°/h1/2,零偏稳定性为3.4°/h,数字部分功耗为15.8 mW.实现了高精度硅微陀螺仪的低功耗和低噪声的全数字正交解调输出,提高了硅微陀螺仪的集成度和实用性.