Differential Capacitor Research Articles

Differential capacitive mass sensing based on mode localization in coupled microbeam arrays

In this paper, we developed a multi-physics model of an electrostatic MEMS resonator made of an array of mechanically-coupled beams and investigate its potential use for mass detection applications. Experiments were conducted on two- and three-coupled beams under electrostatic actuation to verify the capability of the model to predict the mechanical response of coupled beam arrays. The fabricated device, comprising polysilicon-coupled microbeams, is produced using the Multi-User MEMS Processes, followed by an experimental investigation. Numerical results were found in good agreement with their experimental counterparts. The developed model was used to demonstrate the possible adjustment of the electrostatic actuation to enhance the sensitivity of the dynamic response of the coupled MEMS resonator to mass perturbations. By leveraging the mode localization phenomenon and incorporating a novel differential capacitance sensing mechanism, a notable 84% improvement in sensitivity when switching from two-beam to three-beam system while operating near the second mode in the linear regime. Actuating the MEMS device at higher voltages enabled to achieve higher sensitivity thanks to the activation of nonlinear effects such as bifurcation and softening. We observed the transition from nonlinear to nearly-linear dynamic response of the coupled beams upon the addition of mass and demonstrated how bifurcations that cause a sudden shift to a high-amplitude motion can be utilized in differential capacitance-based mass sensing. Additionally, the suggested detection mechanism allows for overcoming the inherent parasitic capacitance, thereby mitigating low signal-to-noise ratios.

A 78 dB 0.417 mW Second-Order NS SAR ADC with Dynamic Amplifier-Assisted Integrator

The noise-shaping (NS) successive approximation register (SAR) analog-to-digital converter (ADC) is an innovative hybrid structure that offers performance advantages. The NS-SAR ADC leverages the SAR ADC as its foundation and combines oversampling technology and noise-shaping technology found in Sigma-Delta ADC. This integration effectively combines the strengths of both structures and enhances overall performance. The ADC features a simple circuit structure, compact chip area, and high energy efficiency, which has positioned it as a prominent research area. In this paper, leveraging the TSMC 65 nm GP process, the NS-SAR ADC is designed with a power supply voltage of 1 V. This design adopts an 8-bit differential capacitor structure, operates at a sampling frequency of 16 MS/s, and achieves an oversampling rate of 16 times the desired performance indicators. Through extensive circuit post simulation verification, the SNR obtained reaches 78 dB, providing an effective bit resolution of 12.7 bits. The core chip area of the ADC measures 366 × 333 μm2, while the power consumption is impressively low at 417 μW and FoMs is 168 dB.

Formulation Analysis and Follow-Up Study of Differential MEMS Touch-Mode Sensor Utilizing Capacitive Vacuum Gauge Framework for Low-Pressure Measurements

Differential capacitance diaphragm gauges have become more popular in pressure measurements as they yield superior sensitivity and lesser non-linearity for pressure differential measurements. In addition, differential capacitance diaphragm gauges do not require a high vacuum reference cavity which reduces their manufacturing complexity. Efficient analysis for modelling differential capacitance diaphragm gauges is thus increasingly becoming vital due to their innumerable use cases. The higher sensitivity of circular diaphragm for the same side length in comparison to square diaphragm makes it ideal for sensor design. In this work, a complete formulation for analysis of differential capacitive vacuum gauge with the circular diaphragm in normal and touch mode operation has been presented for the low-pressure range of (1 to 1500 pascals). A comprehensive study of sensor parameters like capacitance, diaphragm deflection, capacitive and mechanical sensitivity has been formulated to aid the choice of sensor characteristics. Computationally complex methods have been used in the past for analysis of circular diaphragms. MATLAB and COMSOL have been used to compute and simulate results.

A Calculation Method for the Optimal Initial Polar Distance of Capacitive Force Sensors

For capacitive sensors, the initial polar distance of capacitors has a vital influence on the performances of capacitive sensors; however, there are few current studies on the method of calculating the initial polar distance of capacitors, leading to a lack of corresponding theoretical basis for the design of capacitive sensors. In this article, a calculation method for the optimal initial polar distance based on minimum error is proposed. The total error expression is derived from error analysis, which clarifies the complex relationship between the total error and the initial polar distance, and the optimal initial polar distance is solved by Newton’s method. A capacitive torque sensor is used in the experiment to verify the calculation method for the optimal initial polar distance, the theoretical error and experimental error of the sensor are compared, and the results show that the experimental error is consistent with the theoretical error curve. The optimal initial polar distance obtained by the calculation method is 0.8479 mm, which is within the range of 0.8–0.9 mm determined by the experiment. The theoretical minimum total error is 0.211% and the experimental minimum total error is 0.208%. The total error expression proposed in this article is accurate, and the calculation method of the initial polar distance is effective. In addition, theoretical analysis reveals that the differential parallel plate capacitor has the characteristic that any small deformation of the moving plate can be equivalent to a translation whose magnitude is the mean value of the deformation.

A Current-Mode Interface With Mixed Single/Dual Slope Integration for Differential Capacitive Sensors

A current-mode interface (CMI) with mixed single/dual slope integration (MSDSI) for differential capacitive sensors (DCSs) is presented in this paper. The proposed design is based on the integration of the reference current flowing through the capacitors of the DCS. The integration on the capacitor of a smaller capacitance is performed with a dual slope. Contrary, the integration on the capacitor of a larger capacitance is performed with only one slope. The normalized differential capacitance (NDC) defined as the difference-to-sum ratio of the DCS capacitances is proportional to the duration of only one time interval which is digitized using the counting method. There is no need for post-processing in the proposed NDC-to-time-to-digital conversion. It has been prototyped using discrete off-the-shelf components mounted on a printed circuit board, with a single supply voltage of 3.3 V. The measured NDC is in the range |NDC| < 0.612, with the constant sum of DCS capacitances of 970 pF. Achieved full scale error is smaller than 0.3 %, with a range of conversion speed from 1770 to 2755 NDC-to-time-to-digital conversions per second.

An 11-Bit 10 MS/s SAR ADC with C–R DAC Calibration and Comparator Offset Calibration

An 11-bit 10 MS/s successive approximation register (SAR) analog-to-digital converter (ADC) is proposed for low-power and small-area applications. A 10-bit differential capacitor–resistor (C–R) digital-to-analog converter (DAC) is used to minimize the area of a DAC. The use of a C–R DAC reduces the capacitor area of a SAR ADC used CDAC by 75%. A capacitor calibration for the upper 5-bit capacitors of the C–R DAC is proposed to increase the linearity of the C–R DAC. To evaluate the proposed SAR ADC, an 11-bit 10 MS/s SAR ADC is implemented using a 180 nm 1-poly six-metal CMOS process with a supply of 1.8 V. The proposed SAR ADC has an effective number of bits (ENOBs) of 10.3 bits at a sampling rate of 10 MS/s for a 3.6-VPP differential sinusoidal analog input with a frequency of 4.789 MHz. The measured ENOBs is 10.45 bits when the frequency of the analog input signal is 42.39 kHz. The proposed C–R DAC calibration including comparator offset calibration improves the performances of differential nonlinearity (DNL) and integral nonlinearity (INL) from −1/+1.26 LSBs and −1.98/+1.96 LSBs to −0.97/+0.85 LSBs and −0.79/+0.83 LSBs, respectively.

Design and optimization of a novel capacitive six-axis force/torque sensor based on sensitivity isotropy

Sensitivity isotropy is a crucial index to evaluate the measurement accuracy of the capacitive six-axis force/torque sensor. This paper presents a novel capacitive six-axis force/torque sensor with good sensitivity isotropy. A novel elastic structure with a composite beam is proposed as the sensitive element, and six differential capacitors are used as the conversion elements. This elastic structure and capacitor arrangement are beneficial for the sensor to achieve sensitivity isotropy. Then, the mathematical model of the mapping matrix between the six-axis force/torque and capacitance change is established. The evaluation index function of sensitivity isotropy is established based on the condition number of the mapping matrix to optimize the sensor. The optimization of the sensor by the mathematical model can effectively shorten the design and optimization cycle. The experimental results show that the sensor has good sensitivity isotropy, and the relative error of measurement is less than 1.86 %FS.

An 80 dB Second-order Noise Shaping SAR ADC using Differential Integral Capacitors and Comparator with Voltage Gain Calibration

A second-order noise shaping (NS) successive approximation register (SAR) analog-to-digital converter (ADC) is proposed for sensor interface applications. It consists of a capacitor-resistor hybrid digital-to-analog-converter (C-R DAC) with 10-bit resolution, a comparator with three inputs, a SAR logic, and a second passive integrator using two differential capacitors. The use of a C-R DAC and two differential capacitors reduces the capacitor area of the conventional NS SAR ADC by 86.25%. Voltage gain calibration for the three-input comparator is proposed to maximize the performance of the NS SAR ADC. The proposed second-order NS ADC is designed using a 180-nm CMOS process with a supply of 1.8 V. The proposed second-order NS SAR ADC with an over sampling ratio of 8 has a SNDR of 80.18 dB and an ENOB of 13.03 bits. Its area and power consumption are 0.165 ㎟ and 248 μW, respectively.

A High-Gain Multiphase Interleaved Differential Capacitor Clamped Boost Converter

A step-up for a non-isolated interleaved differential capacitor clamped boost (IDCCB) DC–DC converter is proposed in this manuscript. Because of its ability to produce high voltage gains, it is used in high-power applications. This converter’s modelling and control design are applicable to any number of phases. A six-phase interleaved differential capacitor clamped boost prototype is tested in this work, with an input voltage of 60 V, an output voltage of 360 V, and a nominal output power of 2.2 kW. The components of the converter are placed and controlled in such a way that the output voltage is the sum of the two capacitor voltages and the input voltage, which is two times higher than the supply voltage when compared to a conventional interleaved differential dual-boost converter. This converter reduces the stress on the capacitor with reference to the conventional interleaved differential boost converter for the same conversion gain. This prototype is considered and the developed approach is applied, after which the experimental results are obtained. This converter has potential for application in areas such as renewable energy conversion and electric vehicles.

Design and Simulations of High-Sensitivity Multi-Directional Inertial Sensor

This paper proposed the high sensitive linear and rotational based differential capacitive inertial sensor. The designed sensor consists of a proof of mass, which resides in an air medium — the acceleration measured along with a change of displacement and the differential capacitance. Sensor modeling and simulation have done with CoventorWare software. SOIMUMPS fabrication process has described because it allows pattern on both sides of an SOI wafer. Solid mechanics and electrostatic analysis have applied for measurement of acceleration. The high sensitivity of 981.28fF/g has observed. The simulated results have tabulated. Finally, performance and future scope of the inertial sensor has discussed.

Research on the function failure of accelerometer servo circuit caused by hydrolysis and corrosion

This paper studied the function failure of a quartz flexible accelerometer servo circuit manufactured by a thick-film hybrid integrated process. The circuit adopts the epoxy glue bonding process of the metal shell and the ceramic cover plate to encapsulate, and it is a non-airtight package. After the circuit is powered on, the quiescent current output is abnormal, and the DC voltage output is constant high potential, the acceleration detection function cannot be realized. In response to this phenomenon, the fault tree method is used to locate the failure location, and the fault is located at the abnormal function of the differential capacitor voltage converter chip. Using microscopic analysis and characterization methods, it can be seen that the hydrolysis and corrosion of the surface of differential capacitance-to-voltage converter chip causes leakage in the active area inside the chip, leads to the function failure of the circuit. The above research is of great significance to the design, storage and application of non-hermetic hybrid integrated circuits.

Model Predictive Current Control Based on Virtual Voltage Vector Method for Parallel Three-Level Inverters

The parallel three-level neutral-point clamp (3L-NPC) inverters are widely solicited today to satisfy the higher power demand by using low-rated switching devices in industrial applications such as renewable power generation. With the 3L-NPC in parallel, the zero-sequence circulating current (ZSCC) occurs in the closed circuit and decreases the performances of the current response if the two 3L-NPCs share the same dc bus with no galvanic isolation at the ac side. From the analysis of the ZSCC equivalent circuit, the virtual voltage vectors are proposed and exploited by the finite control set model predictive control (FCS-MPC) for mitigating the ZSCC and improving the current accuracy. In order to keep the neutral-point balance and reduce the switching loss, the differential capacitor voltage and the average switching frequency are considered in the proposed MPC. An experimental platform based on the Simulink-Real-Time system is presented for further verification of the effectiveness of the proposed method. The simulation and the experimental results obtained under the proposed strategy show that the ZSCC is reduced to near zero, and the current response provided has lower THD.

Design of a three-dimensional capacitor-based six-axis force sensor for human-robot interaction

Multi-dimensional force sensing capability of the robot plays a critical role in its interaction with the human and environment. The six-axis force sensor as a typical representative of the multi-axis force sensor, however, has not been extensively used in the field of human-robot interaction due to its high price. A low cost, a good sensing accuracy, and a high integration level six-axis force sensor is highly desirable to create. In this paper, to weaken the crosstalk phenomenon between the six-axis and optimize the sensitivity of overall system, a 3D capacitor structure with a cross-shape configuration of the shear force sensing cell was proposed. Eight electrodes were arranged on three perpendicular planes of the Cartesian coordinate system independently. The cross-shape differential capacitor was designed to achieve the improvement of sensitivity along the shear force direction. With Polyoxymethylene (POM) selected as the substrate material, a monolithic spatial structure was manufactured using CNC technology, and then conductive copper paint was sprayed on the specific surfaces of this 3D structure. The cost-effective prototype sensor has been manufactured without the manual work and experimentally validated by comparing it with a commercial six-axis force sensor. The characteristics of the prototype were analyzed in terms of its linearity, interference error, hysteresis, time domain response, SNR, offset repeatability and time drift. Finally, to verify the instrumented six-axis force sensor further, a controlled lab test was performed to measure the interaction forces with the Baxter Research Robot in a simulated scenario.

2.5D Flexible Wind Sensor Using Differential Plate Capacitors.

In this paper, a novel 2.5-dimensional (2.5D) flexible wind sensor is proposed based on four differential plate capacitors. This design consists of a windward pillar, two electrode layers, and a support layer, which are all made of polydimethylsiloxane (PDMS) with different Young’s moduli. A 2 mm × 2 mm copper electrode array is located on each electrode layer, forming four parallel plate capacitors as the sensitive elements. The wind in the xy-plane tilts the windward pillar, decreasing two capacitances on the windward side and increasing two capacitances on the leeward side. The wind in the z-axis depresses the windward pillar, resulting in an increase of all four capacitances. Experiments demonstrate that this sensor can measure the wind speed up to 23.9 m/s and the wind direction over the full 360° range of the xy-plane. The sensitivities of wind speed are close to 4 fF·m−1·s and 3 fF·m−1·s in the xy-plane and z-axis, respectively.

A two degrees of freedom comb capacitive-type accelerometer with low cross-axis sensitivity

In this paper, we report on a SOI-based comb capacitive-type accelerometer that senses acceleration in two lateral directions. The structure of the accelerometer was designed using a proof mass connected by four folded-beam springs, which are compliant to inertial displacement causing by attached acceleration in the two lateral directions. At the same time, the folded-beam springs enabled to suppress cross-talk causing by mechanical coupling from parasitic vibration modes. The differential capacitor sense structure was employed to eliminate common mode effects. The design of gap between comb fingers was also analyzed to find an optimally sensing comb electrode structure. The design of the accelerometer was carried out using the finite element analysis. The fabrication of the device was based on SOI-micromachining. The characteristics of the accelerometer have been investigated by a fully differential capacitive bridge interface using a sub-fF switched-capacitor integrator circuit. The sensitivities of the accelerometer in the two lateral directions were determined to be 6 and 5.5 fF/g, respectively. The cross-axis sensitivities of the accelerometer were less than 5%, which shows that the accelerometer can be used for measuring precisely acceleration in the two lateral directions. The accelerometer operates linearly in the range of investigated acceleration from 0 to 4g. The proposed accelerometer is expected for low-g applications.

Design Guidelines for MEMS Optical Accelerometer based on Dependence of Sensitivities on Diaphragm Dimensions

This work deals in specifying the design considerations while constructing a Micro Electro Mechanical Systems (MEMS) optical accelerometer working on capacitive sensing technique. Sensitivity is one of the most demanded characteristics of any sensor. The sensor considered is a MEMS capacitive accelerometer in which both displacement and capacitance are the primary sensing characteristics. This differential capacitive accelerometer causes change in displacement due to applied acceleration and further produces change in capacitance. So, the main focus in this work is to improve or select the suitable diaphragm dimensions of the differential capacitor in order to get optimal capacitive and displacement sensitivity. This is done for an Optical MEMS (MOEMS) based sensor where slight change has a large-scale impact. The electrical signal is converted to optical by adding an Optical Interferometer. Mach–Zehnder Interferometer (MZI) is used to carry out the intensity modulation which also gives protection in inflammable surroundings. This makes the system suitable for working in high temperature regions.

A Triaxial Accelerometer Based on Differential Resonant Beams and Force-Balanced Capacitive Plates

This paper presents the design, simulation, fabrication, and experiment of a triaxial accelerometer based on differential resonant beams and force-balanced capacitive plates. The triaxial accelerometer is composed of a proof mass, four bridge resonators with both end clamped and operating in flexure vibration mode, four L-type supporting beams, and a top plate and a bottom plate. The in-plane acceleration is measured by bridge resonators. The gravity center of the proof mass and the neutral layer of L-type supporting beams are located within the same plane to minimize the rotation of the proof mass subjected to in-plane acceleration. The cross-axis sensitivities of X-axis and Y-axis resonant beams under lateral in-plane acceleration are 1.97% and 1.71%, respectively. A force-balanced differential plate capacitor composed of a proof mass, a top plate, and a bottom plate is used to detect acceleration along Z-axis. The small displacement of the proof mass in the normal direction of the chip reduces the cross-axis sensitivity of the bridge resonators subjected to acceleration along Z-axis. The complementation of the resonance detection mechanism and the force balance capacitance mode makes the triaxial accelerometer exhibit low cross-axis sensitivity. The simulated and experimental results prove this conclusion.

A VCII-Based Stray Insensitive Analog Interface for Differential Capacitance Sensors

In this paper, a novel approach to implement a stray insensitive CMOS interface for differential capacitive sensors is presented. The proposed circuit employs, for the first time, second-generation voltage conveyors (VCIIs) and produces an output voltage proportional to differential capacitor changes. Using VCIIs as active devices inherently allows the circuit to process the signal in the current domain, and hence, to benefit from its intrinsic advantages, such as high speed and simple implementation, while still being able to natively interface with voltage mode signal processing stages at necessity. The insensitiveness to the effects of parasitic capacitances is achieved through a simple feedback loop. In addition, the proposed circuit shows a very simple and switch-free structure (which can be used for both linear and hyperbolic sensors), improving its accuracy. The readout circuit was designed in a standard 0.35 μm CMOS technology under a supply voltage of ±1.65 V. Before the integrated circuit fabrication, to produce tangible proof of the effectiveness of the proposed architecture, a discrete version of the circuit was also prototyped using AD844 and LF411 to implement a discrete VCII. The achieved measurement results are in good agreement with theory and simulations, showing a constant sensitivity up to 412 mV/pF, a maximum linearity error of 1.9%FS, and acknowledging a good behavior with low baseline capacitive sensors (10 pF in the proposed measurements). A final table is also given to summarize the key specs of the proposed work comparing them to the available literature.

Piezoelectrically actuated vibrating flexible differential capacitances for electrostatic detection

Space exploration requires reliable measurements of space-radiation induced charge or its electric potential in a wide range in a satellite. Here, we report one pair of 3D printed soft multilayer differential capacitors, which are piezoelectrically actuated in vibration to convert the input static DC charge (high electric potential) into a measurable small dynamic AC output signal through charging and discharging between two differential capacitors. The fabricated prototype features linear responses to a high potential change and also high reliability. Moreover, the method proposed in this work is promising to achieve rapid manufacturing of functional devices in batch processing.

A Capacitance-to-Time Converter-Based Electronic Interface for Differential Capacitive Sensors

In this paper we present an oscillating conditioning circuit, operating a capacitance-to-time conversion, which is suitable for the readout of differential capacitive sensors. The simple architecture, based on a multiple-feedbacks structure that avoids ground noise disturbs and system calibrations, employs only three Operational Amplifiers (OAs) and a mixer implementing a square wave oscillator that provides an AC sensor excitation voltage. It performs a Period Modulation (PM) and a Pulse Width Modulation (PWM) of the output signal proportionally to the sensor differential capacitance values. The sensor variation range and the detection sensitivity can be easily set through the additional resistors. Preliminary PSpice simulation results have shown a good agreement with theoretical calculations as well as a linear response with a high detection sensitivity of differential capacitive sensors having a baseline in the range [2.2 ÷ 180 pF]. Moreover, different experimental measurements have been also performed by implementing the circuit on a laboratory breadboard using commercial discrete components so validating the idea and providing the circuit performances with different kind of differential capacitive sensors achieving detection resolutions of about 0.1 fF in an overall differential capacitive variation range that is equal to ±15.8 pF. The achieved results demonstrate that the proposed interface solution is suitable for on-chip integration with different kinds of differential capacitive sensing devices, such as Micro-Electro-Mechanical-System (MEMS), force/position, and humidity sensors in biomedical and robotics applications.