Maximum Nonlinearity Error Research Articles

Hybrid ALM-DSP TDC in Intel Arria 10 FPGA

The article presents the first implementation of a time-to-digital converter (TDC) using a digital signal processing (DSP) block from an Intel field-programmable gate array (FPGA) device. The design and configuration capabilities of the DSP blocks of the leading FPGA manufacturers, AMD and Intel, are compared in the context of time/digital conversion. Next, three variants of TDCs are presented. The problem of ultra-wide bins observed in both the classic version of the converter based on the Adaptive Logic Modules (ALM) and the version built using only DSP blocks has been mitigated in a hybrid variant, combining both solutions. The proposed variant of the hybrid ALM-DSP TDC implemented in Arria 10 FPGA from Intel (20 nm process node) achieved a resolution of 2.1 ps, a single-shot-precision better than 6.36 ps and reduced the maximum differential nonlinearity (DNL) error from 74.5 ps to 12.7 ps.

A three-dimensional fiber Bragg grating wrist force sensor with separation elastic structure

PurposeThe use of a force sensor to estimate the external force of manipulator not only needs to deal with the signal noise of the sensor itself but also needs to solve the coupling interference of the sensor itself, especially the axial force. The purpose of this paper is to develop a three-dimensional fiber Bragg grating (FBG) wrist force sensor, which has a simple structure and reduces the coupling influence between several axes.Design/methodology/approachA particular separation elastic structure with four FBGs is devised for the three-axial force sensor. One FBG is suspended on the profile of central cylinder and the other three FBGs are pasted on the elastic beam surface of the over and under measuring bodies, respectively. Finite element analysis (FEA) simulation has been implemented to the strain distribution characteristics, the output characteristics of each direction and the coupling effects of the structure. Furthermore, theoretical derivation and experimental results are used to compare, which have a good consistency.FindingsThe experiment results show that the maximum repeatability error of the sensor is 6.75%, the maximum nonlinear error is 5.36%, the maximum coupling interference is 4.73% and the minimum sensitivity is 1.58 pm/N.Originality/valueA three-dimensional force sensor based on FBG adopts a particular separation elastic structure. The sensor can reduce the coupling influence between several axes, especially the coupling interference in the z-direction is 0.

Temperature-Decoupled Single-Crystal MgO Fiber-Optic Fabry-Perot Vibration Sensor Based on MEMS Technology for Harsh Environments.

A high-temperature-resistance single-crystal magnesium oxide (MgO) extrinsic Fabry-Perot (FP) interferometer (EFPI) fiber-optic vibration sensor is proposed and experimentally demonstrated at 1000 °C. Due to the excellent thermal properties (melting point > 2800 °C) and optical properties (transmittance ≥ 90%), MgO is chosen as the ideal material to be placed in the high-temperature testing area. The combination of wet chemical etching and direct bonding is used to construct an all-MgO sensor head, which is favorable to reduce the temperature gradient inside the sensor structure and avoid sensor failure. A temperature decoupling method is proposed to eliminate the cross-sensitivity between temperature and vibration, improving the accuracy of vibration detection. The experimental results show that the sensor is stable at 20-1000 °C and 2-20 g, with a sensitivity of 0.0073 rad (20 °C). The maximum nonlinearity error of the vibration sensor measurement after temperature decoupling is 1.17%. The sensor with a high temperature resistance and outstanding dynamic performance has the potential for applications in testing aero-engines and gas turbine engines.

A Five-Hole Pressure Probe Based on Integrated MEMS Fiber-Optic Fabry-Perot Sensors.

The five-hole pressure probe based on Micro-Electro-Mechanical Systems (MEMS) technology is designed to meet the needs of engine inlet pressure measurement. The probe, including a pressure-sensitive detection unit and a five-hole probe encapsulation structure, combines the advantages of a five-hole probe with fiber optic sensing. The pressure-sensitive detection unit utilizes silicon-glass anodic bonding to achieve the integrated and batch-producible manufacturing of five pressure-sensitive Fabry-Perot (FP) cavities. The probe structure and parameters of the sensitive unit were optimized based on fluid and mechanical simulations. The non-scanning correlation demodulation technology was applied to extract specific cavity lengths from multiple interference surfaces. The sealing platform was established to analyze the sealing performance of the five-hole probe and the pressure-sensitive detection unit. The testing platform was established to test the pressure response characteristics of the probe. Experimental results indicate that the probe has good sealing performance between different air passages, making it suitable for detecting pressure from multiple directions. The pressure responses are linear within the range of 0-250 kPa, with the average pressure sensitivity of the five sensors ranging from 11.061 to 11.546 nm/kPa. The maximum non-linear error is ≤1.083%.

Adaptive multipole models of optically pumped magnetometer data.

Multipole expansions have been used extensively in the Magnetoencephalography (MEG) literature for mitigating environmental interference and modelling brain signal. However, their application to Optically Pumped Magnetometer (OPM) data is challenging due to the wide variety of existing OPM sensor and array designs. We therefore explore how such multipole models can be adapted to provide stable models of brain signal and interference across OPM systems. Firstly, we demonstrate how prolate spheroidal (rather than spherical) harmonics can provide a compact representation of brain signal when sampling on the scalp surface with as few as 100 channels. We then introduce a type of orthogonal projection incorporating this basis set. The Adaptive Multipole Models (AMM), which provides robust interference rejection across systems, even in the presence of spatially structured nonlinearity errors (shielding factor is the reciprocal of the maximum fractional nonlinearity error). Furthermore, this projection is always stable, as it is an orthogonal projection, and will only ever decrease the white noise in the data. However, for array designs that are suboptimal for spatially separating brain signal and interference, this method can remove brain signal components. We contrast these properties with the more typically used multipole expansion, Signal Space Separation (SSS), which never reduces brain signal amplitude but is less robust to the effect of sensor nonlinearity errors on interference rejection and can increase noise in the data if the system is sub-optimally designed (as it is an oblique projection). We conclude with an empirical example utilizing AMM to maximize signal to noise ratio (SNR) for the stimulus locked neuronal response to a flickering visual checkerboard in a 128-channel OPM system and demonstrate up to 40 dB software shielding in real data.

Aspherical interferometric probe with wave-plate-array detection: system design and nonlinearity analysis.

Optical probes are the preferred choice for high-precision surface metrology, necessitating improved flexibility and a broader range of motion to adapt to the increasing complexity of surfaces. This study introduces an interferometric probe designed for measuring aspheric surfaces, utilizing a wave-plate-array detection component. By integrating splitter elements into the detector, the probe improves integration and dynamic scanning performance, while maintaining high-precision measurement capability. The system design and working principle are explored, and comprehensive nonlinear models based on the Jones matrix theory are established. These models focus on the nonlinear errors arising from alignment errors in various cases. Moreover, rigorous numerical simulations and optical experiments are conducted to validate the proposed models. When the alignment error reaches 10°, it results in a maximum nonlinear error of 3.02nm. The experimental results demonstrate the effectiveness of the models in capturing nonlinear errors induced by alignment errors, providing a theoretical foundation for error reduction and compensation.

Novel contactless torque sensor based on optical coherence

This work proposes a novel contactless sensor to measure the micro torque of a rotating shaft based on the optical coherence displacement measurement (OCDM) principle. The experimental system features a simple mechanical testing system to measure the torque, a calibration device to establish the measurement baseline, and a polyetheretherketone (PEEK) shaft to improve the theoretical resolution of the system up to 0.003 Nm. The torque measurement results indicate that this sensor achieved a maximum nonlinearity error of 0.0484 %, maximum repeatability error of 0.2771 %, and maximum hysteresis error of 0.2252 %. This high accuracy of our system stems from the use of high-precision optical principles and the novel physical mapping of the torque (i.e., processing scales on the shaft surface to represent the twist angle by designing a laser engraving system) capable of resisting the negative effects of radial vibrations. Additionally, our torque measurement sensor possesses broader applicability by effectively resisting the impacts of temperature variations and electromagnetic interference. These attributes make it excel other torque sensors presented in the literature in recent years.

A Time-of-Flight Image Sensor Using 8-Tap P-N Junction Demodulator Pixels.

This paper presents a time-of-flight image sensor based on 8-Tap P-N junction demodulator (PND) pixels, which is designed for hybrid-type short-pulse (SP)-based ToF measurements under strong ambient light. The 8-tap demodulator implemented with multiple p-n junctions used for modulating the electric potential to transfer photoelectrons to eight charge-sensing nodes and charge drains has an advantage of high-speed demodulation in large photosensitive areas. The ToF image sensor implemented using 0.11 µm CIS technology, consisting of an 120 (H) × 60 (V) image array of the 8-tap PND pixels, successfully works with eight consecutive time-gating windows with the gating width of 10 ns and demonstrates for the first time that long-range (>10 m) ToF measurements under high ambient light are realized using single-frame signals only, which is essential for motion-artifact-free ToF measurements. This paper also presents an improved depth-adaptive time-gating-number assignment (DATA) technique for extending the depth range while having ambient-light canceling capability and a nonlinearity error correction technique. By applying these techniques to the implemented image sensor chip, hybrid-type single-frame ToF measurements with depth precision of maximally 16.4 cm (1.4% of the maximum range) and the maximum non-linearity error of 0.6% for the full-scale depth range of 1.0-11.5 m and operations under direct-sunlight-level ambient light (80 klux) have been realized. The depth linearity achieved in this work is 2.5 times better than that of the state-of-the-art 4-tap hybrid-type ToF image sensor.

A Simple Approach to Connecting Pt100 by Utilizing an Electroacoustic Resonance Tube

Temperature transducers are frequently employed to keep track of process variables with different kinds of industrial controllers. One of the widely used temperature sensors is Pt100. A novel approach of utilizing an electroacoustic transducer in signal conditioning for Pt100 is proposed in this paper. A "signal conditioner" is a resonance tube filled with air, which is operated in a free resonance mode. The Pt100 wires are connected to one of the leads of the speaker in the resonance tube where the temperature changes, which is related to Pt100 resistance. The resistance affects the amplitude of the standing wave that is detected by an electrolyte microphone. An algorithm for measuring the amplitude of the speaker signal is described, as well as the building and functioning of the electroacoustic resonance tube signal conditioner. The microphone signal is acquired as a voltage using LabVIEW software. A virtual instrument (VI) developed under LabVIEW provides a measure of the voltage using standard VIs. The findings of the experiments reveal a link between the measured amplitude of the standing wave within the tube and the change in Pt100 resistance as the ambient temperature changes. Additionally, the suggested method may interface with any computer system when a sound card is added to it without the need for any extra measuring tools. The maximum nonlinearity error at full-scale deflection (FSD) is estimated at roughly 3.77%, and the experimental results and a regression model are used to assess the relative inaccuracy of the developed signal conditioner. When comparing the proposed approach with well-known approaches for Pt100 signal conditioning, the proposed one has several advantages such as its simplicity of connecting Pt100 to a personal computer directly via the sound card of any personal computer. In addition, there is no need for a reference resistance to perform a temperature measurement using such a signal conditioner.

A Novel Structure of an Eddy Current Sensor for Speed Measurement of Rotating Shafts

This paper presents a novel structure of an eddy current sensor for the measurement of rotational speed. The sensor has a perpendicular configuration of the excitation coil and the pick-up coil. Its maximum nonlinearity error is 0.15%. The excitation coils and the pick-up coils are divided into two identical parts with a coil span of 180 degrees. Various solid iron cylinders with different electrical and magnetic characteristics, one solid aluminum cylinder and one solid copper cylinder, were used as the rotating shafts. A novel 2D analytical method in cylindrical coordinates has been developed for fast parametric analysis of this sensor. 2D and 3D time-stepping finite-element methods that take into consideration the shaft motion are used for a performance analysis of the eddy current sensor. The measurements of the speed sensor are performed at various frequencies and speeds and are compared with the calculations for detailed analysis. The effects of the rotating shaft materials are evaluated both in the measurements and in the calculations.

Experimental Investigation of Microcontroller-Based Acoustic Temperature Transducer Systems

Temperature transducers are commonly used to monitor process parameters that are controlled by various types of industrial controllers. The purpose of this study is to design and model a simple microcontroller-based acoustic temperature transducer based on the variations of resonance conditions in a cylindrical resonance tube. The transducer's operation is based on the generation of an acoustic standing wave in the free resonance mode of generation within a cylindrical resonance tube which is converted into a train of pulses using Schmitt trigger circuit. The frequency of the generated standing wave (i.e., the train of pulses) is measured by the Arduino Uno microcontroller, where a digital pin is used to acquire pulses that are counted using a build-in software function in an Arduino IDE environment. Experimental results are performed for three sizes of diameters to investigate the effect of the diameter of resonance tube on the obtained results. The maximum nonlinearity error according to Full-Scale Deflection (FSD) is about 2.3 percent, and the relative error of the transducer is evaluated using experimental findings and the regression model. The circuit simplicity and design of the suggested transducer, as well as the linearity of its measurements, are notable.

A Multivector Variable Area Type Capacitive Angular Displacement Encoder Based on a Rotating Electric Field and Improvement of Its Demodulation Method

The problems of the traditional type grating angular displacement encoder make it difficult to balance the measurement performance of miniaturization, high precision and high resolution, and the ability to resist vibration and shock is poor. In this article, a multivector variable-area capacitive angular displacement encoder based on a rotating electric field is proposed. Based on the principle of constructing a rotating electric field, a three-layer transmissive sensing structure with upper and lower layers of electrode plates and a modulation rotor as the middle layer is proposed and designed. A single-channel signal is used as the input excitation signal of the capacitive sensor to avoid the problem of mismatching multiple input signals. A pair of quadrature signals reflecting the spatial angle information is obtained through electric field demodulation and differential processing. The phase demodulation method based on the time scale is further adopted to improve the precision of demodulation. Simulations and experiments show that the sensor has a diameter of 50 mm, a thickness of 5 mm, a resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.81''$ </tex-math></inline-formula> , an 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">$2.5''$ </tex-math></inline-formula> , and a maximum nonlinear error of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$40''$ </tex-math></inline-formula> . The design is verified to be feasible, which provides a new solution for capacitive angular position sensor design.

Flexible conductive film based on silver nanowires in patients’ sports rehabilitation

The flexible conductive film, which is composed of high aspect ratio silver nanowires, multi walled carbon nanotubes and PDMS, has a good application prospect in the field of flexible wearable sensors. Based on the above background, the purpose of this study is to analyze the application and effect of flexible conductive film based on silver nanowires in patients' sports rehabilitation. In this study, an improved one-step polyol method was used, and copper chloride was used as the nucleation control agent to prepare high aspect ratio silver nanowires with uniform shape and size. The flexible conductive film was prepared by combining carbon nanotubes and polyurethane (PU) doped with self-made silver nanowires. Then, using self-made silver nanowires and multi wall carbon nanotubes as conductive materials, PDMS as flexible substrate, silver nanowires and multi wall carbon nanotubes were uniformly deposited on PDMS to make flexible conductive film, and then assembled into a simple flexible tensile strain sensor. The flexible strain sensor was installed on the fingers, wrists, elbows and knees of the patients. The experimental results show that the linearity of flexible strain sensor is greatly improved, the maximum nonlinear error is 3.54%, and the minimum hysteresis error is 5.18%. The flexible strain sensor based on silver nanowire is installed in the rehabilitation movement part of patients for monitoring. The sensor can convert the movement signal of each part into electrical signal curve, and can identify the movement part of patients and the movement state of the movement part according to the electrical signal curve.

A Reconfigurable Multisensor Based on Printed Circuit Board Technology for Measuring Moisture Content and Temperature in Stored Grain

We present the design and fabrication of a reconfigurable smart-sensor for measuring moisture content (MC) and temperature in grains stored in silos, using a capacitance fringing field interdigitated sensor and using a resistance temperature detector (RTD), both implemented on a single conventional printed circuit board. The sensor was tested in laboratory, using corn kernels with percent MC in the range of MC <inline-formula> <tex-math notation="LaTeX">$= 8\%$ </tex-math></inline-formula> to MC <inline-formula> <tex-math notation="LaTeX">$= 32 \%$ </tex-math></inline-formula> and, using a simple relaxation oscillator and a frequency-to-voltage converter, we measured a capacitance variation of <inline-formula> <tex-math notation="LaTeX">$\Delta C = 4.99$ </tex-math></inline-formula> pf, with a sensitivity <inline-formula> <tex-math notation="LaTeX">$S = 0.21 \, \rm {pF}/\%$ </tex-math></inline-formula>MC. The RTD sensor, which uses the copper resistance of the PCB tracks, was characterized in the 10 <inline-formula> <tex-math notation="LaTeX">$^\circ \text{C}$ </tex-math></inline-formula>&#x2013;<inline-formula> <tex-math notation="LaTeX">$50~^\circ \text{C}$ </tex-math></inline-formula> temperature range and the measured results presented a very linear behavior (<inline-formula> <tex-math notation="LaTeX">$R^{2} = 0.99888$ </tex-math></inline-formula>) when compared to the measured temperature values using a commercial sensor (LM135). A modified bridge circuit was developed, where a linear behavior of the differential output was obtained. The developed configuration allowed for the independent adjustment of both the offset and the gain in the output voltage <inline-formula> <tex-math notation="LaTeX">$V_{\text {out}}$ </tex-math></inline-formula> of the bridge. The bridge signal processing circuit was calibrated using an endpoint method, and the measured points between the calibration points presented a maximum endpoint nonlinearity error of <inline-formula> <tex-math notation="LaTeX">$|E_{\text {nl}}| =\,\,0.64\,\,^\circ \text{C}$ </tex-math></inline-formula>.

A Position Sensor With Novel Configuration of Linear Variable Differential Transformer

This paper presents a position sensor based on a novel configuration of linear variable differential transformer. Design and optimization of the position sensor using finite element method are presented. The measurements are also conducted to validate experimentally the sensor performance. The sensor has short air core coils and long magnetic armatures. The axis of the rectangular excitation coil and two antiserially connected rectangular pick up coils is perpendicular to the motion direction of the position sensor. The coils are located between two parallel silicon steel laminations serving as the armatures. The position sensor is optimized with compromise between minimization of nonlinearity error and maximum sensitivity. The main advantage of the proposed position sensor is the small ratio of coils dimensions to the working range. The position sensor is operated for excitation frequencies of 500 Hz, 1000 Hz, and 2000 Hz. The maximum nonlinearity error is less than 1.5% for the theoretical results and it is less than 2% for the measured results in ±90 mm position range.

Bidirectional Active Piezoelectric Actuator Based on Optimized Bridge-Type Amplifier.

Piezoelectric actuators based on bridge displacement amplifying mechanisms are widely used in precision driving and positioning fields. The classical bridge mechanism relies on structural flexibility to realize the return stroke, which leads to the low positioning accuracy of the actuator. In this paper, a series bridge mechanism is proposed to realize a bidirectional active drive; the return stroke is driven by a piezoelectric stack rather than by the flexibility of the structure. By analyzing the parameter sensitivity of the bridge mechanism, the series actuation of the bridge mechanism is optimized and the static and dynamic solutions are carried out by using the finite element method. Compared with the hysteresis loop of the piezoelectric stack, the displacement curve of the proposed actuator is symmetric, and the maximum nonlinear error is improved. The experimental results show that the maximum driving stroke of the actuator is 129.41 μm, and the maximum nonlinear error is 5.48%.

High-Linearity High-Resolution Time-of-Flight Linear-Array Digital Image Sensor Using Time-Domain Feedback.

This paper presents a high-linearity high-resolution time-of-flight (ToF) linear-array digital image sensor using a time-domain negative feedback technique. A coarse ToF measurement loop uses a 5-bit digital-to-time converter (DTC) and a delayed gating-pulse generator for time-domain feedback to find the zero of the difference between ToF and the digital estimate of the gating-pulse delay while maintaining a constant operating point of the analog readout circuits. A fine ToF measurement uses a delta-sigma modulation (DSM) loop using the time-domain feedback with a bit-stream signal form. Because of the self-contained property of the DSM for low distortion and noise exploited by the oversampling signal processing, the proposed technique provides high-linearity and high-range resolution in the fine ToF measurement. A prototype ToF sensor of 16.8 × 16.8 μm2 two-tap pixels and fabricated in a 0.11 μm (1P4M) CMOS image sensors (CIS) process achieves +0.9%/−0.47% maximum nonlinearity error and a resolution of 0.24 mm (median) for the measurement range of 0–1.05 m. The ToF sensor produces an 11-bit fully digital output with a ToF measurement time of 22.4 ms.

Correction of nonlinearities in series structure-based resistance thermometry readouts.

Series structure-based resistance thermometry readouts offer several advantages for multi-point temperature measurements. However, because of the diversity of nonlinear error sources and differences among channels in such readouts, existing nonlinear error correction methods are ineffective. In view of this situation, a nonlinear error correction method based on error source analysis is proposed. The proposed method first determines the impacts of error sources by analyzing the circuit architecture. The contributions of the common-mode rejection ratio and the mismatch between positive and opposite exciting currents are then eliminated using resistance bridge calibrators. Finally, the residuals are fitted to various polynomial functions. The results of experiments show that correction based on the proposed method results in a maximum nonlinear readout error of 1.87 × 10-5, compared with 4.01 × 10-5 using the classical method. Thus, the proposed method of nonlinear error correction is effective for series structure-based resistance thermometry readout.

Nonlinear characteristics analysis of sodium flow measurement based on the principle of turbulent fluctuation

The permanent magnet sodium flowmeter (PMSF) used to measure the coolant flow in fast reactors has to be calibrated in situ due to operating conditions and measurement requirements. When the large-diameter PMSF is calibrated in situ based on the cross-correlation method, there is no bluff body in the flow tube, the sodium flow measurement relied only on the turbulent fluctuation of the sodium flow, so the relationship between the cross-correlation flow rate and the standard flow rate has nonlinearity. The reasons for the nonlinear characteristics are analyzed from a mechanism perspective. The sodium flow measurement experiments based on the cross-correlation method are performed for DN150 PMSF without bluff body at a temperatures of 250 °C, and also conducted for DN300 PMSF without bluff body at the temperatures of 250 °C, 360 °C and 400 °C, respectively. The experimental data of electrodes at different positions and distances are processed by the biased cross-correlation function estimation, the maximum nonlinearity error between the standard flow rate and the cross-correlation flow rate is found to be up to 90%, and the quadratic function model is established to describe their relationship. The flow rate distribution between adjacent electrodes and the degree of nonlinearity between different electrode pairs are investigated, proving that the larger the flow rate, the more serious the distortion of the primary magnetic field, and the distortion of the primary magnetic field at different electrode positions is different. The influence of pipe diameter on the degree of nonlinearity is analyzed, the larger the diameter, the greater the degree of nonlinearity. The effect of the temperature of liquid sodium on the degree of nonlinearity is studied, the higher the temperature, the smaller the degree of nonlinearity.

Angle measurement technology based on magnetization vector for narrow space applications

With the wide application of laser in the field of skin plastic surgery, micro laser galvanometer scanner has made great progress in this field with its portability. However, the measurement method used to measure the deflection angle of laser galvanometer in the narrow space of scanner with high precision remains to be studied. In this paper, an angle measurement method based on magnetic field is proposed, and the effect of the shapes of permanent magnets (PMs) on the measurement is studied by theoretical and experimental study under the condition that the maximum available space for the PMs is a 10 mm side cube. An angle measuring experimental device is set up, and the contrast experiment is carried out with different PMs which are the same as simulation. The experimental results show that cylindrical PM is more suitable than other PMs, which is consistent with the simulation results, and the maximum nonlinearity error is 0.562%. This method has the advantages of small volume, non-contact measurement, small moment of inertia, good dynamic response and no external excitation for the PMs, so it has a broad application prospect in micro laser galvanometer scanner.