Phase-sensitive Demodulation Research Articles

High-Precision Inertial Sensor Charge Ground Measurement Method Based on Phase-Sensitive Demodulation

Inertial sensors are the key payloads in space gravitational wave detection missions, and they need to ensure that the test mass (TM), which serves as the inertial reference, freely floats in the spacecraft without contact, so that the TM is not disturbed by the satellite platform and the cosmic environment. Space gravitational wave detection missions require that the residual acceleration of the TM should be less than 3×10−15ms−2Hz−1/2. However, the TM with charges will interact with surrounding conductors and magnetic fields, introducing acceleration noise such as electrostatic force and Lorentz force. Therefore, it is necessary to carry out charge management on the TM, in which the high-precision measurement of charge is crucial. Space gravitational wave detection missions require a residual charge measurement accuracy of 3×10−13C for the TM. In this paper, we design a high-precision inertial sensor charge measurement method based on phase-sensitive demodulation (PSD). By establishing a torsion pendulum rotation model based on the force modulation method, the characteristics of the TM torsion angle signal are analyzed. The PSD is used to extract the amplitude of the specific frequency signal component containing the charge information, and then to calculate the value of the accumulated charges. The method is compared with the Butterworth band-pass filtering method, and the simulation results show that the method has a higher measurement accuracy, shorter settling time, and stronger anti-interference ability, meeting the TM residual charge measurement accuracy index requirement.

Design of a multidimensional data collection system based on DRS4 scheme

A high-speed data acquisition system based on DRS4 waveform digitization is designed to meet the requirements of high sampling rate, multi-parameter measurements, and long-distance transmission in some particle physics experiments. The system consists of a waveform digitization front-end board, a high-speed data transmission board, and an upper computer software. Test results show that the system has a high data transmission rate and a low BER and that the collected data can reconstruct and restore the input signal waveform well. In addition, we have analyzed the single-electrode dual-mode sensor, excitation signal generation module, resistor/capacitor conversion circuit, and phase-sensitive demodulation unit in the system. The experiments show that the system is stable in operation, flexible in use, and can significantly extend the measurement range.

A Picofarad Capacitance Meter Based on Phase-Sensitive Demodulation for Tomography Application

Electrical capacitance volume tomography (ECVT) is an imaging technique based on the object’s capacitance value. To provide a representative image of the object under study, the ECVT system requires a method that can measure the capacitance value in the order of picofarads (pF). This level of resolution poses a difficulty for typical commercial capacitance measuring devices, hence raising the need for a specialized method with dedicated signal conditioning circuitry. The capacitance meter based on phase-sensitive demodulation (PSD) is made to solve the aforementioned issue and it is then compared with the characteristics of a capacitance meter-based commercial Arduino setup. The designed PSD-based capacitance measuring device has 97.894% accuracy, precision of 0.704 pF, sensitivity of 0.1197 V/pF, linearity with a coefficient of determination 0.9983, and stability of 0.028 pF/min. In comparison, the capacitance meter based on Arduino has 97.943% accuracy, precision of 0.027 pF, linearity with a coefficient of determination 0.9999, and stability of 0.04 pF/min. Testing is done on an 8-electrode ECVT sensor using dielectric materials of air and water. The nearest electrode pair on the condition of air as the dielectric medium has a capacitance value of 2.62218 pF for PSD-based measuring devices and 3.4027 pF for Arduino-based measuring devices, while the pair of electrodes on the condition of water as a dielectric medium has a capacitance value 9.8229 pF for measuring device based on PSD and 9.1069 pF for Arduino-based measuring devices. The opposite and farthest electrode pair on the condition of air as a dielectric medium has a capacitance value of 0 pF for PSD-based measuring devices and 0,0798pF for Arduino-based measuring devices, while the pair of electrodes on the condition of water as a dielectric medium has a capacitance value of 4.652 pF for PSD-based measuring devices and 0.1224 pF for Arduino-based measuring devices.

A dual-axis high-order harmonic and single-axis phase-insensitive demodulation atomic magnetometer for in situ NMR detection of Xe

Based on the parametric oscillation process, we demonstrate the dual-axis phase-sensitive demodulation (PSD) and single-axis phase-insensitive demodulation (PISD) for the atomic magnetometer in an in situ nuclear magnetic resonance (NMR) detection system, which can separate the precession signals of NMR from the oscillating magnetic fields. The two orthogonal magnetic fields can be detected simultaneously and independently by selecting the optimal demodulation phases with the traditional PSD method. The response signals of the parametric modulation magnetometer demodulated with high order harmonic signals are evaluated, which is a new exploration. The first order harmonic demodulation can present the best sensitivity about 250 fT/Hz1/2. The high order harmonic demodulation technology supplies a twofold 3 dB bandwidth. With the PISD method, a single-axis demodulation technique is proposed. The transverse nuclear spin precession magnetic fields can be extracted effectively with the demodulation R signal outputs by setting a specific longitudinal modulation magnetic field amplitude, which is a new demodulation strategy compared with the traditional demodulation method for the NMR system.

Phase-resolved visualization of radio-frequency standing waves in superconducting spiral resonator for metamaterial applications

Superconducting microcircuits and metamaterials are promising candidates for use in new generation cryogenic electronics. Their functionality is largely justified by the macroscopic distribution of electromagnetic fields in arranged unit cells, rather than by the microscopic properties of composite materials. We present a new method for visualizing the spatial structure of penetrating microwaves with microscopic resolution in planar superconducting macroscopic resonators as the most important circuit-forming elements of modern microelectronics. This method uses a low-temperature laser scanning microscope that examines the phase (i.e., direction) and amplitude of local radio-frequency currents versus the two-dimensional coordinates of the superconducting resonant structure under test. Phase-sensitive contrast is achieved by synchronizing the intensity-modulated laser radiation with the resonant harmonics of the microwave signal passing through the sample. In this case, the laser-beam-induced loss in the illuminated area will strongly depend on the local phase difference between the RF carrier signal and the spatially temporal structure of the focused laser oscillation. This approach eliminates the hardware limitations of the existing technique of radio-frequency microscopy and brings the phase-sensitive demodulation mode to the level necessary for studying the physics of superconducting metamaterials. The advantage of the presented method over the previous method of RF laser scanning micros-copy is demonstrated by the example of the formation of standing waves in a spiral superconducting Archimedean resonator up to the 38th eigenmode resonance.

A Blended Lab on Phase-Sensitive Demodulation for Undergraduate Electronic Circuit Design Course

This paper proposes the blended lab concept for mitigating the lack of practical lab sessions due to constraints on hardware resources or pandemic such as COVID. Virtual labs, which use computer aided simulation to enhance learning experience, can replace some aspects of the practical lab activities, but not all. Deficiency in practical skills caused by the lack of practical lab sessions can be observed evidently from post-pandemic students. The proposed blended lab combines computer-based simulation with practical activities that can be carried out readily at home. This concept has been applied in an undergraduate electronic circuit design course at Manchester and Tianjin. Students use mobile phones as simple signal generators/scopes to visualise sound/light/audio-jack signals from circuits built on breadboard at home. This approach has proved to enhance student experience when physical lab is limited.

Employing dual frequency phase sensitive demodulation technique to improve the accuracy of voltage measurement in magnetic induction tomography and designing a labratoary prototype

Employing dual frequency phase sensitive demodulation technique to improve the accuracy of voltage measurement in magnetic induction tomography and designing a labratoary prototype

Survey of signal clamping for digital phase sensitive detector.

Electrical capacitance tomography (ECT) is a multiphase flow detection technology, which has the advantages of nonradioactive, noninvasive, and on-line visualization measurements. In ECT measurements, the digital phase sensitive demodulation (PSD) plays an important role in guaranteeing the accuracy of small capacitance measurements. Generally, the clamping circuit is implemented to protect the A/D converter. In the measuring circuit, a programmable gain amplifier is usually employed to expand the dynamic range of PSD. However, the measured signal may exceed the measurement range from time to time, which induces the signal clamping effect. In this case, the digital PSD will present large errors in the capacitance measurements. In consideration of the frequency spectrum characteristic of the clamped signal, two digital PSD methods have been proposed. The proposed methods have been implemented in a field programmable gate array based measurement system. The experimental results show that the proposed multisine PSD method could expand the dynamic range by a factor of 5, at a relatively low error, i.e., ≤2%.

New Contactless Velocity Measurement Sensor for Bubble/Slug Flow in Small Scale Pipes

A new contactless velocity measurement sensor for bubble/slug flow in small scale pipes is developed with the contactless impedance detection (CID) technique. The new sensor consists of two same-designed CID modules (an upstream and a downstream) and an information processing module. In the upstream/downstream CID module, the capacitive reactance elimination principle is introduced to eliminate the adverse influence of coupling capacitances, and the analog phase sensitive demodulation (APSD) technique is adopted to obtain the fluid impedance signals (real part and imaginary part) of the gas-liquid two-phase flow. In the information processing module, the cross-correlation method is introduced to determine two initial bubble/slug velocities with real part and imaginary part of the fluid impedance, respectively. Then for each flow pattern, a velocity fusion model is established to fuse the two initial velocities. Based on the flow pattern identification result by a flow pattern classifier, the corresponding velocity fusion model is applied to determine the fused bubble/slug velocity. Three prototypes of the new sensor are developed and experiments are carried out. Experimental results show that the new sensor has good velocity measurement performance for bubble/slug flow in small scale pipes. For all the three prototypes, the maximum relative errors of velocity measurement are less than 3.0%. Results also indicate that the capacitive reactance elimination can successfully overcome the adverse influence of the coupling capacitances and taking full advantage of the total fluid impedance signals is an effective way to improve the velocity measurement accuracy.

Wide Dynamic Range Multichannel Lock-In Amplifier for Contactless Optical Sensors With Sub-pS Resolution

A multichannel impedance-sensing CMOS chip for the readout of noninvasive light detectors in silicon photonics (SiP) is presented. The performance of the lock-in phase-sensitive demodulator is improved thanks to a capacitive feedback transimpedance amplifier (TIA) equipped with an active discharge network, able to keep a dc output offset lower than 3 mV for leakage currents up to 4 nA while injecting a noise lower than 40 fA/ $\sqrt {\mathrm{ Hz}}$ . The addition of a sensor capacitance compensation system at the input of the chip allows a 30-fold increase of the stimulation amplitude, enabling the tracking of sub-picoSiemens conductance variations on a baseline of few $\mu \text{S}$ , with a bandwidth of 70 Hz. The chip performance opens the way to multipoint monitoring of complex photonic systems, addressing the challenges posed by the growing complexity of these architectures.

Phase-coherent THz-wave demodulation with a photomixer

The nonlinear electrical response from a low temperature grown GaAs photomixer driven with the optical beat of two continuous-wave lasers allows frequency mixing between radiofrequency and THz-waves. Phase-sensitive demodulation of the signal from a modulated THz-wave is theoretically and experimentally demonstrated using a photomixer electrically driven with an alternative voltage at the modulation frequency.

Study on defect type in eddy‐current testing based on phase spectrum analysis

This article proposes the use of phase angle gradient as a feature to detect and classify different types of defects. Based on the principle of eddy-current testing (ECT), the ECT platform was designed and manufactured. Based on phase-sensitive demodulation principle, the phase angle and gradient of the detected signal are analysed. The results show that the phase angles and phase angle gradients of different types of defect detection signals show different trends; the phase angle gradient of the integrated position direction and frequency direction can effectively identify the defect type.

Signal Demodulation Methods for Electrical Tomography: A Review

The amplitude and phase of each sinusoidal frequency component in a signal can be obtained by phase-sensitive demodulation, which is commonly used in electrical tomography (ET) and greatly influences the performance of the ET system. In the past decades, many demodulation methods have been developed for the ET system. This paper reviews the latest development in demodulation methods for the ET system, including the traditional methods and several newly proposed methods. To support the standpoints in the review, we implemented these methods in a self-made ECT system and then compared the performances of these methods, including the demands on hardware resources, demodulation time, and accuracy, by simulation and experiments. The main objective of the review is to provide guidance on the selection of appropriate demodulation method for a specific application.

Characterization of Pressure Sensor for Liquid-Level Measurement in Sloshing Condition

To achieve a reliable and accurate liquid-level detection, a differential pressure-based instrument is proposed in this article. The phase-sensitive demodulation of the signal is performed by the discrete Fourier transform (DFT) through a microcontroller. A good linearity in both ac and dc measurements has been observed. AC-based-level sensing demonstrated reliable and robust-level detection compared with dc, in both steady state conditions and while experiencing turbulence on the surface. In addition, thermal behavior of the proposed instrument is characterized and compensated, in order to evaluate its uncertainty as a liquid-level sensor. The obtained results show a combined uncertainty lower than 1 mm, which is mainly limited by sloshing conditions.

Synchronous in-phase and quadrature demodulation technique for resonant micro-optic gyroscope.

The phase modulation and demodulation technique is widely used in resonant optical gyroscopes to accurately detect resonance frequencies, which directly affect gyro sensitivity. In order to overcome the influences of the system phase fluctuations, an in-phase and quadrature (IQ) demodulation technique is introduced for a resonant micro-optic gyroscope (RMOG). The phase fluctuations in the RMOG are measured, and their influence on the demodulation slope at the resonance point is compared between the traditional sinusoidal demodulation and the IQ demodulation both theoretically and experimentally. It can be concluded that the output of the proposed IQ demodulation is not affected by any phase fluctuations. The demodulation slope is always at its maximum value, thus improving the signal-to-noise ratio of the detection system. By using the IQ demodulation technique, a random walk coefficient of 0.5°/√h is carried out. A long-term bias stability of 9°/h is successfully observed, which is improved by a factor of 1.6 compared with that obtained using the traditional phase-sensitive sinusoidal demodulation technique.

2-D Median Filter-Based Impulsive Noise Reduction in Multifrequency Phase-sensitive Demodulation of Electrical Impedance Tomography

Multifrequency phase-sensitive demodulation (PSD) plays an important role in electrical impedance tomography (EIT). In the presence of Gaussian noise, multifrequency PSD can be regarded as a matched filter and an optimal linear filter for the acquired signal. However, the additive noise often has the characteristics of impulsive noise in a real measurement system. Thus, it is a challenging task to reduce the impulsive noise effectively in multifrequency PSD. Considering the periodicity of multifrequency signal and the significant properties of 2-D median filter (MF), a method for impulsive noise reduction in multifrequency PSD of EIT was proposed in this paper. This paper mainly focused on reducing the impulsive noise by using the characteristics of signal itself and the 2-D MF. Numerical simulations and experiments were set up to verify the proposed method. Both results demonstrated that the proposed method can reduce the impulsive noise in multifrequency PSD effectively, and it can also provide demodulation information with higher signal-to-noise ratio and stronger robustness.

New capacitively coupled electrical resistance tomography (CCERT) system

This work focuses on the hardware improvement of a CCERT system. An inductor module is developed by the simulated inductor technique. With the inductive reactance of the developed inductor module, the capacitive reactance of the coupling capacitances is eliminated by the impedance elimination principle and the unfavorable influences of the coupling capacitances are overcome. The digital phase-sensitive demodulation technique is introduced to obtain the total impedance of gas–liquid two-phase flow, including the real part, the imaginary part and the amplitude. Finally, a new CCERT system prototype is developed. Impedance measurement experiments and practical image reconstruction experiments are conducted. The research results show that the design of the new CCERT system is successful. The unfavorable influences of the coupling capacitances are effectively overcome and the signal-to-noise ratio of the new system is improved. Compared with the previous CCERT system, the accuracy of the impedance measurement and the quality of image reconstruction of the new system are improved. Meanwhile, the new CCERT system can also obtain the total impedance of gas–liquid two-phase flow.

A Sub-0.1°/h Bias-Instability Split-Mode MEMS Gyroscope With CMOS Readout Circuit

This paper describes a split-mode tuning fork MEMS gyroscope with CMOS readout circuit. The gyroscope achieves 0.008°/ $\surd \text{h}$ angle random walk (ARW) and 0.08°/h bias instability (BI). The noise and phase requirements of the MEMS sensing element and the readout circuit are analyzed, from which the system-level design guidelines are proposed. The MEMS sensing element is optimized to enhance its mechanical sensitivity with reduced quadrature coupling and thermoelastic damping. Front ends with 5.9-fA/ $\surd $ Hz input-referred current noise floor and less than 0.5° phase delay are achieved to reduce the gyroscope’s ARW and thermal drift. A low flicker noise automatic amplitude control circuit and digitized phase-sensitive demodulation are adopted to improve the gyroscope’s BI. After temperature compensation, the temperature coefficients (TCOs) of the scale factor and the zero-rate output are 27 ppm/°C and 1.7°/h/°C from −40 °C to +60 °C, respectively. The overall power consumption is 8.5 mW under a 3.3-V supply.

Amplitude demodulation for electrical capacitance tomography based on singular value decomposition.

Amplitude demodulation is essential in image reconstruction for electrical capacitance tomography (ECT). In this paper, an amplitude demodulation method is proposed based on singular value decomposition (SVD), which can substitute the role of phase-sensitive demodulation in ECT. First, an M × N Hankel matrix is constructed based on a set of discrete samples. Then, SVD operation is performed on the matrix. Finally, the mathematical expression between the sinusoid amplitude and effective singular values is given; i.e., the first two singular values are used to estimate the amplitude information of the acquired signal. The proposed method has the following advantages: (1) since no reference signals are needed, the synchronization between the acquired and reference signals is not necessary; (2) this method can obtain the amplitude information of the acquired signal with a high signal-to-noise ratio (SNR), even in the case of non-integrity period sampling; and (3) SVD itself can also implement the filtering function; thus, no additional low-pass filters are required in the signal conditioning module. The demodulation accuracy and feasibility of the proposed method were verified by numerical simulations and experiments, indicating that it can provide amplitude demodulation with excellent SNR and robust performances.

Singular value decomposition based impulsive noise reduction in multi-frequency phase-sensitive demodulation of electrical impedance tomography.

As an important means in electrical impedance tomography (EIT), multi-frequency phase-sensitive demodulation (PSD) can be viewed as a matched filter for measurement signals and as an optimal linear filter in the case of Gaussian-type noise. However, the additive noise usually possesses impulsive noise characteristics, so it is a challenging task to reduce the impulsive noise in multi-frequency PSD effectively. In this paper, an approach for impulsive noise reduction in multi-frequency PSD of EIT is presented. Instead of linear filters, a singular value decomposition filter is employed as the pre-stage filtering module prior to PSD, which has advantages of zero phase shift, little distortion, and a high signal-to-noise ratio (SNR) in digital signal processing. Simulation and experimental results demonstrated that the proposed method can effectively eliminate the influence of impulsive noise in multi-frequency PSD, and it was capable of achieving a higher SNR and smaller demodulation error.