Capacitive Displacement Transducer Research Articles

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 (TM), 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

–In the present paper, a modified linear capacitive displacement transducer is developed, where the measurement errors and non-linearity errors due to the various effects such as the effect of the change of atmospheric parameters, the effect of parasitic fringe capacitance, the effect of stray capacitance, the effect of parallel position shifting of the sensing plates, etc. are minimized, and the output is linearly related with displacement for any range. The transducer consists of a sensing capacitor and a similar reference capacitor, each of which has a noninductive double layer short-circuited winding wound on an insulating uniform hollow cylinder. The sensing cylinder has a thin circular conducting disk, which is easily displaceable by the moving object along the inside walls of the cylinder from the outside by means of a thin conducting disk rod attached to the central position of the disk. The reference cylinder has a similar disk with a disk rod fixed at the reference zero position. The transducer circuit measures the difference of the combined cylindrical-perpendicular plate capacitances between the short-circuited terminal of vertical noninductive winding and the horizontal conducting disk of the two capacitors and gives an output that is found to be linearly related with displacement for the entire length of the sensing cylinder. The measurement is free from the non-linearity error for any range because the factors producing nonlinearity are similar for the two capacitors and tend to cancel each other. The derived characteristic equations are supported by the experimental results with very good accuracy and repeatability.

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.

Comparison study of high-sensitivity area-changed capacitive displacement transducers with low-impedance and high-impedance readout circuits.

Area-changed capacitive displacement transducers (CDTs) are widely used in the high-precision displacement measurement due to their high accuracy and large dynamic range. The preamplifier circuit is used to convert the capacitance variation signal into voltage, which requires low noise and is significant for the high-sensitivity area-changed CDTs. Current CDT preamplifiers are mainly categorized as the low-impedance preamplifier and the high-impedance preamplifier; however, their characteristics and application scopes have not been systematically compared. This paper builds comprehensive models of the low-impedance and the high-impedance preamplifiers. Then, three-electrode configurations with different electrode separations and gaps are designed to carry out displacement variation experiments with low-impedance and high-impedance readout circuits, respectively. The results show that the sensitivity decrease caused by the gap change with the high-impedance preamplifier is 70%, while the counterpart of the low-impedance preamplifier is 85%. When the gap is 0.1mm and the width-to-separation ratio varies from 1:1 to 5:1, the sensitivity of the CDT based on the low-impedance preamplifier is increased by 64%, while the counterpart with the high-impedance preamplifier is increased by 22%. Hence, this paper gives the universal guiding rules of preamplification circuit selections for different CDT electrode configurations and application requirements. For a capacitive sensor design with large and unavoidable parasitic capacitance, the low-impedance preamplifier and a CDT with a large electrode width-to-separation ratio match best. For a capacitive sensor design requiring both a large sensitivity and good robustness to out-of-plane interferences, the high-impedance preamplifier and a CDT with a small electrode width-to-separation ratio match best.

Design, Modeling, and Evaluation of a Class-A Triaxial Force-Balance Accelerometer of Linear Based Geometry

Abstract A new class-A force-balance accelerometer (FBA) is designed, simulated, and evaluated. The focus of this work was to design a low-cost but high-performance instrument. The FBA has output voltage proportional to ground acceleration, flat response from direct current to 200 Hz, output range ± 10 V differential (40Vpp, peak-to-peak) and sensitivity 2.5 V/g, which provides a ± 4g range. Unlike other well-established designs with rotational pendulum systems and single-coil actuators that present partially nonlinear performance, the proposed design is based on a linear motion spring-mass mechanism with two parallel leaf springs and a double symmetrical magnet-coil force actuator. This architecture ensures that the displacement transducer’s response is linear and that an acting force on the seismic mass is not disturbed by any cross-axial motion. This force depends on displacement only, as imposed by the electronic control circuit, which is implemented on a small high-density printed circuit board (PCB) mounted on top of the mechanical construction. The plates of the variable capacitance displacement transducer consist of ordinary PCBs for cost efficiency. The coils of the force actuator are placed on each side of the moving plate of the capacitive transducer and the magnets are placed on the aluminum rigid frame of the device. The central moving plate of the variable capacitor and the attached force actuator coils, along with some extra aluminum mass, consist the accelerometer’s seismic mass. The performance of the accelerometer is evaluated in terms of earthquake data records and in comparison of its response with that of a commercial FBA with corresponding specifications. The instrument’s self-noise was also measured over a long period of operation and proved to comply with typical FBA application requirements and commercial product standards.

A high-resolution area-change-based capacitive MEMS tilt sensor

Tilt sensors have been widely used in many applications, such as instrumentation leveling, oil drilling and structural health monitoring. With the rapid development of the micro-electromechanical system (MEMS) technology, MEMS accelerometer-based high-performance tilt sensors are capable of replacing conventional tilt sensors in most of application fields. High-sensitivity MEMS resonant accelerometers (MRAs) are fully qualified for tilt sensing. However, MRA chips have to be vacuum packaged and require complex circuits; therefore, they are difficult to be miniaturized and commercialized. In this case, this paper introduces a commercial-oriented capacitive MEMS accelerometer for tilt sensing with both high-resolution and compact size. The proposed MEMS sensor utilizes simplified fabrication processes, the area-change-based capacitive displacement transducer and the capacitance-to-voltage conversion application specific integrated circuit (ASIC) for low-cost, high-sensitivity, low power consumption and miniaturization. The developed MEMS sensor has a package dimension of 14 mm × 14 mm × 3.6 mm with a single +5 V power supply and analog voltage output. Several evaluation experiments have been conducted with the results showing that the developed MEMS tilt sensor has a full measurement range of ±180°, a linear measurement range of ±30° with a nonlinearity of ±2.8%, a sensitivity of 33.6 mV/°, a noise floor of 2 × 10−4°/√Hz, a bandwidth of 100 Hz and an angle resolution of 7 × 10−4° with an integral time of 0.5 s. Compared with other commercial MEMS tilt sensors, the proposed sensor has a better resolution, a lower noise floor, a larger bandwidth, a lower power consumption and a smaller package. The simplified fabrication process and high performance suggest the developed MEMS tilt sensor is promising to be competitive in the market.

A method for improving out-of-plane robustness of an area-changed capacitive displacement transducer used in a micro-accelerometer

Area-changed capacitive displacement transducers have been widely applied in micro-electro-mechanical-system (MEMS) sensors such as sandwich-type MEMS accelerometers to detect in-plane displacement with a high sensitivity. The cross-axis disturbance could result in out-of-plane displacement of the proof mass, which brings a gap variation of sensing capacitor electrodes and lead to an undesirable variation of the accelerometer’s scale factor. In order to solve this problem, this paper presents a novel method to improve out-of-plane robustness of an Area-changed capacitive displacement transducer in a MEMS accelerometer. An on-chip capacitor, sensitive to the out-of-plane displacement of proof mass, was integrated as the feedback capacitor of the charge amplifier. Thus, the influence of the out-of-plane displacement on the scale factor caused by cross-axis disturbance is compensated. The method was verified by theoretical calculation, simulation and experiments. The results indicated that the cross-sensitivity of the MEMS accelerometer with an on-chip feedback capacitor was less than 1/3 of that with off-chip feedback capacitor when acceleration was applied on the out-of-plane direction. Besides, the noise floor of the accelerometer maintained at 60 ng/√Hz regardless of the on-chip or off-chip feedback capacitors.

Temperature Gradient Method for Alleviating Bonding-Induced Warpage in a High-Precision Capacitive MEMS Accelerometer.

Capacitive MEMS accelerometers with area-variable periodic-electrode displacement transducers found wide applications in disaster monitoring, resource exploration and inertial navigation. The bonding-induced warpage, due to the difference in the coefficients of thermal expansion of the bonded slices, has a negative influence on the precise control of the interelectrode spacing that is essential to the sensitivity of accelerometers. In this work, we propose the theory, simulation and experiment of a method that can alleviate both the stress and the warpage by applying different bonding temperature on the bonded slices. A quasi-zero warpage is achieved experimentally, proving the feasibility of the method. As a benefit of the flat surface, the spacing of the capacitive displacement transducer can be precisely controlled, improving the self-noise of the accelerometer to 6 ng/√Hz @0.07 Hz, which is about two times lower than that of the accelerometer using a uniform-temperature bonding process.

Quality factor tuning of micromechanical resonators via electrical dissipation

Sensitive capacitive transduction of micromechanical resonators can contribute significant electrical dissipation, which degrades the quality factor of the eigenmodes. We theoretically and experimentally demonstrate a scheme for isolating the electrical damping of a mechanical resonator due to Ohmic dissipation in the readout amplifier. The quality factor suppression arising from the amplifier is strongly dependent on the amplifier feedback resistance and parasitic capacitance. By studying the thermomechanical displacement noise spectrum of a doubly clamped micromechanical beam, we confirm that electrical dissipation tunes the actual, not effective, quality factor. Electrical dissipation is an important consideration in the design of sensitive capacitive displacement transducers, which are a key component in resonant sensors and oscillators.

A MEMS Micro-g Capacitive Accelerometer Based on Through-Silicon-Wafer-Etching Process.

This paper presents a micromachined micro-g capacitive accelerometer with a silicon-based spring-mass sensing element. The displacement changes of the proof mass are sensed by an area-variation-based capacitive displacement transducer that is formed by the matching electrodes on both the movable proof mass die and the glass cover plate through the flip-chip packaging. In order to implement a high-performance accelerometer, several technologies are applied: the through-silicon-wafer-etching process is used to increase the weight of proof mass for lower thermal noise, connection beams are used to reduce the cross-sensitivity, and the periodic array area-variation capacitive displacement transducer is applied to increase the displacement-to-capacitance gain. The accelerometer prototype is fabricated and characterized, demonstrating a scale factor of 510 mV/g, a noise floor of 2 µg/Hz1/2 at 100 Hz, and a bias instability of 4 µg at an averaging time of 1 s. Experimental results suggest that the proposed MEMS capacitive accelerometer is promising to be used for inertial navigation, structural health monitoring, and tilt measurement applications.

A Universal High-Sensitivity Area-Variation Capacitive Displacement Transducer (CDT) Based on Fringe Effect

Capacitive displacement transducers (CDTs) have been widely used in many physical sensors, attributing to high-resolution, simple electricity and easy manufacturing process. Gap-variation CDTs generally have higher displacement resolution due to small electrode gaps but suffer from the pull-in effect, the nonlinear effect and squeeze-film damping; whereas area-variation CDTs have intrinsically good linearity and much smaller slide-film damping. However, the parallel-plate-based area-variation CDTs have the electrode width much larger than the electrode gap with negligible fringe effect; therefore, the sensitivity is limited by periodic electrode numbers. In this paper, we introduce a novel fringe-effect dominated area-variation CDT with a much higher sensitivity within a certain electrode-deployable area. Both theoretical and numerical analysis are applied to investigate the working principle of the CDT design. The proposed fringe-effect-based CDT benefits from a much larger capacitance-to-displacement sensitivity than the traditional periodic array parallel-plate-based CDT, due to the more displacement-sensitive fringe field and more deployable electrode periods. A set of experiments are designed, and the proposed area-variation CDTs are evaluated. Experimental results suggested that the proposed CDT design, which had equal electrode width, separation and gap, could universally be applied to sensors with different featured dimensions either in macroscale or microscale. Angular misalignments with both out-of-plane tilts and in-plane rotations, which affect the output offset and sensitivity, should be minimized or alleviated. The proposed fringe-effect-based CDT are successfully applied to a single-axis in-plane sensing micro-electromechanical systems (MEMS) accelerometer, showing a noise floor as low as 0.25 ng/Hz 1/2 @1 Hz. The corresponding displacement noise of the proposed CDT is 0.1 pm/Hz 1/2 .

Film thickness of free falling water flow on a large-scale ellipsoidal surface

Falling water film flow on large-scale curved dome of passive containment, of which the data is very scarce, plays a crucial role for the thermal-hydraulic behaviors of passive containment cooling system (PCCS) in advanced nuclear power plant. It exhibits a developing phenomenon in nature because of continuous changes of the inclined angle, the width and the extend angle of the flow channel in the longitudinal direction. In order to examine the influences of these continuously varying factors on the flow characteristics, the film thickness of free falling water flow on a large-scale ellipsoidal surface with continuously varying inclined angle and extend angle has been measured experimentally. The working fluid is the low hardness municipal water, of which the inlet temperature is the same as ambient environment. Capacitive non-contact displacement transducers, Micro-Epsilon capaNCDT-CS10 sensors, are used to measure the film thickness at different locations with inclined angle ranging from 18° to 76°. The range of the film Reynolds number is from 360 to 2175. Detailed analyses on the relationship between the dimensionless film thickness and the film Reynolds number at different longitudinal positions on the dome surface are carried out. No obvious influence on the evolution of falling film caused by the continuous changes of the inclined angle, the width and the extend angle of flow channel on the dome can be observed. A new empirical correlation of film thickness on the ellipsoid dome surface is suggested based on the data obtained in the present experiments. Most of experimental data points fall in the range of ±15% around its prediction. Comparisons are also made between the suggested correlation with other theoretical or empirical correlations of film thickness in straight channels reported in the literature, as well as the numerical results on curved surface by computational fluid dynamics software COMMIX and GASFLOW-MPI. Fairly good agreements are observed, proving that the suggested correlation can predict the film thickness on the curved dome surface of PCCS with much accuracy and then provide a more reliable basis for further analysis of the conjugate heat and mass transfer of PCCS.

Assessment Criterion of Rigidity of Comb Electrodes Fingers of Microelectromechanical Converters

The assessment criterion of rigidity of comb electrodes fingers of the microelectromechanical converters is developed. The assessment criterion allows to estimate the maximum electrodes fingers length to decrease approach probability of snap-down effect. The modeling results have been analyzed. The estimations of the maximum length of electrodes fingers are obtained. The estimates depend on length of electrodes fingers overlapping and applied voltage. The dependences of the maximum length of comb electrodes fingers on length of their overlapping and applied voltage are showed. Since all of the electromechanical converters are reversible, i.e. the converters can work as electrostatic actuators, as well as capacitive displacement transducers. If certain conditions occurs, the capacitive displacement transducers will start to work like electrostatic actuators. The criteria allowed to define these invertibility condition can be obtained from the equilibrium equations of sensitive elements of micromechanical devices. The proposed assessment criterion of the maximum length of combs electrodes fingers can be used to design micromechanical devices.

Joining of Dissimilar alloy Sheets (Al 6063&AISI 304) during Resistance Spot Welding Process: A Feasibility Study for Automotive industry

Present design trends in automotive manufacture have shifted emphasis to alternative lightweight materials in order to achieve higher fuel efficiency and to bring down vehicle emission. Although some other joining techniques are more and more being used, spot welding still remains the primary joining method in automobile manufacturing so far. Spot welds for automotive applications should have a sufficiently large diameter, so that nugget pullout mode is the dominant failure mode. Interfacial mode is unacceptable due to its low load carrying and energy absorption capability. Strength tests with different static loading were performed in, to reveal the failure mechanisms for the lap-shear geometry and the cross-tension geometry. Based on the literature survey performed, venture into this work was amply motivated by the fact that a little research work has been conducted to joining of dissimilar materials like non ferrous to ferrous. Most of the research works concentrated on joining of different materials like steel to steel or aluminium alloy to aluminium alloy by resistance spot welding. In this work, an experimental study on the resistance spot weldability of aluminium alloy (Al 6063) and austenitic stainless steel (AISI304) sheets, which are lap joined by using a pedestal type resistance spot welding machine. Welding was conducted using a 45-deg truncated cone copper electrode with 10-mm face diameter. The weld nugget diameter, force estimation under lap shear test and T – peel test were investigated using digital type tensometer attached with capacitive displacement transducer (Mikrotech, Bangalore, Model: METM2000ER1). The results shows that joining of Al 6063 and AISI 304 thin sheets by RSW method are feasible for automotive structural joints where the loads are below 1000N act on them, it is observed that by increasing the spots per unit length, then the joint with standing strength to oppose failure is also increased linearly incase of interfacial failure mode and non linear for pullout failure mode.

High resolution space quartz-flexure accelerometer based on capacitive sensing and electrostatic control technology

High precision accelerometer plays an important role in space scientific and technical applications. A quartz-flexure accelerometer operating in low frequency range, having a resolution of better than 1 ng/Hz(1/2), has been designed based on advanced capacitive sensing and electrostatic control technologies. A high precision capacitance displacement transducer with a resolution of better than 2 × 10(-6) pF/Hz(1/2) above 0.1 Hz, is used to measure the motion of the proof mass, and the mechanical stiffness of the spring oscillator is compensated by adjusting the voltage between the proof mass and the electrodes to induce a proper negative electrostatic stiffness, which increases the mechanical sensitivity and also suppresses the position measurement noise down to 3 × 10(-10) g/Hz(1/2) at 0.1 Hz. A high resolution analog-to-digital converter is used to directly readout the feedback voltage applied on the electrodes in order to suppress the action noise to 4 × 10(-10) g/Hz(1/2) at 0.1 Hz. A prototype of the quartz-flexure accelerometer has been developed and tested, and the preliminary experimental result shows that its resolution comes to about 8 ng/Hz(1/2) at 0.1 Hz, which is mainly limited by its mechanical thermal noise due to low quality factor.

Portable seismic sensor

The problems related to design of a portable seismic sensor working in a frequency range of 0.01–40 Hz are considered. Its main parts (pendulum, capacitive displacement transducer, magnetoelectric converter), structural diagram, and amplitude-frequency characteristic are described.

Characterization of the Damping Behavior of a Nanoindentation Instrument for Carrying Out Dynamic Experiments

A new displacement modulation based dynamic indentation method is demonstrated and shown to be effective for viscoelastic characterization of a glassy polymer. The analysis of dynamic experiments requires a complete understanding of the measuring system’s dynamic characteristics especially the damping. Accordingly, an improved method, based on the use of a wire spring, is developed for determining the damping characteristics. In general, damping in an indentation instrument is contributed by two elements: the eddy current damping from the electromagnetic loading coil and the squeeze film damping from the capacitive displacement transducer. Therefore, a method to determine the relative contribution from the different damping elements present in the system is demonstrated and the results are compared with the calibration obtained from the wire spring method. Finally, dynamic indentation tests are carried out on a glassy polymer to obtain the complex modulus; the values of which are compared with those obtained from bulk dynamic mechanical analysis (DMA) tests. Storage modulus values are found to be in good agreement with bulk data but some divergence in the case of loss modulus is observed. The calibration procedure of the measuring instrument is critically examined in view of these observations. Overall, displacement modulation based dynamic indentation is shown to be a promising method for viscoelastic characterization at the micron length scales.

Two-Dimensional Space-Time Analysis and Matrix Represen-Tation on the Principle of the Capacitive Displacement Transducer

In order to provide a design method of the capacitive displacement transducer and to improve its measuring performance it is desperately needed to offer a refined mathematic model of the transducer of mulitiphase drive and phase-modulated. On the basis of fully considering its characteristic of digital signals, first it is found that their actual waveforms and space-time characteristics could be tersely represented by matrixes [uij], [cj] and [vi], and corresponding matrix elements uij, cj and vi through deeply analyzing space-time and quantum characteristics of their mulitiphase driving signals Ui(t), capacitive coupling signals Cj(x) and output signal V(t). and space-time transform function possessed by U(x,t) itself. Then the basic expression of the relations of the transducer is derived, which is expressed by matrixes, thereby the characteristics of space-time transform and phase modulation are brought to light. The demodulation process and demodulated waveforms and its characteristics in the transducer are also expressed by demodulated matrixes [bij]. Finally, the reason for the principle and periodic error produced in the transducer is revealed by sampling matrix [sij]. Thus the full process of the produce of driving signals, modulation, demodulation and space-time transform that happen in the transducer, also waveforms and characteristics of various signals in the process are concisely expressed by two-dimensional space-time matrixes. Experimental results indicate that the use of the mathematical model enables its resolving power to reach 1 µm, and the mathematical model proposed is an all-things-considered model to express processes that happen in the transducer.

Smart floating element flowmeter based on a capacitive angular displacement transducer

Based on the detection mechanism of a capacitive angular displacement transducer, a new type of smart floating element flowmeter with a higher accuracy is provided in this paper. It mainly describes the principle of the flowmeter, design of the transducer, the intelligent signal processor, the calibration of the prototype and analysis of errors. Experiment results show that the accuracy of the kind of prototype investigated is better than 1%.