Design and test of a micromachined resonant accelerometer with high scale factor and low noise
Introduction
Micromachined accelerometers have been widely used in numerous applications such as inertial navigation [1], consumer electronics, vehicle safety [2] and land seismic acquisition [3]. Micromachined resonant accelerometer (MRA) is a type of high-precision inertial sensor based on accurate force-frequency characteristics of the high-Q resonators. When an input acceleration acts on the proof mass, the inertia force along the sensitive axis causes the inherent frequency shifting of two resonant beams on both sides of the proof mass in the opposite directions. The change in differential frequency is proportional to the input acceleration within a certain measurement range. The MRA is very attractive for high-precision applications due to its high sensitivity, low noise, large dynamic range and insensitivity to disturbances as a result of direct frequency output [4], [5], [6].
Silicon-based MRAs have drawn much attention of researchers with various MRA devices reported in the literature. Among them, much attention has been focused on high performance applications, such as high-precision inertial navigation and low noise seismic data acquisition. Early development of an inertial-grade MRA was reported by Draper Laboratory (USA) for navigation and guidance applications [7]. The test data showed a scale factor stability of better than 1 ppm and a bias stability of less than 1 μg by precise temperature control. A novel design of the two-stage micro-lever mechanism was proposed in 2005 by University of California, Berkeley, USA [8]. The developed MRA prototype showed a scale factor of 158 Hz/g with a relatively small proof mass area (0.27 mm2). Recently, Pohang University of Science and Technology (South Korea) presented a novel robust resonant accelerometer without micro-levers, of which the Q-factor reached up to 3.7 × 105 [9]. University of Cambridge (UK) reported recently a high-sensitivity resonant accelerometer for seismic acquisition, of which the scale factor was as high as 18816 Hz/g within an ultra-low range of ±0.05 g [10]. The measured acceleration noise, including ambient vibration effect, was 3.22 and the intrinsic noise floor of the resonator was only 144 . Nanjing University of Science and Technology (China) and National University of Singapore jointly designed a CMOS read-out circuit for their resonant accelerometer [11]. The measured noise level was reduced down to 2 , which is the lowest noise result ever reported.
It is known that noise level is an important performance parameter for inertial-grade MRAs which directly limits the attainable resolution. Increasing the scale factor is an effective method to reduce the sensor noise [8], [12], [13], [14], where the scale factor is defined as the change in differential frequency per unit input acceleration. Large scale factor is also desirable because it decreases the degree of frequency stability required to resolve a given acceleration level [7]. Currently, much attention has been focused on the optimization of various micro-lever mechanisms to achieve high sensitivity while the interaction effect within the sensing structure was neglected [8], [14]. Moreover, the noise analyses of the MRA are focused mainly on the phase noise in most of the published works [15], [16], [17], [18]. Although the amplitude-to-frequency conversion of the resonator operated at nonlinear vibration mode has been modeled [19], the noise characteristics associated with vibration amplitude need to be further verified experimentally. How to set an optimal vibration amplitude for the automatic amplitude control (AAC) loop and thus minimize the overall accelerometer noise is one of the most challenging aspects in design of a high-performance MRA [16], [20].
This paper presents the design, fabrication and experimental study of a MRA with high scale factor and low noise, which is aimed for high-accuracy inertial navigation application. By optimizing the structure dimensions composing of the micro-lever, resonant beam and bearing beam, the scale factor of the MRA has been increased greatly from 66.30 Hz/g (our previous work) to 244.15 Hz/g at a full scale range of ±15 g. Moreover, the nonlinear vibration noise, frequency measurement noise and vibration amplitude-independent noise are modeled and discussed to address the acceleration measurement noise. The relationship between the overall noise and the vibration amplitude is also evaluated experimentally to obtain the optimal drive voltage setting. The theoretical model and the experiment results show that the total noise reaches its minimum when the nonlinear vibration noise is equal to the frequency measurement noise. With the improved structure dimensions and optimized drive voltage, the measured noise reduces down to 0.38 , which demonstrates a fine acceleration resolution of 0.63 μg.
Section snippets
Structure and operation of the MRA
A typical silicon structure of our MRAs consists of four parts: proof mass, one-stage micro-levers, double-ended tuning fork (DETF) resonators and bearing beams. Half of the fully symmetric device structure is illustrated schematically in Fig. 1. The movable silicon structure is bonded to a glass substrate via a set of anchors. The motion of the DETF resonators are excited by an electrostatic comb drive and sensed by a capacitive vibration amplitude detection.
When an input acceleration occurs
Modeling and optimization of the vibration amplitude-dependent noises
The frequency noise of the MRA is composed of various sources, such as mechanical noise, position sensing noise, frequency measurement noise and electrostatic actuation noise. This paper focuses on evaluation of the frequency noise closely related to the vibration amplitude of the resonator. In the following noise analysis, the frequency noise is classified into three kinds of sources: nonlinear vibration noise, frequency measurement noise and vibration amplitude-independent noise.
The block
The MRA setup
A schematic of the MRA setup is shown in Fig. 13. The MRA prototype, which consists of a MRA device, a capacitive vibration amplitude sensing printed circuit board (PCB) stacked with a closed-loop resonator control PCB, was fixed on a precise turntable by the test fixture. The MRA device was sealed in a vacuum metallic package and mounted on the sensing PCB. The accelerometer was tested by using the tilt method in the Earth’s gravitational field, where the input acceleration is a function of
Conclusions
A micromachined resonant accelerometer has been designed and experimentally evaluated with high sensitivity and low noise for future inertial navigation applications. The scale factor model of the MRA is presented and various design considerations to increase the scale factor are discussed. The structure parameters of the MRA are optimized by ANSYS Workbench software to produce a measured scale factor of 244.15 Hz/g, which increases by 268% compared with our previous work. Moreover, the
Aknowlegements
This work was supported by the National Natural Science Foundation of China [grant numbers 61374207, 41774189].
Yonggang Yin received the B.S. degree in mechanical engineering and automation from Tsinghua University, Beijing, China, in 2014. He is currently working toward the Ph.D. degree in instrumentation science and technology in Tsinghua University. His research interests include MEMS resonant accelerometers and 3-axis electrostatically suspended accelerometers.
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Yonggang Yin received the B.S. degree in mechanical engineering and automation from Tsinghua University, Beijing, China, in 2014. He is currently working toward the Ph.D. degree in instrumentation science and technology in Tsinghua University. His research interests include MEMS resonant accelerometers and 3-axis electrostatically suspended accelerometers.
Zhengxiang Fang received the B.S. degree in mechanical engineering and automation from Tsinghua University, Beijing, China, in 2015. He is currently working toward the Ph.D. degree in instrumentation science and technology in Tsinghua University. His research interests include MEMS resonant accelerometers and interface circuit design.
Fengtian Han received the B.S. degree in automation instrumentation from Nanjing University of Science and Technology, Nanjing, China, in 1990, the M.S. degree in industrial automation from Beijing University of Aeronautics and Astronautics, Beijing, China, in 1996, and the Ph.D. degree in precision instrumentation from Tsinghua University, Beijing, China, in 2002. From 2002 to 2004, he was a Post-Doctoral Scholar with the Department of Precision Instrument, Tsinghua University, where he is currently a Professor. His research interests include MEMS inertial sensors and inertial navigation.
Bin Yan received the B.S. and Ph.D. degrees in Department of Precision Instrument from Tsinghua University, Beijing, China, in 2011 and 2016, respectively. His research interests include MEMS resonant accelerometers and capacitive sensing. He is currently working in Huawei Technologies Co. Ltd., Beijing.
Jingxin Dong received the M.S. degree in Department of Precision Instrument from Tsinghua University, Beijing, China, in 1981. From 1996 to 1997, he was a senior visiting scholar in Moscow Power Engineering Institute, Russia. He is currently a Professor in Department of Precision Instrument, Tsinghua University. His research interests include control engineering, inertial sensors and inertial navigation.
Qiuping Wu received the B.S., M.S., and Ph.D. degrees in precision instrumentation from Southeast University, Nanjing, China, in 1994, 1997, and 2000, respectively. From 2000 to 2002, he was a Post-Doctoral Scholar with the Department of Precision Instrument, Tsinghua University, Beijing, China, where he is currently an Associate Professor. His research interests include inertial sensors, integrated navigation, and gravity gradiometers.