France



There are many different ways and methods for measuring displacement. The influence of the magnetic material on the inductance of the inductor in its vicinity has been well investigated and used for the realization of various sensors, as well as displacement sensors [1, 2]. However, it has been shown that an improvement in the inductance of the inductor can be achieved if the grooves are realized on the surface of the magnetic film [3], which gives the great potential for the realization of magnetic sensors with better characteristics.&lt;br/&gt;With advances in development of materials in recent years, 3D printing technology allows a very fast fabrication of prototypes. It can be used for development of electronic components, sensors and actuators. It is a very simple, high-quality and precise way to create complex geometric structures using different materials which enable the realization of sensors of different characteristics.&lt;br/&gt;This paper presents a wireless magnetic displacement sensor realized in heterogeneous integration technology. The sensor is realized using additive 3D printing technology and magnetic disc with improved design. The wireless measurement method enables simpler and more precise measurement and data collection compared to the classic wired method.&lt;br/&gt;The exploded 3D model of the sensor is shown in the Fig. 1. The proposed sensor consists of three parts: the inductor, the sensor’s casing with spacer and the ferrite disk with grooves. The inductor windings are turned downwards towards the ferrite.&lt;br/&gt;The inductor is realized in Printed Circuit Board Technology, in the form of a spiral with an outer diameter of 25 mm and 22 turns (the width of the conducting lines is 500 μm and the conductor spacing is 730 μm).&lt;br/&gt;Using the Mn&lt;sub&gt;0.5&lt;/sub&gt;Zn&lt;sub&gt;0.5&lt;/sub&gt;Fe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;4&lt;/sub&gt; powder, the ferrite disc with grooves is pressed and sintered at a temperature of 1275 °C for 2 hours in a chamber furnace. The ferrite disc has a diameter of 25 mm. It has three concentric rings and a circle in the center on its surface.&lt;br/&gt;The part of the sensor that allows the sensor to be sensitive to displacement is the spacer. The spacer is printed using a 3D technology. It was made of Ninjaflex, one of the leading flexible 3D filaments. It is in the shape of the ring with the thickness of 500 µm.&lt;br/&gt;Using a Polylactic acid (PLA) filament, the sensor’s housing is 3D printed in which the sensor parts are connected and fixed. The applicator of displacement that acts on the surface of the sensor is also 3D printed.&lt;br/&gt;Displacement measurement is performed wirelessly using an impedance analyzer HP4194A. A coil (antenna) is placed around the sensor and the impedance and the phase of the antenna-sensor system are measured, from which the resonant frequency is determined. The displacement operation on the sensor is performed using a manual translation stage which enables the precise movement of the sensor surface in the steps of 50 μm. The characteristic of the antenna-sensor is shown in the Fig. 2. During the action of the displacement, the spacer is compressed and the ferrite approaches the inductor, which causes an increase in inductance, i.e. a decrease in the resonant frequency of the antenna-sensor system.

**References:**

1. M. Kisic, N. Blaz, Lj. Zivanov and M. Damnjanovic, AIP Advances, Vol. 10, paper no. 015017, p. 1-4 (2020)&lt;br/&gt;2. M. G. Kisic, N. V. Blaz, Lj. D. Zivanov and M. S. Damnjanovic, IEEE Transactions on Magnetics&lt;i&gt;,&lt;/i&gt; Vol. 53, no. 11, Art no. 4004104, p. 1-4 (2017)&lt;br/&gt;3. X. Zhou, Y. Wen, Y. Mu and P. Li, 64th Annual Conference on Magnetism and Magnetic Materials, MMM2019, November 4-8. 2019, Las Vegas, Nevada, Book of abstracts, paper no. DV-05, p. 437-438&lt;br/&gt;4. Available online at: https://ninjatek.com/ninjaflex/, accessed 05.01.2021.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/eb2563e4c8b8f330d15ac98f997429ff.jpg)
Fig.1. The exploded 3D view of the sensor.

![](https://assets.underline.io/uploads/markdown_image/1/image/4dd0398f6f53d10c2624bcdc7dd3ddf0.jpg)
Fig. 2. The dependence of the resonant frequency on the displacement.

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 Heterogonous Integrated Displacement Sensor with Grooved Ferrite

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There are many different ways and methods for measuring displacement. The influence of the magnetic material on the inductance of the inductor in its vicinity has been well investigated and used for the realization of various sensors, as well as displacement sensors [1, 2]. However, it has been shown that an improvement in the inductance of the inductor can be achieved if the grooves are realized on the surface of the magnetic film [3], which gives the great potential for the realization of magnetic sensors with better characteristics. With advances in development of materials in recent years, 3D printing technology allows a very fast fabrication of prototypes. It can be used for development of electronic components, sensors and actuators. It is a very simple, high-quality and precise way to create complex geometric structures using different materials which enable the realization of sensors of different characteristics. This paper presents a wireless magnetic displacement sensor realized in heterogeneous integration technology. The sensor is realized using additive 3D printing technology and magnetic disc with improved design. The wireless measurement method enables simpler and more precise measurement and data collection compared to the classic wired method. The exploded 3D model of the sensor is shown in the Fig. 1. The proposed sensor consists of three parts: the inductor, the sensor’s casing with spacer and the ferrite disk with grooves. The inductor windings are turned downwards towards the ferrite. The inductor is realized in Printed Circuit Board Technology, in the form of a spiral with an outer diameter of 25 mm and 22 turns (the width of the conducting lines is 500 μm and the conductor spacing is 730 μm). Using the Mn0.5Zn0.5Fe2O4 powder, the ferrite disc with grooves is pressed and sintered at a temperature of 1275 °C for 2 hours in a chamber furnace. The ferrite disc has a diameter of 25 mm. It has three concentric rings and a circle in the center on its surface. The part of the sensor that allows the sensor to be sensitive to displacement is the spacer. The spacer is printed using a 3D technology. It was made of Ninjaflex, one of the leading flexible 3D filaments. It is in the shape of the ring with the thickness of 500 µm. Using a Polylactic acid (PLA) filament, the sensor’s housing is 3D printed in which the sensor parts are connected and fixed. The applicator of displacement that acts on the surface of the sensor is also 3D printed. Displacement measurement is performed wirelessly using an impedance analyzer HP4194A. A coil (antenna) is placed around the sensor and the impedance and the phase of the antenna-sensor system are measured, from which the resonant frequency is determined. The displacement operation on the sensor is performed using a manual translation stage which enables the precise movement of the sensor surface in the steps of 50 μm. The characteristic of the antenna-sensor is shown in the Fig. 2. During the action of the displacement, the spacer is compressed and the ferrite approaches the inductor, which causes an increase in inductance, i.e. a decrease in the resonant frequency of the antenna-sensor system.

**References:**

1. M. Kisic, N. Blaz, Lj. Zivanov and M. Damnjanovic, AIP Advances, Vol. 10, paper no. 015017, p. 1-4 (2020) 2. M. G. Kisic, N. V. Blaz, Lj. D. Zivanov and M. S. Damnjanovic, IEEE Transactions on Magnetics, Vol. 53, no. 11, Art no. 4004104, p. 1-4 (2017) 3. X. Zhou, Y. Wen, Y. Mu and P. Li, 64th Annual Conference on Magnetism and Magnetic Materials, MMM2019, November 4-8. 2019, Las Vegas, Nevada, Book of abstracts, paper no. DV-05, p. 437-438 4. Available online at: https://ninjatek.com/ninjaflex/, accessed 05.01.2021.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/eb2563e4c8b8f330d15ac98f997429ff.jpg)
Fig.1. The exploded 3D view of the sensor.

![](https://assets.underline.io/uploads/markdown_image/1/image/4dd0398f6f53d10c2624bcdc7dd3ddf0.jpg)
Fig. 2. The dependence of the resonant frequency on the displacement.

poster

1. Introduction With the increasing penetration of power electronic devices, wide-bandwidth oscillation events are frequently reported in recent years [1]. To meet the demand of analyzing wide-bandwidth oscillation without prior knowledge of detailed parameters of the concerned system, the impedance-based stability method [2] is now a widely used technique. However, the accuracy of the impedance-based stability method heavily relies on the precise measurement of the impedance of the concerned system, which is determined by following three critical factors. 1) Response Signal Sensing: The limited bandwidth of sensor can jeopardize the accuracy of impedance measurement over a wide bandwidth. In [3], shunt resistor is used to measure the current response from 1 Hz to 1 kHz. The drawback of shunt resistor is that the resistance shifts with ambient temperature, frequencies and rated current. Besides, the Hall-effect current transducers can be used to obtain the current response. However, the narrow bandwidth of Hall-effect current transducers makes them not suitable for wide bandwidth impedance measurement [4]. 2) Perturbation Injection: Most existing work sets the current or voltage injection as 10% of rated value to obtain a good signal-to-noise ratio [5]. However, for certain concerned systems, especially under weak grid, even 10% disturbance can make the system deviates from the equilibrium point and interferes with the normal operation of the system. Besides, it is also costly and challenging to design an injection source with high injection capacity and broadband injection at the same time in high-power application. 3) Response Components Extraction: Another inevitable problem is the inaccurate response components extraction due to the spectral leakages of FFT-based algorithm. A Hanning window in [6] is applied to improve the accuracy of measured impedance by solve the spectral leakages in Fourier analysis. However, the impedance measurement results vary significantly with the selection and design of window function. To overcome these limitations, this paper proposes a wide bandwidth impedance measurement technique with a small perturbation injection based on magnetic sensing and Prony-FFT extraction algorithm. Firstly, a low-cost tunnel magnetoresistance (TMR) sensor is applied to measure the desired impedance result over a wide bandwidth. Besides, the high sensitivity of TMR sensor enables the impedance measurement with small perturbation injection. Finally, to extract the magnitude and phase of the response component precisely from the sensing response signal, an improved algorithm based on Prony-FFT is developed to avoid the spectral leakages and lighten the computation burden in high frequency band. Hence, the proposed measurement technique can potentially be an effective tool in modern power system because of its wide bandwidth, high sensitivity, light computation burden. 2. Experiments For a selected frequency band of interest, the impedance of a RL circuit was measured experimentally by proposed impedance measurement technique. The result was compared with the one measured with a commercial AC current clamp (i400s, FLUKE). Meanwhile, the reference impedance value of the RL was obtained by a vector network analyzer (VNA, E5061B, Keysight). A programmable AC power source (61704, Chroma) was used to inject a wide-bandwidth perturbation into the RL circuit as shown in Fig. 1. Thirty injection frequencies were spaced between 10 Hz to 2 kHz. Then, the voltage of the RL was measured by a differential voltage probe (A042, PICO). Meanwhile, a TMR sensor (TMR2305M, MultiDimension Technology) with high sensitivity of 25 mV/V/Oe was selected to measure the input current of the RL circuit. The output of TMR sensor was amplified by a differential amplifier (AD620). The frequency response of TMR sensor with amplifier was investigated as shown in Fig. 2(a). The gain deviation of the TMR sensor was within 0.2 dB over the bandwidth whereas the variation of phase was within 3 degree. Thus, the TMR sensor could enable wideband impedance measurement with constant gain and negligible phase shift. Then, the impedance measurement results with 10% injection magnitude based on the proposed technique and AC current clamp were compared in Fig. 2(b). Compared with the impedance measured by the VNA, the average magnitude deviation measured by the TMR sensor was 0.9 Ω whereas that measured by the AC current clamp was 1.6 Ω. Besides, the phase deviation of impedance based on TMR sensor was within 2 degree, while the maximum phase deviation of the result measured by the AC current clamp reached 8 degree over the wide frequency band of measured. Furthermore, the impedance measurement with 3% injection magnitude based on proposed technique was compared with the 10% injection magnitude based on AC current clamp in Fig. 2(c). The measured result with 3% injection magnitude based on TMR sensor had maximum phase deviation of 3 degree, which was still smaller than the result measured by the AC current clamp with 10% injection magnitude. 3. Results and Discussion Compared with the impedance measured by the AC current clamp, the proposed impedance measurement technique based on TMR sensor achieved higher accuracy in magnitude and less phase shift over a wide bandwidth. Meanwhile, the proposed technique can measure the impedance under smaller injection magnitude without sacrificing the measurement accuracy. In the full paper, the details of the impedance extraction algorithm based on Prony-FFT and more experimental results will be presented.

**References:**

[1] M. Amin, M. Molinas, and L. Jing, "Oscillatory phenomena between wind farms and HVDC systems: The impact of control," IEEE, 2015, pp. 1-8. [2] S. Jian, “Impedance-Based Stability Criterion for Grid-Connected Inverters,” TPEL, vol. 26, no. 11, pp. 3075-3078, 2011. [3] D. A. Howey, P. D. Mitcheson, V. Yufit, G. J. Offer, and N. P. Brandon, “Online Measurement of Battery Impedance Using Motor Controller Excitation,” TVT, vol. 63, no. 6, pp. 2557-2566, 2014. [4] A. Patel, and M. Ferdowsi, “Current Sensing for Automotive Electronics-A Survey,” TVT, vol. 58, no. 8, pp. 4108-4119, 2009. [5] T. Roinila, M. Vilkko, and S. Jian, “Online Grid Impedance Measurement Using Discrete-Interval Binary Sequence Injection,” JESTPE, vol. 2, no. 4, pp. 985-993, 2014. [6] C. Xin, Z. Yang, W. Shanshan, C. Jie, and G. Chunying, “Impedance-Phased Dynamic Control Method for Grid-Connected Inverters in a Weak Grid,” TPEL, vol. 32, no. 1, pp. 274-283, 2017.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dd1018161f3d683c061223415b4b4bd0.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/99bcc99e9e6d954a79fbfad5ce62f54f.jpg)

 A wide-bandwidth impedance measurement technique with small perturbation injection based on magnetic sensing

Pipelines have played an essential role in transporting basic energy sources such as oil, natural gas and hydrogen. In recent years, non-destructive testing (NDT) technology for the structural integrity of various pipes has increased their demands due to the increase and deterioration of the energy resource network. There are various types of NDT methods, and magnetic flux leakage (MFL) and eddy current testing (ECT) technologies are most widely used for evaluating the integrity of pipelines, steam generator tube and aircraft components [1], [2]. Both MFL and ECT have inherent several weaknesses from their operation principle. A defect signals by MFL inspection have an ambiguity in distinguishing between defects in the inner surface and outer surface. ECT inspection must consider the effect of skin effect, thus the driving frequency is strictly limited by material and thickness of specimen. Consequently, each limit greatly affects the inspection performance and speed, so that this makes the bottleneck for the precise and versatile evaluation. In order to overcome constraints of conventional MFL and ECT, many research and development have been conducted by combining MFL and ECT into a single sensor [3]. This method inspects the ferromagnetic steel by applying DC biased magnetic field to the steel and measuring the outer surface or subsurface of steel wall with an ECT sensor. If the DC magnetic flux is distorted due to the existence of the defect, the magnetic permeability changes based on the nonlinear and hysteretic characteristics of the ferromagnetic material. Then, the defect signal can be measured as the perturbation of the permeability. Consequently, the skin effect no longer limits to the measurement of specific defects at the given frequency. Compared to other NDT methods, DC-biasing ECT is relatively recently introduced so that detailed descriptions of methodologies for the design and analysis are still short including optimal operating conditions, and signal analysis. To estimate the operating performance of DC-biasing ECT, both static magnetic field by permanent magnet or electromagnet, and time-harmonic magnetic field must be considered simultaneously. The finite element method (FEM) can compute the problem accurately, but the fine discretization of near surface, which requires high computational resources and time. The driving conditions are different depending on the application environment of the sensor, and a design is required for this, which causes a large time and cost aspect for development. In this paper, a semi-analytical method using finite element method for static magnetic field computation and analytical method for eddy current problem is suggested. The time consumption for determining the operating condition of DC-biasing ECT sensor can be greatly reduced by using the suggested approach. Fig. 1 illustrates the traditional method and proposed method to evaluate the performance of DC- biasing ECT. Both methods requires the calculation of static magnetic field by permanent magnet (PM) or electromagnet (EM), and the subsequent calculation of time-harmonic magnetic field by sensor coil. The ferromagnetic specimen includes both nonlinear and hysteretic characteristics, but this study would not consider the effect of magnetic hysteresis, which will be dealt in a future research. The magnetic flux density in each element is calculated by inputting the magnetization curve of the specimen, and the permeability determined by the magnetic flux density is stored for time-harmonic field problem. Since the amplitude of time-varying magnetic field by sensor coil is very small compared to the magnitude of static magnetic field, the permeability can be considered as the derivatives of the magnetization curve at the operating point of static field. Computation of high frequency magnetic field by using FEM requires very large number of discretization due to severe skin effect near surface of sensor coil. The performance of DC-biasing ECT sensor depends on many parameters such as static field and, frequency and the material of specimen. Thus, the computational time and cost should be reduced for the efficient sensor design. In this study, analytical method is used as an alternative to the calculation of time-harmonic field problem. The transformer model is formulated in analogy with the interaction between the sensor coil and eddy currents. Then, the different permeability distribution on the specimen is transformed in to a homogenized plane to reduce computational complexity. The detailed formulation of the transformer model and homogenization will be included in the full manuscript. Fig. 2(a) shows the schematic diagram of DC-biasing ECT. The electromagnet was used to control DC magnetic field and reflection probe constructed with coaxial driving coil and sensing coil. The impedance response is calculated and results are shown in Fig. 2(b). The number of turns of electromagnet is 400 and exciting current is 3.5A. The calculated values of both normal and defective specimen are compared, and measurement setup and result will be dealt to complement the correspondence with the prototype. When the frequency increases, the normalized value of imaginary part of sensing voltage decreases while the real part of voltage increases. The proposed method can estimate the response of the sensor throughout the wide frequency range.

**References:**

[1] J. Wu et al, IEEE Transactions on Magnetics, vol. 54, pp. 1-8 (2018) [2] Y. Xu, Y. Yang and Y. Wu, IEEE Sensors Journal, vol. 20, pp. 10502-10510 (2020) [3] J. Wu, J. Zhu, H. Xia, C. Liu, IEEE Transactions on Industrial Informatics, vol. 15, pp. 6252-6259 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/45a7b2687e110c66e5844a4cacd37a36.jpg)
Fig. 1. Comparison of calculation scheme between traditional and proposed method

![](https://assets.underline.io/uploads/markdown_image/1/image/a85ded0cae883d868e1252099f9dc2a5.jpg)
Fig. 2. (a) Schematic diagram of DC-biasing ECT and (b) comparison of two calculated results

 Semi-Analytical Modeling of High Frequency Eddy Current Sensor in Ferromagnetic Steel with DC Bias

Fluxgate sensors are among the most sensitive devices for the detection of weak magnetic fields (in the range of 10-6 T) with resolutions of 100 pT at room temperature [1]. In conventional configuration, a fluxgate magnetometer consists of two ferromagnetic cores around which two coils for excitation and two coils for detection are wound and differentially connected. The residence times difference (RTD) fluxgate sensor first proposed by Bruno Andò, et al [1] consist of a single soft ferromagnetic core and two coils (one for excitation and one for detection). The sensor detects the external magnetic field strength through its corresponding relationship with the residence times difference of the induced peeks that appear when the excitation field cycles the magnetization of the core. One of the materials showing potential for the development of RTD sensors is represented by the glass-coated microwires exhibiting large Barkhausen effect, i.e., magnetization switching in a single step when the external excitation field is reversed. Recently, a new method to switch the axial magnetization in bistable glass-coated microwires has been reported [2, 3]. The method, detailed in [2], consists in applying a current directly through a magnetic sample subjected to controlled torsion. Using this method as a basis, we report here the development of a new RTD magnetic sensor that does not require an excitation coil. The sensor electronics was built using a dsPIC microcontroller which generates the signal for sensor excitation and measures the time difference between induced peaks (Fig.1). The time resolution of the electronics is about 1/(384x106) s. The sensor performance was studied comparatively using as sensitive elements glass-coated microwires with nominal compositions of the magnetic core Fe77.5Si7.5B15, Co68.18Fe4.32Si12.5B15 and Fe73.5Si13.5B9Cu1Nb3 (FINEMET), having metallic core diameters (Φmetal) of 10, 20 and 30 mm, respectively, and 7 mm glass coating thickness. The transfer functions (time difference versus applied field) were measured for different configuration of the sensor excitation current and torsion values. The value of the sensor sensitivity (S) decreases, and the dynamic range (DR) increases when the excitation current amplitude (I) increases. For annealed Co68.18Fe4.32Si12.5B15 microwires, having a metallic core diameter of 20 μm, we obtained a sensitivity value of 84 μs/(A/m), with a dynamic range of 17 A/m, for an excitation current amplitude of 10 mA. For an excitation current with an amplitude of 40 mA we obtained a sensitivity value of 11.7 μs /(A/m) and a dynamic range of 180 A/m. For current amplitudes of 50 mA and above, the dynamic range decreases due to the fact that the induced peaks become poorly defined, with low amplitudes, and cannot be easily distinguished by the electronic detection system. The annealed Co68.18Fe4.32Si12.5B15 microwires show wider measuring range and higher linearity of the transfer function as compared to all the other analyzed compositions (DR = ± 130 A/m for Φmetal = 20 μm and I=30 mA). The Fe77.5Si7.5B15 microwires show a fairly high noise on the measured transfer graph and lower dynamic range as compared to the Co68.18Fe4.32Si12.5B15 microwires (DR = ± 32 A/m for Φmetal = 20 μm and I=30 mA). The annealed Fe73.5Si13.5B9Cu1Nb3 wires show an extremely low linear variation transfer function (± 9 A/m for Φmetal = 20 μm and I=30 mA) as compared to the other compositions analyzed. For annealed Co68.18Fe4.32Si12.5B15 microwires with different core diameters, we observed that for the same excitation current of 30 mA and the same torsion of 483 Rad/m, the sensitivity of the sensor decreases from 27.7 μs/(A/m) for wires with a diameter of 10 μm, to 12.7 μs/(A/m) for wires having 30 μm in diameter, the dynamic range increasing at the same time from 41 A/m for wires with 10 μm in diameter, to 200 A/m for the samples with 30 μm in diameter (Fig 2). This behavior follows the evolution of the switching field of the same samples, which decreases from 45 A/m for wires with a diameter of 10 μm to 21 A/m for wires with a diameter of 30 μm. The influence of torsion on the transfer function of the sensor is relatively low. Thus, for Co68.18Fe4.32Si12.5B15 wires with a diameter of 30 μm we obtained a sensitivity of 12 μs/(A/m) for a torsion of 120 Rad/m (one end rotation of 450 on a wire with a length of 6.5 mm) and 12.7 μs/(A/m) for 483 Rad/m (one end rotation 1800 on a wire with a length of 6.5 mm). For higher torsion values, a sharp decrease in field sensitivity is observed, most likely due to the strong increase of the mechanical stresses induced in the wire. Work supported by the Nucleu Programme (Project PN 19 28 01 01) and Contract No. 11PFE/16.10.2018 financed by the Romanian Ministry of Education and Research.

**References:**

1. B. Andò, S. Baglio, A.R. Bulsara et al., IEEE Instrum Meas Mag, Vol.8(4), 2005 2. S. Corodeanu, H. Chiriac, A. Damian et al., Scientific Reports, Vol. 9, No. 5868, 2019. 3. V. Zhukova, J. M. Blanco, A. Chizhik et al., AIP Adv. 7, 056026, 2017.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bfb14137e3ddfb99b934821adb3b5624.jpg)
Fig. 1. Schematic representation (a) and picture (b) of the RTD fluxgate sensor and the typical output voltage for a sinusoidal excitation signal (c).

![](https://assets.underline.io/uploads/markdown_image/1/image/232054e41dfbb608104ce6b41997f805.jpg)
Fig. 2. The transfer graph obtained for Co68.18Fe4.32Si12.5B15 microwires, annealed at 3000C-1h, having different diameters of the metallic core.

 RTD fluxgate sensors based on current induced magnetization reversal in twisted glass-coated microwires

I. Introduction To achieve a higher power density of power electronic modules, the switching frequency of the power electronic devices is increasing significantly. Especially, the next-generation power electronic devices utilizing wide-bandgap semiconductor materials such as SiC and GaN which can realize the switching frequency in megahertz [1]. The current sensing is essential for the control purpose, condition monitoring, protection, and power management in power electronic modules. Although the shunt resistor can be used to measure the current, it is non-isolated and the parasitic impedance introduced may incur extra power losses and jeopardize the reliability of power electronic modules [2]. The Hall-effect current transducers are extensively exploited for current measurement in power electronic modules. Nevertheless, they are inapplicable in high-bandwidth current sensing due to the limited bandwidth of typically less than 200 kHz [3]. Since the magnetic sensor such as magnetoresistive (MR) sensor can measure current up to several megahertz non-invasively [4], there are researches on using the MR sensors for current measurement in power electronics [5-8]. Due to the skin effect, the high-bandwidth current tends to be distributed on the surface of a conductor and the skin depth decreases with the frequency. Thus, the main challenge is that the magnetic field of current varies with frequency causing the nonlinearity of MR sensors. It was studied that the frequency response can be improved by placing a copper sheet around the MR sensor [5]. Although the planar copper concentrator can concentrate the magnetic field [6], the magnetic flux density (B) still varies with the frequency. The copper foil is used to wrap the MR sensor to achieve a unity normalized gain until 83.3 kHz, but the gain increases for higher frequency [7]. Besides, the field summing and decoupling methods are adopted to reduce the phase shift and extend the bandwidth to 1 MHz with an error of 5 % by using two MR sensors [8]. Therefore, the technique for a single magnetic sensor to measure a high-bandwidth current is still lacking. In this paper, a technique using a specially designed wire loop and differential amplifier based calibration circuit is developed for the magnetic sensor to measure high-bandwidth current. The skin effect of rectangular wire on the printed circuit board (PCB) is analyzed mathematically. The effects of concentrators in various structures on B are investigated based on simulation results. The effectiveness of the proposed wire loop on concentrating magnetic field of current up to 10 MHz is evaluated. The experimental results verify that the proposed technique using the wire loop and differential amplifier based calibration circuit can sense the high-bandwidth current in high accuracy. II. Analysis of High-Bandwidth Current Sensing Technique Generally, the PCB trace of a power electronic module is rectangular as shown in Fig. 1 (a). Considering a 1 oz copper trace in a width of 2.54 mm, the height is 35 μm which is much less than the width. Thus, magnetic vector potential (A) of the position (x, y) can be calculated by [9] A=Iμo/8πw{(w+x)log[(w+x)2+y2]+(w-x)log[(w-x)2+y2]+2y[tan-1(w+x)/y+tan-1(w-x)/y]-4w} where 2w and 2h are the width and height of the PCB wire respectively, μo is the vacuum permeability. When the trace is carrying a high-bandwidth current, the skin effect should be considered. The skin depth can be calculated by δ=√(2ρ/ωμo) where δ is the skin depth, ρ is the electrical resistivity of copper, ω is the angular frequency. The skin depth decreases with the frequency. This affects the A and thus the B since B = ▽×A. As shown in Fig. 1 (b) and (c), the magnetic sensor is located on the top layer of the PCB and the trace with a current of 1 A is on the bottom layer, the average B of the magnetic sensor located region (Bavg) decreases from 0.0746 mT to 0.0725 mT when the frequency increases from 1 kHz to 1 MHz. A copper sheet of 25.4 μm can be used to concentrate the Bavg to 0.141 mT at 1 MHz as shown in Fig. 1 (d). However, in this case, the Bavg increases with the frequency. The problem that Bavg varies with frequency still exists. A wire loop is designed to reduce the variation of Bavg with frequency as shown in Fig. 2 (a). The bottom-layer current passes through a rectangular wire with a cross-section of 0.2 mm × 0.2 mm located 0.35 mm above the magnetic sensor and then passes to the top layer. In this way, the Bavg is 0.242 mT when the frequency is 1 kHz and 100 kHz as shown in Fig. 2 (b) and (c). It only decreases by 0.826 % to 0.240 mT at 10 MHz. Thus, a stable B can be achieved by this method, and thus current can be sensed accurately by the magnetic sensor despite the high frequency. In the full paper, the influence of skin effect on high-bandwidth current sensing will be analyzed. The effects of concentrators in various structures on B will be investigated and presented. The principle of the proposed wire loop and differential amplifier based calibration circuit will be elaborated. The effectiveness of the proposed technique for high-bandwidth current sensing will be verified and evaluated experimentally.

**References:**

[1] E. Santi, K. Peng, and H. A. Mantooth, IEEE Transactions on Electron Devices., Vol. 62, pp. 434-442 (2015). [2] S. Ziegler, R. C. Woodward, and H. H.-C. Iu, IEEE Sensors Journal., Vol. 9, pp. 354-376 (2009). [3] A. Patel and M. Ferdowsi, IEEE Transactions on Vehicular Technology., Vol. 58, pp. 4108-4119 (2009). [4] J. Lenz and S. Edelstein, IEEE Sensors Journal., Vol. 6, pp. 631-649 (2006). [5] P. E. Schneider, M. Horio, and R. D. Lorenz, IEEE Transactions on Industry Applications., Vol. 48, pp. 1432-1439 (2012). [6] S. J. Nibir and B. Parkhideh, IEEE Transactions on Industrial Electronics., Vol. 65, pp. 2766-2774 (2018). [7] S. Shao, N. Yu, and X. Xu, IEEE Transactions on Power Electronics., Vol. 35, pp. 10930-10944 (2020). [8] M. Sheng, M. H. Alvi, and R. D. Lorenz, IEEE Journal of Emerging and Selected Topics in Power Electronics., (2020). [9] K. J. Binns and P. J. Lawrenson, Analysis and Computation of Electric and Magnetic Field Problems. Elsevier (2013).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ed98288a51e289100f50bc2581a3c0e8.jpg)
Fig. 1. PCB trace. (a) Cross-section. Magnetic flux at (b) 1 kHz, (c) 1 MHz, and (d) 1MHz with a copper concentrator.

![](https://assets.underline.io/uploads/markdown_image/1/image/30af824e42f7b3345abdd284eed45dd0.jpg)
Fig. 2. Wire loop. (a) Layout. Magnetic flux at (b) 1 kHz, (c) 100 kHz, and (d) 10 MHz.

 High-Bandwidth Current Sensing Technique Based on Magnetic-Field Sensing Using a Wire Loop and a Differential Amplifier Calibration Circuit

In recent years, magnetoelectric (ME) composites consisting of magnetostrictive and piezoelectric phases mechanically coupled to each other have received widely attention due to the tremendous potential applications for functional devices such as magnetic sensors, phase shifters, transformers or gyrators, current sensors and energy harvesters. In the field of magnetic sensors, the ME magnetic sensors are composed of ME composites that show many excellent advantages, such as low cost, high sensor performances (sensitivity, linearity, resolution), small volume perfect and simplified electronic circuits [1]. These advantages offer the potential of ME magnetic sensor to be a new generation of magnetic sensors. There are enormous investigations activities in recent years on ME magnetic sensor. Previous research shows that ME magnetic sensor exhibit high AC/DC magnetic sensor performances at room temperature under resonance conditions [2]. Additionally, the ME magnetic field sensors have been drawn significant interests for numerous applications, such as bio-magnetism detecting apparatuses, earth magnetic field detection, non-destructive material testing, and aerospace instruments[3]. However, these ME magnetic sensor need to be strictly parallel to the magnetic field when measuring the magnetic field due to the ME laminates of configurations of square, or rectangular geometries have high anisotropy, otherwise will cause enormous deviation and affect the stability of ME magnetic sensors. It is thus desirable to develop ME magnetic sensor with ultra-lower anisotropy, along with high sensor performances. In this study, a toroidal ME magnetic sensor in composite of strictly concentric ferrites/piezoelectric rings with toroidal solenoid wound around was fabricated and developed. Compared with the previously reported ME magnetic sensor of configurations of square, or rectangular geometries, the toroidal ME magnetic sensor has ultra-lower shape-induced anisotropy, high stability and high sensor performances, which voltage output is almost unaffected by the angle between the ME magnetic sensor and the magnetic field. These excellent stability and sensor performances characteristics offer unique possibilities for possible use of ME magnetic sensor.

**References:**

[1] J. Zhai, Z. Xing, S. Dong, Appl. Phys. Lett. Vol. 88, p.062510 (2006). [2] H. Xi, M. Lu, Q. Yang, Sensor Actuat A-Phys. Vol. 311, p.112064 (2020). [3] J. Gao, L. Shen, Y. Wang, J. Appl. Phys. Vol. 109, p.074507 (2011).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ec5e0db2329771e70db9c72da54c82bb.jpg)
Fig.1. Schematic diagram of the presented magnetic field sensor.

![](https://assets.underline.io/uploads/markdown_image/1/image/c6f133ff964c062f2b382cef753f9eca.jpg)
Fig.2. The effect of DC magnetic field angle on the ME output voltage measured for toroidal ME sensor. The inset indicates the direction of the DC magnetic fields in a top view

 Ultra-lower anisotropy magnetic field sensor in ferrite/piezoelectric toroidal magnetoelectric composites

1. Background and problem considered Metal tube and wire are used in variety parts of infrastructures. Defects like holes and cracks in the products can cause serious accidents. They are inspected in manufacturing processes by using Non-Destructive Techniques (NDTs). The inspection speed and sensitivity are important because the tube and wire are long. The Eddy Current Testing (ECT) is one of NDTs and widely used in the processes. The ECT is better than the ultrasonic testing, the X-ray testing and other NDTs on the speed and sensitivity. However tube and wire manufacturers need faster inspection speed and better inspection sensitivity, because the speed is closely related to the production speed. The speed is determined by the vibration of the inspection sample caused by the transport of the sample. The vibration has an impact on detection signals of the ECT [1]. In previous studies, signals caused by vibration are removed from the detection signal by suppressing the vibration of the transport device, and/or signal processing [2-4]. We propose a new ECT probe to suppress the vibration component in the detection signal. The novelty of the proposed probe is that it has two outer coils for electromagnetically suppressing the vibration components outside of the two inner coils for flaw detection. The principle that the proposed method reduces the detection signal due to the vibration is explained. 2. Vibration Signal Suppression Probe The proposed probe has four coils and is used with a variable amplifier and a phase shifter which is known as an all-pass filter. It is possible that effect of the vibration in the detection signal can be equal to zero by using the variable amplifier and phase shifter which adjust the amplitude and the phase of the excitation current flowing through the outer coil. Fig. 1 shows the structure of the probe with four coils. L2 and L3 are defined as the inner coils. L1 and L4 are defined as the outer coils. The inside coils form a self-induced differential sensor. The outer and inner coils form a mutually induced differential sensor with the outer coil as excitation and the inner coil as detection. The detection signals of the sensors due to the displacement of the rod is defined as the displacement signal. The displacement signal of the probe is equal to the total output of the self-induced and mutual-induced sensors. We simplify discussion by limiting static displacement. The displacement is defined the offset between axes of the rod and coils and rotation of the rod. As shown in Fig. 1, axis of the rod has the offset from axis of coils to the radius direction. The rod rotates around a point on the plane containing the axes of the rod and coil. To demonstrate the effectiveness of the method, the displacement signals of the ECT were simulated by the 3D finite element method. In the simulation, excitation current was 10 mA at 16 kHz, a brass rod with a conductivity of 1.26×107 S/m was used, and dCoils was 6 mm. Simulated detection signals are shown in Fig. 2. The detection signal of the ECT is obtained as a point on the complex plane. The horizontal and vertical axes of the plane represent in-phase and quadrature components of the signals for the excitation current. The solid and dotted lines in Fig. 2 show simulated results of displacement signals when the inner or outer coils are used as the excitation coils. The lines show the displacement signals generated when the balance of the electromotive force was lost due to the displacement. The phases of the displacement signals were constant. The amplitudes of the displacement signals were proportional to the rod of offset and rotation. The dash dot line shows that displacement signal with the amplitude and phase of the outer excitation signal adjusted using a variable amplifier and phase shifter. The amplitude and phase were adjusted so that it is equal to the inverted phase of the inner excitation signal and the amplitude of the inner excitation signal. The displacement signals cancel each other when inner and outer coils are used as excitation coil at the same time. In this case, the gain of the amplifier was 4.59 and the phase of the phase shifter was -44.8 degrees. The detail of the experimental method and results will be presented in our presentation.

**References:**

[1] C. Reboud, D. Prémel, G. Pichenot, and D. Lesselier, International Journal of Applied Electromagnetics and Mechanics, Vol. 25, No. 1-4, pp. 313-317(2007) [2] Cheng-Chi Tai, James H. Rose, and John C. Moulder, In Review of Progress in Quantitative Nondestructive Evaluation, pp. 1593-1600(1997). [3] L. Janousek, Z. Chen, N. Yusa, and K. Miya, NDT & E International, Vol. 38, No. 6, pp. 508-515(2005) [4] W. Yin, and A. J. Peyton, NDT & E International, Vol. 40, No. 1, pp. 43-48(2007)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/374558b7ee841ebcdba2ff4816bbbf11.jpg)
Fig. 1. Structure of the vibration suppression probe. The inside coils, L2 and L3, form a self-induced differential sensor. The outer, L1 and L4, and inner coils form a mutually induced differential sensor with the outer coil as excitation and the inner coil as detection.

![](https://assets.underline.io/uploads/markdown_image/1/image/256978b252c8d9537c973c2b60778bbb.jpg)
Fig. 2. Simulated displacement signals. The solid line is the signal with the inner excitation. The dot line is the signal with the outer excitation. The dash dot line is the signal adjusted from the outer excitation signal. The total signal of inner and adjusted outer signals is equal to zero.

 New Eddy Current Probe for Vibration Signal Suppression

Many ferromagnetic substances are naturally magnetized under the influence of the geomagnetic field, and information about the corresponding objects can be obtained based on the analysis of monitoring the magnetic fields generated around magnetic targets. The detection and tracking of magnetic targets is the current research hotspot, and the target monitoring based on magnetic signals as well as widely used in various fields. Currently, the magnetic target localization method is commonly used to obtain the relative position of the target by inversion of the magnetic field gradient tensor matrix. However, this method has a detection blind spot, and even if the final results are corrected by mean filtering, there is still a certain amount of error. Therefore, the correction of the localization results needs to be based on the information of the magnetic field gradient matrix collected at the detection point. This paper uses the magnetic field gradient tensor target localization algorithm as the basis of single-point localization, analyzes its error in detection, and proposes a weighted route fitting method based on magnetic field gradient matrix information for the characteristics of route calculation which is vulnerable to great errors. After simulation experiments, the method can reduce the fluctuation of detection results to a certain extent, and can effectively propose the influence of the extreme error generated by the detection blind area on the positioning results. To investigate the sources of error in target localization, we designed a series of experiments for the magnetic field gradient matrix-based localization method. The location of the detection blind zone is verified by changing the relative position of the magnetic target to the detection point. When the position vector is perpendicular to the magnetic moment vector, the error rate increases significantly. The experimental results are consistent with the theoretical formula, and the higher the accuracy of the magnetic sensor, the smaller its detection blind zone. When the detection point out is in the detection blind area, its magnetic field gradient matrix is a non-full-rank matrix, so the accuracy of target detection is often inversely proportional to the dispersion of its matrix eigenvalues. Therefore, by introducing a weighted fitting method based on the gradient matrix, the detection error can be reduced to a certain extent and the interference caused by abnormal data can be eliminated. Experiments are designed to verify the feasibility of the method. The schematic diagram of the positioning detection experiment is shown in Figure 1 below, where ABCED represents the location of different detection points, and the oval dashed line is its detection range. The magnetic target is set to come out from the coordinates (-0.5m,0m) and advance along a straight line to (0.5m,0m), and the comparison of its route monitoring results is shown in Figure 2 below. Based on the results, it can be concluded that the error-corrected route is closer to the set simulation route.

**References:**

Zhao G, Han Q, Tong X, et al. Adaptive filtering method for magnetic anomaly detection[J]. Journal of Applied Remote Sensing, 2018, 12(2):1-10. Kim K Y, Jeong E, Kim S, et al. Magnetic Anomaly Detection Using Continuous Angle Alignment of Three-Axis Magnetic Signal[J]. IEEE sensors journal, 2019, 19(2):743-750. Zheng J, Fan H, Zhang Q, et al. Magnetic Anomaly Target Recognition Based on SVD and SVMs[J]. IEEE Transactions on Magnetics, 2019, 55(9):1-8. Shen Y, Wang J, Shi J, et al. Interpretation of Signature Waveform Characteristics for Magnetic Anomaly Detection Using Tunneling Magnetoresistive Sensor[J]. Journal of Magnetism and Magnetic Materials, 2019, 484(AUG.):164-171. Huang Y, Wu L H, Sun F. Underwater Continuous Localization Based on Magnetic Dipole Target Using Magnetic Gradient Tensor and Draft Depth[J]. IEEE Geoscience and Remote Sensing Letters, 2014, 11(1):178-180. Nara T, Ito W. Moore–Penrose generalized inverse of the gradient tensor in Euler's equation for locating a magnetic dipole[J]. Journal of Applied Physics, 2014, 115(17PT.3):3646-3648.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c3e0fd30c505b2a24e40c70d1a568e97.jpg)
Fig.1 Schematic diagram of magnetic target movement route monitoring

![](https://assets.underline.io/uploads/markdown_image/1/image/18c7f44678b5fffecd2245e1eb1c5fc9.jpg)
Fig.2 Comparison chart of route fitting correction results

 Magnetic Target Motion Monitoring Based on Weighted Route Fitting

Low frequency and weak magnetic field sensors based on magnetoelectric effect have received extensive attention due to their valuable characteristics, such as low-cost materials and fabrication, room-temperature response, low size, self-powered and non-contact sensing, high sensing resolution and large dynamic range1. In order to improve the sensitivity of magnetoelectric sensors, it is necessary to use soft magnetic materials (such as magnetic amorphous alloys, nickel, permendur, galfenol, Terfenol, ferrites) with low coercivity, low residual magnetization and high permeability as magnetostrictive phase2. The characteristics of soft magnetic field determine that the magnetoelectric sensor can quickly respond to the change of the external magnetic field, obtain the induced electromotive force, and timely recover to the state of complete demagnetization when the external magnetic field disappears. However, the output voltage generated by the magnetoelectric composite is an ambiguous function of the applied DC magnetic field due to non-negligible hysteresis loss in soft magnetic materials. The intrinsic hysteresis loop of magnetic materials is a multivalued function, which causes the magnetoelectric composites to output an uncertain voltage under the same external DC magnetic field. The non-negligible hysteresis behavior of magnetic media leads to the absolute measurement error of DC magnetic field sensor and reduces the signal-to-noise ratio (SNR). This will limit the measurement stability and accuracy of magnetoelectric sensors. Therefore, the use of magnetostrictive materials with smaller remanence may be a way to further improve the working stability of magnetoelectric sensors. In this study, by comparing three typical magnetostrictive materials with different properties, the effect of intrinsic hysteretic properties of the materials on the stability of the sensor will be studied. Furthermore, the advantages of permalloy such as low coercivity and low remanence have been used to fabricate a ME sensor with high stability. Each vibration mode of permalloy shows consistency for at least 110 hours without any demagnetization. The stable vibration mode indicates that the stability of magnetoelectric sensor based on permalloy will reach a higher order of magnitude than NZFO and Terfenol-D. Compared to previously reported counterparts, this ME sensor can achieve higher precision measurement and produce higher stability signal.

**References:**

1 Hu J M, Chen L Q and Nan C W, Adv. Mater., Vol. 28, p.15-39 (2016) 2 Burdin D A, Chashin D V and Ekonomov N A, J. Magn. Magn. Mater., Vol. 449, p.152-156 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/325c0e3bc1c866f9e9b23231c59ea03d.jpg)
Three different magnetostrictive material magnetization curves. The insert shows initial part of the curve in expanded scale.

![](https://assets.underline.io/uploads/markdown_image/1/image/c6859ec992e58cfac796facb7c4412d0.jpg)
The dynamic d33 spectrum which sampled under the condition of resonance and the same applied magnetic field for 120h.

 High-stability magnetic sensors in permalloy/piezoelectric magnetoelectric heterostructure using inappreciable hysteresis

With the development of the Internet of things, the demand for wearable flexible sensors is increasing. In order to research the new type of flexible magnetic sensors, in this paper, aiming at the vacancy of the application surface acoustic wave(SAW) devices in the field of wearable flexible magnetic sensors, the SAW magnetic sensors with ZnO/FeGa/PI structure are modeled and simulated[1,2], and the resonant characteristics and wave modes are studied. The frequency domain analysis of four kinds of devices with different thickness of 1.2 μm, 2 μm, 3.4 μm and 4 μm is carried out respectively. It is found that the device has multiple wave modes in each case, and the resonance peak of the device shifts to high frequency with the increase of the thickness of the piezoelectric layer. By comparing the modal deformation figure, it is found that the main modes of piezoelectric film with different thickness are various. For example, for 1.2 μm, the main mode is mode 2, while for 2 μm, the main mode is mode 4. The reason is that the device is composed of multi-layer thin films, in which the acoustic wave is not only affected by the piezoelectric medium, but also by the magnetostrictive layer and flexible substrate. Therefore, the optimal working mode is different for different thickness devices. In this paper, the flexible magnetic sensor is designed according to different thickness structure, and its optimal working mode is studied. When the maximum resonant mode is used as the working mode, the linear region of the magnetic sensor is basically unchanged, which is between 2 and 10 Oe. When the thickness of ZnO is 2 μm, the sensitivity in the linear region is the largest, about 253.3 kHz/Oe, and the working frequency is about 70MHz. When the thickness of ZnO is 3.4 μm, the sensitivity is only 30.5 kHz/Oe, but the working frequency is the highest, about 106MHz. This provides a theoretical basis for the development and application of flexible magnetic sensors. It is also found that when the thickness of ZnO is 1.2 μm, the maximum absolute value of admittance is only 0.0564, while for the structure with 4 μm, the maximum absolute value of admittance is 10.3413, which is of great significance for the subsequent design of impedance matching of wireless SAW magnetic sensor.

**References:**

[1] Datta S, Atulasimha J, Mudivarthi C, et al. Stress and magnetic field-dependent Young's modulus in single crystal iron-gallium alloys[J]. Journal of Magnetism and Magnetic Materials, 2010, 322(15): 2135-2144. [2] Chung G S, Phan D T. Finite Element Modeling of Surface Acoustic Waves in Piezoelectric Thin Films[J]. Journal of the Korean Physical Society, 2010, 57(3): 446-450.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7b7faa45b7f12d0b6a8f402c537530e5.jpg)
FIG. 1 Absolute value of admittance and deformed shape plot of piezoelectric layers with different thickness (a) 1.2 μm (b) 2 μm (c) 3.4μm (d) 4 μm.

![](https://assets.underline.io/uploads/markdown_image/1/image/d20a6bf2d577a547df1976e022bde57b.jpg)
FIG. 2 (a) Relationship between resonant frequency of main mode and magnetic field intensity when the thickness of ZnO is 1.2 μm. (b) Sensitivity of main modes corresponding to different ZnO thickness.

 Simulation of wave mode of flexible SAW magnetic sensor based on ZnO/FeGa/PI structure

Magnetic field sensors using the magnetoelectric (ME) effect in the composite multiferroic structures have attracted intensive attention due to their convenient operating at room temperature and high sensitivity. Large works have focused on the improvement of sensitivity and linearity by designing novel device structures but put rare attention on the optimization of equivalent noise that is also an important parameter for actual device application. In this work, we present a DC magnetic field sensor consisting of PZT/Metglas/PZT composites. With applying a voltage bias on the bottom PZT piezoelectric layer, the ME coefficient of the top PZT/Metglas bilayers can be increased obviously, as shown in Fig.1(b). This effective increase of ME coefficient will benefit the improvement of the magnetic field-to-voltage transfer coefficient and the reduction of the noise in the magnetoelectric sensor that have been shown in Fig.1(b). By increasing the electric field from 0 V/mm to 360 V/mm, the sensitivity of the sensor can increase from 13.04 mV/Oe to 32.85 mV/Oe at the resonant frequency of 131.6 kHz, and the equivalent magnetic noise of the sensor will decrease from 20 nT/√Hz to 9.8 nT/√Hz, as shown Fig.1(c). This three times increase of sensitivity and two times reduction of equivalent noise in the DC magnetic field detection by using ME effect may offer a new route for the development of novel magnetic field sensors or arrays.

**References:**

1. J. L. Hockel, T. Wu, and G. P. Carman, Journal of Applied Physics, Vol. 109, p. 064106 (2011). 2. V. N. Serov, Y. K. Fetisov, and A. A. Berzin, IEEE Sensors Journal, Vol. 18, p. 8256 (2018). 3. Y. Shen, D. Ma, and J. Gao, IEEE Electron Device Letters, Vol. 39, p. 1417 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/4f90ba99bf370ba612a719e50bcc089f.jpg)
(a) Dependence of the output voltage with the DC magnetic field at different bias voltages; (b) Dependence of the sensitivity with the bias electric field for the proposed magnetic field sensor; (c) Frequency dependent equivalent noise density spectra at different bias electric fields of the proposed sensor.

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