Silicon Resonant Accelerometer Research Articles

Temperature Compensation Method Based on an Improved Firefly Algorithm Optimized Backpropagation Neural Network for Micromachined Silicon Resonant Accelerometers.

The output of the micromachined silicon resonant accelerometer (MSRA) is prone to drift in a temperature-changing environment. Therefore, it is crucial to adopt an appropriate suppression method for temperature error to improve the performance of the accelerometer. In this study, an improved firefly algorithm-backpropagation (IFA-BP) neural network is proposed in order to realize temperature compensation. IFA can improve a BP neural network’s convergence accuracy and robustness in the training process by optimizing the initial weights and thresholds of the BP neural network. Additionally, zero-bias experiments at room temperature and full-temperature experiments were conducted on the MSRA, and the reproducible experimental data were used to train and evaluate the temperature compensation model. Compared with the firefly algorithm-backpropagation (FA-BP) neural network, it was proven that the IFA-BP neural network model has a better temperature compensation performance. The experimental results of the zero-bias experiment at room temperature indicated that the stability of the zero-bias was improved by more than an order of magnitude after compensation by the IFA-BP neural network temperature compensation model. The results of the full-temperature experiment indicated that in the temperature range of −40 °C~60 °C, the variation of the scale factor at full temperature improved by more than 70 times, and the variation of the bias at full temperature improved by around three orders of magnitude.

Phase noise modelling of MEMS resonant accelerometer with non-AGC-driven circuit

Phase noise is an essential performance indicator for microelectromechanical system (MEMS) resonant accelerometers. The optimal resolution achievable is limited by the close-to-the carrier phase noise resulting from the modulation of noise sources by the mechanical resonator and driving circuit. Compared with the frequently used automatic gain control (AGC) circuit, the non-AGC scheme is more concise and can avoid the additional frequency flicker noise and 1/f 5 phase noise introduced by the AGC module. Although the mechanisms of these two kind of control loops are well-known by the communities, the phase noise modelling study on the non-AGC loop, especially compared with that of AGC loop is insufficient. This paper established a phase noise model for the AGC and non-AGC closed loop circuit of MEMS resonant accelerometer. The model includes the effects of resonator thermal noise, random loading noise of proof masses, front-circuit noise, comparator noise, AGC noise and amplitude stiffness coupling on the output noise spectrum of the resonant accelerometer. This paper carries the noise analysis through a behaviour level simulation with Simulink. The measured frequency power spectral density and Allan variance are very close to the theoretical predictions, which verifies the effectiveness of the phase noise model. The test results show that the white noise and the bias instability of the silicon resonant accelerometer are 837 ng (√Hz)−1 and 140 ng respectively, which are in good agreement with the model prediction results.

Analysis of the Scale Factor Nonlinearity of MEMS Differential Silicon Resonant Accelerometer Caused by the DETF’s Force-Frequency Nonlinear Characteristic

The scale factor nonlinearity of MEMS differential silicon resonant accelerometer(DSRA) structure is mainly due to the force-frequency nonlinear characteristic of DETF. This paper presents a detailed analysis of the relationship between the structural parameters, measurement range and the scale factor nonlinearity, which will provide a reference for the parameter design of DETF and overall structure. The inherent force-frequency nonlinearity of DETFs is analyzed, and the effects of structural parameters of DETF and axial force on nonlinearity of frequency variation are revealed. Combining the working principle of MEMS DSRA introduced first, the scale factor nonlinearity is studied. The results show that the structural parameters of the proof mass (determines the conversion between acceleration and inertial force), the support mechanism and the lever mechanism (determines the transfer coefficient of inertial force), and the DETF (determines the inherent force-frequency nonlinearity and affect the transfer coefficient of inertial force), as well as the measurement range, can all affect the scale factor nonlinearity. Moreover, the scale factor nonlinearity is directly proportional to the square of the measurement range and the square of the nominal scale factor, and inversely proportional to the square of the natural frequency of DETF. The finite element simulation is carried out, and the simulation results are in good agreement with the theoretical analysis values. Finally, the experiment on the scale factor nonlinearity of a prototype is carried out. The measured scale factor nonlinearity of the prototype is 1994.09ppm, which is consistent with the theoretical analysis value of 1737.30ppm.

Enhancing the Shock Response Performance of Micromachined Silicon Resonant Accelerometers by Electrostatic Active Damping Control.

This paper presents a micromachined silicon resonant accelerometer based on electrostatic active damping control, which can improve the shock response performance of the accelerometer. In the accelerometer, an electrostatic active damping structure and damping control circuit are designed to improve the equivalent damping coefficient of the system. System-level Simulink modeling and simulation of the accelerometer with an electrostatic active damping closed-loop control link were carried out. The simulation results indicate that the system can quickly return to normal output without an obvious vibration process after the shock. The fabricated and packaged accelerometer was connected to an external test circuit for shock performance testing. The stabilization time of the accelerometer after a 100 g, 3–5 ms half-sine shock was reduced from 19.8 to 5.6 s through use of the damping control. Furthermore, the change in deviation before and after the shock without damping control was 0.8197 mg, whereas it was 0.1715 mg with damping control. The experimental results demonstrate that the electrostatic active damping control can effectively improve the dynamic performance of the micromachined silicon resonant accelerometer.

A Silicon Resonant Accelerometer Embedded in An Isolation Frame with Stress Relief Anchor

Bias thermal sensitivity is a significant performance parameter of a silicon resonant accelerometer (SRA) and is normally used to evaluate the degree of engineering practicability. Theoretical analysis demonstrates that temperature-induced stress is the dominant factor that determines the bias temperature drift of the custom-designed SRA. To solve this issue, this paper presents an SRA embedded in an isolation frame with stress insensitive anchor that prevents the resonant beams suffering from the thermal stress along the sense axis and thus improving the bias stability. Moreover, a high sensitivity device is achieved by integrating the vibrating beams with the comb fingers without conventional additional mass design. The experimental results show that the nominal resonant frequency of the SRA is around 93 kHz with the sensitivity and nonlinearity of 223.7 Hz/g and 5.1‰. The thermal sensitivities of the two resonant beams are −27.6 ppm/°C and −28.8 ppm/°C, respectively, which can be considered as the results owing to temperature change of the Young’s modulus without the thermal stress effect. The bias thermal sensitivity and the stability (1σ) after compensation are tested to be approximately 0.7 mg/°C and 1 mg over the temperature range from −40 °C to 60 °C with ±80 g measurement range.

常温下硅微谐振加速度计零偏稳定性的提高

常温下硅微谐振加速度计零偏稳定性的提高

A High-Sensitivity Micromechanical Silicon Resonant Accelerometer without Mechanical Coupling

Micromechanical silicon resonant accelerometer can easily realize high-accuracy measurement by taking the digital signal as the output. Thus, this accelerometer has become popular in the field of micromechanical accelerometer. One-mass accelerometer with differential structure has blind area in measuring, and to overcome this deficiency, a new structure without mechanical coupling is designed. This new structure can cut off coupling channels by isolating the mass, and vibration decoupling between two resonators can be achieved structurally. Furthermore, the scale factor of the designed accelerometer is as high as 295 Hz/g. This finding indicates that this accelerometer has high mechanical sensitivity, which reduces the difficulty of follow-up testing.

A Differential Resonant Micro Accelerometer for Out-of-plane Measurements

This paper reports the theoretical and experimental characterization of a new z-axis silicon resonant micro accelerometer fabricated by the THELMA© surface micromachining technique, characterized by differential sensing and very small dimensions. The working principle of this device is based on the variation of the electrostatic stiffness of two torsional resonators. This work is a prosecution of the research on resonant accelerometers published in [1,2].

Design and Implementation of a Micromechanical Silicon Resonant Accelerometer

The micromechanical silicon resonant accelerometer has attracted considerable attention in the research and development of high-precision MEMS accelerometers because of its output of quasi-digital signals, high sensitivity, high resolution, wide dynamic range, anti-interference capacity and good stability. Because of the mismatching thermal expansion coefficients of silicon and glass, the micromechanical silicon resonant accelerometer based on the Silicon on Glass (SOG) technique is deeply affected by the temperature during the fabrication, packaging and use processes. The thermal stress caused by temperature changes directly affects the frequency output of the accelerometer. Based on the working principle of the micromechanical resonant accelerometer, a special accelerometer structure that reduces the temperature influence on the accelerometer is designed. The accelerometer can greatly reduce the thermal stress caused by high temperatures in the process of fabrication and packaging. Currently, the closed-loop drive circuit is devised based on a phase-locked loop. The unloaded resonant frequencies of the prototype of the micromechanical silicon resonant accelerometer are approximately 31.4 kHz and 31.5 kHz. The scale factor is 66.24003 Hz/g. The scale factor stability is 14.886 ppm, the scale factor repeatability is 23 ppm, the bias stability is 23 μg, the bias repeatability is 170 μg, and the bias temperature coefficient is 0.0734 Hz/°C.

Temperature Self-Compensation of Micromechanical Silicon Resonant Accelerometer

Temperature is one of the most important factors affecting the accuracy of micromechanical silicon resonant accelerometer (SRA). In order to reduce the temperature sensitivity and improve the sensor performance, a new method of temperature self-compensation for SRA is presented in this paper. Utilizing the differential structure of SRA, the temperature compensation for bias and scale factor can be realized simultaneously in this method. Moreover, because no temperature sensor is needed in this method, the error in temperature measurement due to the temperature gradient between the mechanical sensitive structure and temperature sensor is avoided, and the precision of temperature compensation for SRA can be further improved. The test results obtained on SRA prototype which is developed by MEMS Inertial Technology Research Center show that, by employing the method of temperature self-compensation, the temperature coefficients of bias and scale factor are reduced from 3.1 mg/°C and 778 ppm/°C to 0.05 mg/°C and -9.4 ppm/°C, respectively.

Modeling of Nonlinear Stiffness of Micro-Resonator in Silicon Resonant Accelerometer

Nonlinearities of the resonator in silicon resonant accelerometer (SRA) limit the ultimate short term frequency stability. In SRA, this stability is a measure of the achievable resolution. This paper discusses the nonlinear vibration phenomenon of micro-resonator considering the impact of the entire structure of SRA and builds a model to calculate the micro-resonator nonlinear stiffness K3,eff of the SRA prototype. The dies of SRA were fabricated by Silicon on Insulator (SOI) process. The equivalent model of the micro-resonator is built and the analytical value of the elastic constraint stiffness Ka of micro-resonator is derived as 8.91×104 N/m. It is calculated that K3,eff is equal to 5×1011 N/m3,and as a comparison, the simulation result is 5.026×1011 N/m3. The error between them is 0.52%. The nonlinear vibration experiments show that the maximum error between the theoretical and experimental value of resonance frequency is 2.1%. The prediction for the nonlinear stiffness contributes to further research on nonlinear vibration of the resonant beam. The model in this paper could also provide guidance and reference for optimal design of SRA.

Research on Surface Mounting Technology of Micromechanical Silicon Resonant Accelerometer

Surface mounting technology is a key process in MEMS packaging. The finite element model of package structures was established in this paper according to the designed micromechanical silicon resonant accelerometer. The effects of package substrate materials, adhesive material characteristics, uneven adhesive thickness, and adhesive defects on the micromechanical silicon resonant accelerometer were analyzed with ANSYS software. Results showed that the package substrate material strongly affected the resonance frequency of the resonator after the application of surface mounting technology. The Young’s modulus and thermal expansion coefficient of adhesives were found to be important factors that affect chip thermal stress and warpage. Uneven adhesive thickness and adhesive defects also affect the resonance frequency of the resonator. DOI: http://dx.doi.org/10.11591/telkomnika.v11i5.2475

Phase noise analysis of micromechanical silicon resonant accelerometer

The phase noise in micromechanical silicon resonant accelerometer (SRA) can perturb its frequency output and determines the minimum detectable change in acceleration (sensor resolution). In order to improve the resolution and optimize the sensor performance, the phase noise of SRA is studied in this paper. Theoretical model of phase noise of SRA is set up, especially the effect of the automatic gain control (AGC) circuit in oscillator to phase noise in low frequency range (1/f3 phase noise and 1/f5 phase noise) is analyzed, and the restriction of resolution performance arising from the 1/f3 phase noise caused by AGC is also illustrated. Phase noise experiments are then performed on a SRA prototype developed in MEMS Inertial Technology Research Center and validate the model. Compared to the previous work, the phase noise model in this paper matches the experiments results more precisely, and could provide guidance and reference for design in MEMS inertial device.

Study on Packaging Thermal Stress of Micromechanical Silicon Resonant Accelerometer

Packaging thermal stress is harmful to the performance of the micromechanical silicon resonant accelerometer. In order to decrease the packaging thermal stress, correlations of packaging thermal stress with the material properties, curing temperature and geometrical size of adhesive layers of adhesive materials were discussed. A finite element model of package was developed to analyze the influence of surface mounting technology (SMT） on the micromechanical silicon resonant accelerometer. The simulation results show that the Young’s modulus, thermal expansion coefficient, curing temperature and geometrical sizes of adhesive layers are important influencing factors for packaging thermal stress and the warpage of the chip. The thermal stresses during the process of SMT will cause the resonant frequency shift.

Silicon Resonant Micro Pressure Sensor and Micro Resonant Accelerometer

Silicon micro resonant pressure sensor and accelerometer are kinds of new gauging instruments. Both the silicon micro resonant pressure sensor and accelerometer have the particular advantages and become the key development direction of micro sensors. The introduction of silicon micro resonant pressure sensor is carried out first in this paper. The work theory and development tendency of resonant pressure sensor are discussed in detail. And then, the silicon resonant accelerometer is studied. The research development statuses of resonant beam accelerometer and development tendency are taken to analysis in this paper.

微杠杆在硅微谐振式加速度计中的应用

A micromechanical Silicon Resonant Accelerometer(SRA) prototype fabricated by Deep Dry Silicon on Glass(DDSOG) process was presented.The amplification of single-stage microlever in the SRA to the interial force was researched,then it pointed out that the scale factor of SRA is proportional to the system amplification factor n.The theoretical model of single-stage microlever in SRA was established,and the formulas for microlever amplification factor A and axial stiffness K were derived.On this base,the formula for system amplification factor n was also derived.According to the formula,the theoretical value of system amplification factor n for SRA prototype is calculated to be 21.820.As a comparison,its simulation value of 19 is also achieved by the Finite Element Analysis(FEA).The practical test for the SRA prototype was performed,which shows that the scale factor of the SRA is 143 Hz/g and the system amplification factor is 25.466.As compared with the theoretical value,the errors of simulation and test results are 14.8% and 14.3%,respectively,which are within the acceptable range.

A Resonant Microaccelerometer With High Sensitivity Operating in an Oscillating Circuit

A new micromachined uniaxial silicon resonant accelerometer characterized by a high sensitivity and very small dimensions is presented. The device's working principle is based on the frequency variations of two resonating beams coupled to a proof mass. Under an external acceleration, the movement of the proof mass causes an axial load on the beams, generating opposite stiffness variations, which, in turn, result in a differential separation of their resonance frequencies. A high level of sensitivity is obtained, owing to an innovative and optimized geometrical design of the device that guarantees a great amplification of the axial loads. The acceleration measure is obtained, owing to a properly designed oscillating circuit. In agreement with the theoretical prediction, the experimental results show a sensitivity of 455 Hz/ ( g being the gravity acceleration) with a resonant frequency of about 58 kHz and a good linearity in the range of interest.