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In this paper we present the recent improvement of a silicon micro gyroscope with 10°/h stability in the temperature range from -40° to 60°. The gyroscope sensing element is fabricated in an 80μm-thick SOI process and sealed in a wafer level vacuum package. The gyroscope die and ASIC die are stacked in the ceramic package with low stresses package technology. Under room temperature, the gyroscope has achieved non-linearity 26.9ppm in full-range of ±400°/s, 1.2°/h bias stability (1σ), and 0.03°/√h angle random walk(ARW) and 0.2°/h instability. The bias stability is 10.2°/h(1σ) with 5 temperature cycles, the temperature range is from -40° to 60°.

A calibration method for a batch of micro gyroscopes to obtain their scale factor and bandwidth is presented in this paper, which is based on virtual Coriolis force. And in the detection axis of the micro gyroscope, an electrostatic force is set to simulate the real Coriolis force to calibrate their scale factor and bandwidth. Thirteen micro gyroscopes are tested to verify the feasibility of this method. Compared with traditional method, the proposed method can obtain the scale factor of a batch of gyroscopes with an error less than 0.8%. Besides, the experiment results show that bandwidth of the micro gyroscope measured is 354.3Hz by the virtual scale factor method with a maximum phase error of 3.39 deg, which are in close agreement with the simulation result 349.5Hz

This paper presents a fully differential low flicker noise automatic-amplitude-control (AAC) ASIC for a split-mode MEMS gyroscope. The impact of flicker noise in AAC on the gyroscope’s bias instability is firstly analyzed. Chopper stabilized amplitude detector and error amplifier are employed to remove their flicker noise. A second-order loop filter attenuates the flicker noise from variable gain amplifier (VGA). The ASIC is fabricated in TSMC 0.35μm CMOS process and consumes 1mW power with a 3.3V supply voltage. Experimental results indicate the flicker noise component in the gyroscope’s drive amplitude is greatly reduced.

The in-phase error caused by misalignment of comb fingers leads to bias drift of silicon microgyroscopes which is also susceptible to stress. By periodically making the drive loop close and open and sampling the sense mode output while it’s open, the in-phase error term can be canceled. The calibrated bias of gyro is greatly improved and is no longer susceptible to stress. This method is also applicable to silicon accelerometer and provides a solution for enhancing the long-term stability of MEMS inertial devices.

Compared with traditional AM gyroscope, FM operation brings about wider dynamic range and more stable scale factor and bias. A third-order noise shaping frequency-to-digital converter is proposed in this paper to improve FM gyroscope's ultimate precision. It achieves 8μHz or 10dph resolution in 10Hz bandwidth with only 200kHz reference clock frequency. The full scale is 2000dps, corresponding to a dynamic range of 117dB with 1.26μW power consumption. This ultra-low-noise and low-power frequency-to-digital converter enables the development of high performance FM gyroscope.

This paper presents a modified pierce oscillator based ultra-low power CMOS readout circuit for a MEMS resonant accelerometer. Differential topology is adopted to make the readout circuit compatible with the MEMS sensing element and depress the common mode noise from amplitude control circuit and bias current source. A g m regulated amplitude control strategy is proposed to avoid the MEMS resonator from strong nonlinear region without deteriorating its noise performance. Simulation results indicate the proposed readout circuit only consumes 1.8μW with a supply of 1.8V. Interfaced with a MEMS resonant accelerometer, it could realize a noise floor of 2μg/Hz1/2 but with 1000~10,000x lower power than published works.

A phase noise model is proposed for silicon oscillating accelerometers (SOAs), which can be used to estimate the frequency noise from the accelerometer. This model treats the SOA as a time-varying system and employs a unified approach to decompose the physical system into phase and amplitude modulation paths to predict the phase noise in SOA. Furthermore, the model also reveals the relationship between mechanical displacement amplitude and design specifications, which can serve as a guideline for performance optimization. The soundness of this model has been validated against both time-domain numerical simulations and experimental results. This model is also applicative in microelectromechanical-system (MEMS) oscillators and MEMS oscillator-based sensors.

This paper reports a method to suppress the in-phase error of silicon micro gyroscopes in real time, which can realize long-term stability, without significantly affecting the sensor noise. The in-phase error suppression is by periodically changing the polarity of the drive mode, and the bias (zero rate output) decreases from -7.8deg/s to -3.9deg/s, attenuation amplitude of which is about 3.9deg/s. By sampling the output using information fusion technology, low shirt-time noise and bias instability can be obtained without cutting off the gyroscope and adding additional sensors, the bias instability of which is reduce from 35.0 deg/hr to 10.8 deg/hr. The feasibility of the approach was experimentally evaluated using a MEMS gyroscope with the algorithm implementation on FPGA in real-time.

The effect of external stress on split mode gyroscope bias is identified by experimental approaches for the first time in this paper. A long-term drift relates to installation mode but independent of temperature variation is observed and its origination is explored. Two bias alteration mechanisms are validated, namely, variations of quadrature coupling and in-phase leakage from drive axis. Both of them are believed arisen from anchors' unbalanced displacement due to applied stress. This work is our first step to demystify the stress induced drift and lays a foundation of sensing element and package optimization for low stress sensitivity.

This paper describes a compact and low-power oscillating circuit for silicon oscillating accelerometer (SOA). The influence of oscillation amplitude control strategy on accelerometer performance is analyzed. A rail to rail comparator replaces the traditional AGC (automatic gain control) circuit for oscillation amplitude control. It makes the circuit more compact, lower power consumption, and reduces the flicker noise introduced by amplitude control greatly. The experiment shows the bias stability is 13.3µg from 22.9µg, the bias-instability is 4.3µg from 9.3µg, and the system power consumption is reduced to 200mW from 1.2W.

This article presents a self-temperature compensation method used for MEMS gyroscopes. Drive frequency of gyroscope is employed as temperature compensation source, so that no external temperature sensor needed. When gyroscope starts to work, the circuit generates heat, providing the temperature input. Meanwhile, only 120 seconds is needed to calculate compensation parameters without pre-calibration. Therefore, the efficiency of experiment and study can be improved by this method.

This paper reports a method of measuring the on-chip thermal stress for silicon resonant accelerometer (SRA). This method could be used to evaluate the stress-temperature characteristic of SRA, and that would help to focus the problems exist in SRA. Clamp-clamp Double Ended Turning Fork resonator is used as a basic measurement unit. Analysis of the accuracy and noise in stress measurement is given. An implementation of this method on a silicon resonant accelerometer is detail described. The Experiment shows that the on-chip thermal stress could be precisely measured, and the test result shows a more clear view of the state of the individual SRA.

This paper describes a low temperature drift Z-axis silicon gyroscope with a low temperature sensitivity interface circuit. The gyroscope's temperature drift is optimized from two aspects: MEMS structure and its interface circuit design. Firstly, the sources of zero rate output(ZRO) are analyzed, and then we point out that improving the stability of demodulation phase can reduce thermal drift effectively. A careful designed MEMS structure with wafer level package is introduced and a novel interface circuit is proposed to improve gyroscope's phase stability. Then the newly designed gyroscope is tested, its bandwidth is above 100Hz with a full scale of ±300°/s. In room temperature environment, its bias stability(1a) achieves 0.78°/h, with a temperature coefficient of 6.4°/h/°C in full temperature range (−40°C–60°C).

This paper demonstrates a silicon resonant accelerometer which consists of a MEMS structure and an ASIC readout circuit. The MEMS sensor is fabricated in an 80-µm thick SOI process with a wafer level vacuum package. For noise reduction, several techniques are employed during the circuit design. And in order to reduce the temperature drift due to self heating, the power consumption is carefully limited. Finally, the prototype with these two chips is implemented, and the testing results show it can achieve sub-µg bias instability and equation velocity random walk within ±30g full scale. Moreover, this prototype consumes 3.5mW under 1.5V single supply.

In this paper we present the recent improvement of a silicon micro-mechanical vibrating beam accelerometer (SVBA) which combine the advantage of low cost of silicon MEMS fabrication technology, small size vacuum wafer level package, low noise low power application-specific integrated oscillation circuit and digital frequency demodulation technology. Under room temperature, it has achieved bias instability 1µg (Allan variance), stability 10µg (1σ, one hour), resolution 13µg (direct test result, including all drift and noise), non-linearity 11.4ppm in full-range of ±20g. And the stability of scale factor is 1.5ppm which is tested for seven times during 70mins where temperature be controlled within 0.1°C.

MEMS gyros have sensitivity to acceleration due to asymmetry of their mechanical designs and/or micromachining inaccuracies. This paper describes a tactical grade MEMS gyro with superior acceleration rejection. The MEMS gyro structure has two proof masses and 12 modes. The effects of low-order modes on the gyro were studied by theory analysis and vibration experiments. The gyro modes were reordered with a new anchor beam structure and optimized structural parameters. The gyro structure was fabricated with SOI technology and packaged with wafer level vacuum packaging. The gyro die and ASIC die were stacked assembly in the ceramic package, and the volume is 11.4×11.4×3.8mm3. The gyro's operating rang is ±300°/s, scale factor nonlinearity is 136.6ppm, the bias stability is 1.3°/h (1σ) and the bias repeatability is 0.8 7h(1σ). The g sensitivity and g2 sensitivity are 6.9°/h/g and 0.2°/h/g2 respectively.

In order to improve the bias stabilities in different temperature for silicon resonant accelerometer (SRA), a temperature measurement method, which measure Temperature in package cavity, was proposed based on chip integrated temperature resonator. Firstly, the frequency-temperature characteristics of the resonators in SRA is analyzed. Afterwards, the heat transfer model for SRA based on chip integrated temperature resonator is established, and the temperature measurement error is analyzed. Then, the hysteresis errors of the two temperature measurement methods based on the external temperature sensor and integrated temperature resonator are contrasted. At last, the first-order linear temperature compensation model is established after several tests of accelerometer bias and the temperature related bias is compensated. Experiment results indicate that using integrated temperature measurement resonator, hysteresis error decreases from 200 Hz to 10 Hz and the bias instability from 283.3 ug to 28 ug after temperature compensation. The results exposed that integrated temperature measurement resonator can accurately reflect the cavity temperature of SRA and increase accuracy of temperature compensation.

This paper gives a detail description of a silicon vibration beam accelerometer which was fabricated by SOI technology and encapsulated in a wafer level vacuum package. The wafer level package gives advantage of small size and low cost, but also produce additional residual stresses that increased the temperature coefficient of the vibration beams. To solve this problem, the sensing structure was redesigned and reduce the temperature coefficient from 50Hz/℃ to 10Hz/℃. Moreover, with carefully assembly, control and measure technology, the accelerometer system achieved reliable performance. Experiment result shows that the scale factor was 120Hz/g, measurement rang was ±50g with non-linearity coefficients of 19μg/g2 and 0.06μg/g3, resolution was 10μg/sqrt(Hz), bias Allan variance was 10μg.

This paper describes a silicon resonant accelerometer implemented in SOI technology. With fully differential design and micro-lever system, the accelerometer achieves a sensitivity of 82Hz/g with a nominal frequency of 30 kHz. The MEMS device is placed in a ceramic vacuum package, so gets a quality factor nearly 1e5. Readout circuit is also introduced which includes two differential oscillators and a double channel frequency measure circuit. A novel differential capacitance sense circuit employing high frequency carrier and diodes ring is used to avoid driving signal feed through. And a 90° phase shifter and AAC (automatic amplitude control) are also used to maintain phase and amplitude balance. The frequency measurement circuit is based on all digital multi-bit PLL (phase lock loop) technology, which is implemented by 18bit ADC and FPGA, the accuracy of each channel is better than 1mHz. The complete resonant accelerometer achieves 13.5μg/ √ Hz resolution and 3.6μg bias stability.