Capacitive Displacement Research Articles

Progress in the development of space inertial sensor for TianQin project

The TianQin project is a space gravitational wave detection program proposed by China, imposing strict requirements on inertial sensors. This paper introduces the basic principle and development progress of the TianQin project inertial sensor. At present, key technologies such as test mass, capacitance displacement sensing, and charge management have been developed, with some performance exceeding requirements. Ground-based test systems utilizing torsion pendulums have initially investigated the patch effect, magnetic field effect, residual gas damping, and temperature gradient effect. The inertial sensor is currently undergoing system integration and ground performance tests, and will be tested on TQ-2.

Active micro-vibration isolation system for adaptive vibration suppression tests using piezoelectric stack actuator

An active micro-vibration isolation system for adaptive vibration suppression using piezoelectric stack actuators is presented, along with the discrete time modelling method, real-time adaptive controller design, and hardware implementation. The system comprises piezoelectric stack actuators, capacitive displacement sensors, power amplifiers, signal conditioners, and a real-time computer. A discrete asymmetric Bouc-Wen model is developed to characterize the nonlinear behavior of the piezoelectric stack actuators. System identification is conducted using an improved particle swarm optimization method, specifically the Hybrid PSO-Jaya algorithm, which sequentially integrates the PSO algorithm with the Jaya algorithm. Additionally, an improved adaptive filtering algorithm employing affine projection, referred to as the FXAPA algorithm, is introduced to facilitate real-time control. The efficacy of the proposed active micro-vibration isolation technology is validated through micro-vibration suppression tests.

Sensing offset analysis and compensation of a capacitive displacement transducer for space inertial sensors

Abstract Capacitive displacement transducers play a crucial role in inertial sensors especially for space gravitational wave detection missions. One of the major requirements for the displacement transducer is to have a lower sensing offset. The sensing offset will adversely affect the accuracy of the absolute position measurement of the test mass, providing erroneous data to the drag-free controller and leading to spacecraft mispositioning. Additionally, the offset could introduce multiplicative noise to the sensing output and the closed loop output of the inertial sensor. The asymmetry of the sensing bridge within the front-end electronics has been identified as the primary source of these offsets. This paper analyzes the requirements of the main parameters in the sensing bridge. A method is proposed to reduce the sensing offset by utilizing differentiated resonant capacitors while maintaining the ability to tune the resonant frequency and ensure a sufficiently low sensing noise level. Experimental results show that this approach can effectively reduce the residual sensing offset to (−15.7 ± 5.0) ppm, which satisfies the stringent requirement for space inertial sensors in the TianQin mission.

A modified linear capacitive displacement transducer for any range

A modified linear capacitive displacement transducer for any range

Design of non‐contact capacitive displacement detection methods for magnetic levitated sphere

AbstractTo meet the demand for non‐contact displacement detection of magnetic levitation spheres, single‐ended and differential variable electrode distance capacitance displacement detection schemes are designed in this paper. For these two schemes, finite element simulation models are established in COMSOL Multiphysics software to obtain the relationship between the test capacitance and the displacement of the magnetic levitation sphere. In the single‐ended scheme, there is a non‐linear relationship between the test capacitance and the position of the levitated sphere, and this non‐linearity becomes more significant as the sphere moves away from the electrode plate. In contrast, in the differential scheme, the test capacitance and the displacement of the levitated sphere follow a linear relationship, but the test sensitivity decreases with the expansion of the measuring range. The simulation results of the differential scheme have been verified by building a spherical displacement detection simulator, and thanks to the mature development of capacitive detection circuits, the scheme is expected to achieve better than nanoscale displacement detection resolution in the 6.6 mm displacement range of a magnetic levitation sphere in the future.

Surge current management in Dynamic Reverse Bias reliability testing of WBG devices for automotive application

Surge current management in Dynamic Reverse Bias reliability testing of WBG devices for automotive application

An electrostatically actuated MEMS microgripper with high amplification for precision manipulation

An electrostatically actuated MEMS microgripper with high amplification for precision manipulation

High-Precision Capacitive Displacement Sensor for Gravitational Wave Detection: Sensitive Probe Modeling, Analysis, and Optimization

High-Precision Capacitive Displacement Sensor for Gravitational Wave Detection: Sensitive Probe Modeling, Analysis, and Optimization

Planar Two-Dimensional Capacitive Displacement Sensor Based on Time Grating

Efforts to meet the demand for planar two-dimensional (2D) displacement measurement systems are limited by the difficulties of manufacturing 2D diffraction gratings with high precision over a large area. The present work addresses this issue by capitalizing on the high-precision of one-dimensional capacitive displacement sensors based on time-grating to develop a planar 2D capacitive displacement sensor technology composed of a large-area array of excitation electrodes positioned on a fixed ruler and a small-area array of induction electrodes assembled on a coplanar moving ruler that travels over the fixed ruler at a fixed separation gap. Firstly, the individual traveling wave signals of the induction electrodes on the moving ruler are analyzed theoretically to develop a method for decoupling information pertaining to the separate displacements in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> directions. Then, the feasibility of the proposed decoupling method is verified by simulations based on a three-dimensional electric field model. Finally, the proposed measurement technology is validated experimentally based on tests conducted using a prototype sensor manufactured using standard printed circuit board technology. The experimental results demonstrate that the prototype sensor achieves measurement errors of ±8.2 μm and ±6.8 μm in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> directions, respectively, over the full 200 mm × 200 mm measurement range of the sensor.

Influence of the Injection Bias on the Capacitive Sensing of the Test Mass Motion of Satellite Gravity Gradiometers.

The performance of the capacitive gap-sensing system plays a critical role in a satellite-based gravity gradiometer that is developed using an electrostatic accelerometer. The capacitive sensing gain mainly depends on the stabilized injection bias amplitude, the gain of the transformer bridge, and the trans-impedance amplifier. Previous studies have indicated that amplitude noise is the main factor influencing the noise of capacitive displacement detection. Analyzing the capacitive gap-sensing system indicates that the amplitude, frequency, phase, and broadband noises of the stabilized injection bias have varying levels of influence on the performance of the detection system. This paper establishes a model to clarify the mentioned effects. The validation of the sub-tests demonstrates that the analysis and evaluation results of various noise coefficients are highly consistent with the model's predicted outcomes.

Research and Optimization of High-Performance Front-End Circuit Noise for Inertial Sensors

An inertial sensor is a crucial payload in China’s Taiji program for space gravitational wave detection. The performance of the capacitive displacement sensing circuit in the low-frequency band (0.1 mHz to 1 Hz) is extremely important because it directly determines the sensitivity of the space gravitational wave detection missions. Therefore, significant, yet challenging, tasks include decreasing the low-frequency noise in capacitive displacement sensing circuits and improving the capacitive sensing resolution. This study analyzes the noise characteristics of the pre-amplifier circuit within the capacitive sensing circuit, achieves precise tuning of the transformer bridge, and examines how transformer parameters affect noise. In addition, this study introduces a method using a discrete JFET to reduce the operational amplifier current noise and analyzes how feedback resistance and capacitance in TIA circuits affect the overall circuit noise. The proportional relationship between different transformer noises and TIA noise before and after optimization was analyzed and experimentally verified. Finally, an optimized TIA circuit and a superior transformer were utilized to achieve an increase in the capacitive sensing resolution from 1.095 aF/rtHz @ 10 mHz to 0.84 aF/rtHz @ 10 mHz, while improving the performance by 23%. These findings provide valuable insights into further decreasing circuit noise and increasing the capacitive sensing resolution.

Analysis of the Frequency-Dependent Vibration Rectification Error in Area-Variation-Based Capacitive MEMS Accelerometers.

The presence of strong ambient vibrations could have a negative impact on applications such as high precision inertial navigation and tilt measurement due to the vibration rectification error (VRE) of the accelerometer. In this paper, we investigate the origins of the VRE using a self-developed MEMS accelerometer equipped with an area-variation-based capacitive displacement transducer. Our findings indicate that the second-order nonlinearity coefficient is dependent on the frequency but the VRE remains constant when the displacement amplitude of the excitation is maintained at a constant level. This frequency dependence of nonlinearity is a result of several factors coupling with each other during signal conversion from acceleration to electrical output signal. These factors include the amplification of the proof mass's amplitude as the excitation frequency approaches resonance, the nonlinearity in capacitance-displacement conversion at larger displacements caused by the fringing effect, and the offset of the mechanical suspension's equilibrium point from the null position of the differential capacitance electrodes. Through displacement transducer and damping optimization, the second-order nonlinearity coefficient is greatly reduced from mg/g2 to μg/g2.

Development and experimental investigation of a high-precision capacitive displacement transducer of the inertial sensor for TianQin

Capacitive sensing electronics are critical to space gravitational wave detection missions, providing the test mass motion information for the inertial sensor’s non-sensitive axis control and the drag-free control of the satellite. For the TianQin mission, the capacitive sensor requirement is at 6 mHz, corresponding to a displacement noise of . This paper presents the system design scheme, noise analysis, and performance testing of the capacitive sensor for the TianQin mission. Based on the previous work of our group, a capacitive sensing scheme based on a transformer bridge and modulation–demodulation is adopted. A transformer with a better high LQ product is fabricated, and the preamplifier current noise is reduced to further improve the performance above mHz. The amplitude stability of the AC carrier and the performance of the lock-in amplifier circuit are further improved to reduce the low-frequency noise at and below. Finally, a capacitive sensor prototype is developed and tested, the experimental results show that the capacitance measurement noise is better than above 1 mHz and better than at about , which meets the overall performance requirement of the TianQin mission.

Amplitude Stability Detection of Sinusoidal Excitation Signal for High Precision Sensors

This study presents a high-precision detection method based on biased operational rectifier (BOR) and tracking analog-to-digital converter (TADC) for real-time monitoring of the amplitude drift of sinusoidal excitation signals, which significantly reduces the requirement for ADC&#x0027;s measurement accuracy and improves the signal-to-noise ratio (SNR). BOR modules are proposed innovatively to make the amplitude drift can be detected easily by an ADC with poor precision. Combining with the tracking ADC, the proposed detector could suppress the noise near the cut-off frequency and thus improve SNR. An amplitude drift detector and a lock-in amplifier are designed and tested experimentally. The results show that the voltage resolution of the proposed detector could reach 0.12 ppm for a sinusoidal source with an amplitude of 2.5 V. The SNR is measured 88 dB, which is 8 dB higher than that of the lock-in amplifier. The proposed detector is also applied in a precision capacitive displacement sensor. With the amplitude drift detector, the drift of the capacitive sensor caused by the signal source&#x0027;s amplitude drift could be significantly reduced from 16 nm&#x002F;&#x00B0;C to 2 nm&#x002F;&#x00B0;C. Furthermore, this method is also applicable to other amplitude-modulated types of high-precision sensors.

A novel ultra-simplified flexure-based spring-mass device for relative gravimeter

This study presents the design and test of a novel ultra-simplified flexure-based spring-mass device (NUFSMD) with high sensitivity for relative gravimeters. The NUFSMD is mainly composed of a highly sensitive spring based on flexure hinges (SFH) and a cantilever beam. When the change of gravity causes SFH to rotate, an amplified displacement can be obtained on the tail of the cantilever beam. The displacement is measured by a capacitive displacement sensor. The change of gravitational acceleration can be calculated based on the output of the sensor. A theoretical analysis of the working principle of the NUFSMD is established. A prototype NUFSMD is machined from 304 stainless steel and a series of experiments are carried out. The effectiveness of gravity measurement is demonstrated by finite element simulations and experiments. The experimental results show that the sensitivity of the NUFSMD is about 15.27 μGal nm−1, and the resolution is about 1.83 μGal. The designed NUFSMD shows outstanding performance. And the sensitivity and resolution of the NUFSMD can be further improved by increasing the number of flexible hinges connected in series. Compared with the existing spring-mass devices in high-precision relative gravimeters, the significant advantage of the NUFSMD is that it is simple in structure and easy to machine, which helps to greatly improve performance. Firstly, it is simple in structure, so it can be machined in one piece, which considerately contributes to stability and precision. Secondly, it is easy to machine, so it can be machined from high-performance but difficult-to-machine materials to improve its performance. Thirdly, there are a few parameters that need to be traded off for miniaturization because of the simple structure, so it is easy to be miniaturized to adapt to narrow measurement space. Therefore, it is expected to greatly improve the performance of the existing spring-mass device in relative gravimeters.

Capacitive Linear Displacement Sensors With High Accuracy and Long Range Absolute Positioning Capability Based on a Splicing Technique

Considerable progress has been made in the development of absolute capacitive linear displacement sensors based on time grating that are capable of providing highly accurate absolute position measurements in conjunction with easy fabrication using standard printed circuit board (PCB) technology. The working range of currently available sensor designs has, however, been rather limited. The present work addresses this issue by greatly expanding the measurement range via a technique for splicing multiple identical stationary rulers with individual measurement lengths of 600 mm. Here, absolute positioning is realized in a manner similar to that of Vernier calipers using stationary segments composed of periodic rectangular excitation electrodes with orthogonal excitation signals and a moving component composed of sinusoidal-shaped induction electrodes. The sensor wiring is greatly simplified by transferring the induction signals output by the moving ruler to the stationary rulers via special transmitting and receiving electrodes. Splicing errors are eliminated by applying two sets of induction electrodes, including a front sensing unit (FSU) and a rear sensing unit (RSU) along the measurement direction on the moving ruler. The performance of the proposed design is evaluated experimentally using a two-segment prototype sensor fabricated by PCB technology. The results demonstrate that interference between the FSU and RSU generates a first harmonic error. This is then addressed by increasing the distance between the FSU and RSU, and enhancing the shielding layer between the two units. This yields a measurement accuracy of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm 3.5~\mu \text{m}$ </tex-math></inline-formula> over the full 988 mm measurement range of the sensor.

Design and Parameter Identification for a Positioning Platform with a Large Stroke and High Precision for Segmented Mirrors

An active optical system with three segmented mirrors was proposed to verify the co-focus and co-phase progress. In this system, a kind of large-stroke and high-precision parallel positioning platform was specially developed to help support the mirrors and reduce the error between them, which can move in three degrees of freedom out of plane. The positioning platform was composed of three flexible legs and three capacitive displacement sensors. For the flexible leg, a kind of forward-type amplification mechanism was specially designed to amplify the displacement of the piezoelectric actuator. The output stroke of the flexible leg was no less than 220 μm and the step resolution was up to 10 nm. Further, a linear model was established to identify the amplification ratio between the actuator and the flexible leg, which can increase the precision of the positioning platform. Moreover, three capacitive displacement sensors with a resolution of 2.5 nm were symmetrically installed in the platform to accurately measure the position and attitude of the platform. To improve the stability and precision of the platform, particle swarm optimization algorithm was applied to identify the control matrix, which can help the platform achieve ultra-high precision positioning. The results showed that the theoretical matrix parameters had a maximum deviation of 5.67% from the experimental ones. Finally, abundant experiments verified the excellent and stable performance of the platform. The results proved that while bearing the heavy mirror, which is no more than 5 kg, the platform can realize a 220 μm translation stroke and 2.0 mrad deflection stroke, with a high step resolution of 20 nm and 0.19 μrad. These indicators can perfectly cater to the requirements of the proposed segmented mirror system’s co-focus and co-phase adjustment progress.

MEMS‐based 3‐C borehole gravimeter development

AbstractA micro‐electro‐mechanical‐based 3‐C borehole gravimeter has been developed in China for mineral and hydrocarbon exploration. The 3‐C borehole gravimeter is composed of a three‐axis gravity sensor chip based on a deep silicon etching technique, high‐precision capacitive displacement sensing and weak signal detection circuitry. The gravity‐sensing chip is a silicon‐based integrated spring‐mass block system. Silicon wafer is etched by the micro‐nanofabrication technique to form a high collimation groove. The size of the gravity‐detecting mass block in the sensitive element plays a decisive role in the thermal noise level of the instrument. Deep silicon processing technique can produce a thicker silicon mass block (500 μm), which can obtain a larger mass block in the same area compared with the traditional silicon surface processing technique (10–100 μm). The out diameter of the final tool is 50 mm with 10,000 mGal measurement range, 155°C temperature and 100 MPa pressure rating. Apart from the 3‐C micro‐electro‐mechanical gravity sensor, a 3‐C fluxgate magnetic sensor is also integrated into the downhole tool. This allows us to measure both 3‐C gravity field and 3‐C magnetic field downhole simultaneously and conduct joint inversion of both the downhole 3‐C gravity and 3‐C magnetic data during the data processing stage. The prototype tool was tested in a borehole up to 850 m depth, and the 3‐C gravity sensor inside the tool can measure the vibration of the environment during the stationary measurement downhole. The first test data set shows repeatability near 800 m depth, which verifies the adaptability of the micro‐electro‐mechanical‐based gravimeter to the down instrument environment.

A single quasi-cubic test mass configuration for space-based gravitational wave detection

Two test masses per spacecraft configuration is the main scheme and exhibits a high level of maturity for space-based gravitational wave detection. However, the single test mass configuration is continuously discussed with different designs to reduce technical complexities such as spacecraft control. This paper proposes a new configuration with a single quasi-cubic test mass per spacecraft. The new configuration inherits the existing capacitance displacement sensor and electrostatic actuator. It has the advantage of the suppression of centrifugal force effect due to the coincidence of the center of mass between the spacecraft and test mass. In addition, it has the advantages of simplifying the self-gravity compensation strategy and the drag-free attitude and orbit control strategy due to using a single test mass.

Radial Error Motion Measurement and Its Uncertainty Estimation of Ultra Precision Axes of Rotation with Nanometer Level Precision.

The radial error is the key performance indicator of ultra-precision axis. In order to measure and evaluate the radial error of ultra-precision axis with nanometer accuracy, a measurement system with an accuracy of nanometer based on capacitive displacement probes and standard spheres is developed. The nonlinearity error of capacitive displacement probes, misalignment error of the probes, eccentric error of standard spheres, error caused by environment temperature change, environment vibration and error separation methods are analyzed and the effects of the above factors are obtained; Multiple measurement examples carried out with the measurement system this paaper constructed indicate the repeatability of the measurement system reaches 10.5 nm and the roundness error of artifact separated is less than 4.03 nm. In order to evaluate the measurement dispersion of the ultra-precision axis radial error, the major uncertainty components and the complete process of the comprehensive evaluation of the measurement uncertainty are proposed. The combined uncertainty of radial error motion measurement of the ultra-precision axis with Donaldson reversal is 31.64 nm (k = 2).