France



As one of the emerging neurostimulation techniques, the Transcranial Magnetic Stimulation (TMS) regulates the synaptic activity of neurons to treat several psychiatric conditions and neurological disorders. During TMS, E-fields are induced within the brain through the application of time-varying magnetic fields, using coils located outside the head &lt;sup&gt;[1-4]&lt;/sup&gt;. Different definitions are proposed in the literature to measure the focality of the E-field in the brain and estimate the stimulated area during TMS. However, most of them differ in measurement methodologies, showing lack of homogeneity and diverse criteria toward a unique conception, without evaluating possible scenarios of under or overstimulation of the biological tissue. Another common fact in the field is the use of definitions of “focality” without reference to a target area and/or focal distance, parameters intrinsically related and required for comparison between coils. Furthermore, to evaluate the degree of stimulation, a criterion indicating how well the stimulated area overlaps the targeted area is required. This work proposes a generalized function and methodology for the focality quantification in TMS coils, considering target area, focal distance, maximum magnitude and stimulation threshold. New definitions such as “specific focality (&lt;i&gt;sf&lt;/i&gt;)” and “focality form factor (&lt;i&gt;d&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;)” are introduced, seeking to describe the suitability of coils for specific stimulation applications. The proposed definitions also offer a general framework to compare coils using homogeneous methodology, parameters and nomenclature, with potential impact in the industry on the standardization of TMS measurement methods.&lt;br/&gt;We have performed finite element simulations over an anatomically accurate human head model, including three of the common TMS coils in the literature (single circular coil, figure of eight coil and quadruple butterfly coil &lt;sup&gt;[5]&lt;/sup&gt;). The head model was built based on MRI of an adult healthy subject and defined by layer including the scalp, skull, cerebrospinal fluid, gray matter and white matter. All the layers were assigned typical electromagnetic properties reported in the literature. Magnetic flux densities and electric fields were obtained in the surface of the primary motor cortex (M1) using the head model, over the subregion that controls the first dorsal interosseous (FDI) muscle. Then, the introduced &quot;specific focality&quot; measure was used. This is defined as the normalized dimensionless focality based on new proposed mathematical functions. The functions designed are called &lt;i&gt;Adjusted Even Symmetry Error Function Complement (AES-erfc) &lt;/i&gt;and &lt;i&gt;Corrected&lt;/i&gt;-&lt;i&gt;Adjusted Even Symmetry Error Function Complement (CAES-erfc)&lt;/i&gt;. They define the focality as a quantity between zero and one (interchangeable to a percentage notation), as a function of the defined &quot;focality form factor&quot; (&lt;i&gt;d&lt;sub&gt;n&lt;/sub&gt;&lt;/i&gt;), a normalized ratio between the stimulated area and the targeted area. The result is a measurement system that identifies different scenarios of focal stimulation (d&lt;sub&gt;n&lt;/sub&gt;=0), overstimulation (d&lt;sub&gt;n&lt;/sub&gt;≥0), understimulation (d&lt;sub&gt;n &lt;/sub&gt;≤ 0) or no stimulation (d&lt;sub&gt;n&lt;/sub&gt;=-1 in &lt;i&gt;CAES&lt;/i&gt;-erf) [see Fig.1]. The calculated results of the specific focality over target areas and volumes were compared with other pre-existing measures in the literature, such as the &lt;i&gt;area of the half-value&lt;/i&gt; (&lt;i&gt;A&lt;sub&gt;E½&lt;/sub&gt;&lt;/i&gt;) &lt;sup&gt;[6]&lt;/sup&gt; and &lt;i&gt;area of the half-energy &lt;/i&gt;(&lt;i&gt;AE&lt;sub&gt;E&lt;/sub&gt;&lt;/i&gt;) &lt;sup&gt;[67]&lt;/sup&gt;, for the surface specific focality [Fig.2, table 1], and &lt;i&gt;area of the half-value&lt;/i&gt; (A&lt;sub&gt;½&lt;/sub&gt;) and tangential fields spread (S&lt;sub&gt;½&lt;/sub&gt;) &lt;sup&gt;[6-7]&lt;/sup&gt;, for the volumetric specific focality [Fig.2, table 2]. Our study shows -consistently with other currently used measures- that the QBC is the coil with highest focality for the defined target, followed by the F8C. The proposed specific focality measure assigns a dimensionless value to each coil compared to results in surface units of existing definitions. With this new parameter definition, it becomes easier to evaluate the focality of a TMS coils in the context of a specific target area -or volume- and focal distance, as well as to identify scenarios of stimulation that is focal and with either understimulation or overstimulation with respect to the target size.

**References:**

[1] M. T. Wilson, A. D. Tang, K. Iyer, H. McKee, J. Waas, and J. Rodger, “The challenges of producing effective small coils for transcranial magnetic stimulation of mice,” Biomed. Phys. Eng. Express, vol. 4, no. 3, Apr. 2018, doi: 10.1088/2057-1976/aab525.&lt;br/&gt;[2] P. Rastogi, E. G. Lee, R. L. Hadimani, and D. C. Jiles, “Transcranial Magnetic Stimulation-coil design with improved focality,” AIP Adv., vol. 7, no. 5, May 2017, doi: 10.1063/1.4973604.&lt;br/&gt;[3] Z.-D. Deng, S. H. Lisanby, and A. V Peterchev, “Electric field depth-focality tradeoff in transcranial magnetic stimulation: simulation comparison of 50 coil designs.,” Brain Stimul.,&lt;br/&gt;[4] I. P. de Sousa, C. R. H. Barbosa, and E. C. Monteiro, “Safe exposure distances for transcranial magnetic stimulation based on computer simulations,” PeerJ, vol. 2018, no. 6, 2018.&lt;br/&gt;[5] P. Rastogi, Y. Tang, B. Zhang, E. G. Lee, R. L. Hadimani, and D. C. Jiles, “Quadruple Butterfly Coil with Passive Magnetic Shielding for Focused Transcranial Magnetic Stimulation,” &lt;i&gt;IEEE Trans. Magn.&lt;/i&gt;, vol. 53, no. 11, Nov. 2017, doi: 10.1109/TMAG.2017.2711962.&lt;br/&gt;[6] Z. De Deng, S. H. Lisanby, and A. V. Peterchev, “Electric field depth-focality tradeoff in transcranial magnetic stimulation: Simulation comparison of 50 coil designs,” &lt;i&gt;Brain Stimul.&lt;/i&gt;, vol. 6, no. 1, pp. 1–13, Jan. 2013, doi: 10.1016/j.brs.2012.02.005.&lt;br/&gt;[7] L. M. Koponen, J. O. Nieminen, and R. J. Ilmoniemi, “Minimum-energy coils for transcranial magnetic stimulation: Application to focal stimulation,” &lt;i&gt;Brain Stimul.&lt;/i&gt;, vol. 8, no. 1, pp. 124–134, Jan. 2015, doi: 10.1016/j.brs.2014.10.002.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/348e03c65e29cc891fd71995cd8244f3.jpg)
Fig.1. Proposed AES-erfc and CAES-erfc functions for the focality assesment.

![](https://assets.underline.io/uploads/markdown_image/1/image/80626ad77508d360116122aabb3f6dff.jpg)
Fig.2. Tables 1 and 2.

INTERMAG 2021

 Estimation of the Focality of Coils and Quality of Stimulation of Biological Tissues During Transcranial Magnetic Stimulation

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As one of the emerging neurostimulation techniques, the Transcranial Magnetic Stimulation (TMS) regulates the synaptic activity of neurons to treat several psychiatric conditions and neurological disorders. During TMS, E-fields are induced within the brain through the application of time-varying magnetic fields, using coils located outside the head [1-4]. Different definitions are proposed in the literature to measure the focality of the E-field in the brain and estimate the stimulated area during TMS. However, most of them differ in measurement methodologies, showing lack of homogeneity and diverse criteria toward a unique conception, without evaluating possible scenarios of under or overstimulation of the biological tissue. Another common fact in the field is the use of definitions of “focality” without reference to a target area and/or focal distance, parameters intrinsically related and required for comparison between coils. Furthermore, to evaluate the degree of stimulation, a criterion indicating how well the stimulated area overlaps the targeted area is required. This work proposes a generalized function and methodology for the focality quantification in TMS coils, considering target area, focal distance, maximum magnitude and stimulation threshold. New definitions such as “specific focality (sf)” and “focality form factor (dn)” are introduced, seeking to describe the suitability of coils for specific stimulation applications. The proposed definitions also offer a general framework to compare coils using homogeneous methodology, parameters and nomenclature, with potential impact in the industry on the standardization of TMS measurement methods. We have performed finite element simulations over an anatomically accurate human head model, including three of the common TMS coils in the literature (single circular coil, figure of eight coil and quadruple butterfly coil [5]). The head model was built based on MRI of an adult healthy subject and defined by layer including the scalp, skull, cerebrospinal fluid, gray matter and white matter. All the layers were assigned typical electromagnetic properties reported in the literature. Magnetic flux densities and electric fields were obtained in the surface of the primary motor cortex (M1) using the head model, over the subregion that controls the first dorsal interosseous (FDI) muscle. Then, the introduced "specific focality" measure was used. This is defined as the normalized dimensionless focality based on new proposed mathematical functions. The functions designed are called Adjusted Even Symmetry Error Function Complement (AES-erfc) and Corrected-Adjusted Even Symmetry Error Function Complement (CAES-erfc). They define the focality as a quantity between zero and one (interchangeable to a percentage notation), as a function of the defined "focality form factor" (dn), a normalized ratio between the stimulated area and the targeted area. The result is a measurement system that identifies different scenarios of focal stimulation (dn=0), overstimulation (dn≥0), understimulation (dn ≤ 0) or no stimulation (dn=-1 in CAES-erf) [see Fig.1]. The calculated results of the specific focality over target areas and volumes were compared with other pre-existing measures in the literature, such as the area of the half-value (AE½) [6] and area of the half-energy (AEE) [67], for the surface specific focality [Fig.2, table 1], and area of the half-value (A½) and tangential fields spread (S½) [6-7], for the volumetric specific focality [Fig.2, table 2]. Our study shows -consistently with other currently used measures- that the QBC is the coil with highest focality for the defined target, followed by the F8C. The proposed specific focality measure assigns a dimensionless value to each coil compared to results in surface units of existing definitions. With this new parameter definition, it becomes easier to evaluate the focality of a TMS coils in the context of a specific target area -or volume- and focal distance, as well as to identify scenarios of stimulation that is focal and with either understimulation or overstimulation with respect to the target size.

**References:**

[1] M. T. Wilson, A. D. Tang, K. Iyer, H. McKee, J. Waas, and J. Rodger, “The challenges of producing effective small coils for transcranial magnetic stimulation of mice,” Biomed. Phys. Eng. Express, vol. 4, no. 3, Apr. 2018, doi: 10.1088/2057-1976/aab525. [2] P. Rastogi, E. G. Lee, R. L. Hadimani, and D. C. Jiles, “Transcranial Magnetic Stimulation-coil design with improved focality,” AIP Adv., vol. 7, no. 5, May 2017, doi: 10.1063/1.4973604. [3] Z.-D. Deng, S. H. Lisanby, and A. V Peterchev, “Electric field depth-focality tradeoff in transcranial magnetic stimulation: simulation comparison of 50 coil designs.,” Brain Stimul., [4] I. P. de Sousa, C. R. H. Barbosa, and E. C. Monteiro, “Safe exposure distances for transcranial magnetic stimulation based on computer simulations,” PeerJ, vol. 2018, no. 6, 2018. [5] P. Rastogi, Y. Tang, B. Zhang, E. G. Lee, R. L. Hadimani, and D. C. Jiles, “Quadruple Butterfly Coil with Passive Magnetic Shielding for Focused Transcranial Magnetic Stimulation,” IEEE Trans. Magn., vol. 53, no. 11, Nov. 2017, doi: 10.1109/TMAG.2017.2711962. [6] Z. De Deng, S. H. Lisanby, and A. V. Peterchev, “Electric field depth-focality tradeoff in transcranial magnetic stimulation: Simulation comparison of 50 coil designs,” Brain Stimul., vol. 6, no. 1, pp. 1–13, Jan. 2013, doi: 10.1016/j.brs.2012.02.005. [7] L. M. Koponen, J. O. Nieminen, and R. J. Ilmoniemi, “Minimum-energy coils for transcranial magnetic stimulation: Application to focal stimulation,” Brain Stimul., vol. 8, no. 1, pp. 124–134, Jan. 2015, doi: 10.1016/j.brs.2014.10.002.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/348e03c65e29cc891fd71995cd8244f3.jpg)
Fig.1. Proposed AES-erfc and CAES-erfc functions for the focality assesment.

![](https://assets.underline.io/uploads/markdown_image/1/image/80626ad77508d360116122aabb3f6dff.jpg)
Fig.2. Tables 1 and 2.

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Thermoelectric conversion elements using the spin Seebeck effect (SSE) have attracted much attention owing to their unique physical properties as well as the industrial applications in a relatively simple structure [1-3]. Many studies using Y3Fe5O12 (YIG) have been reported as a magnetic insulator for SSE measurements. Since YIG is an insulator with high Curie temperature that allows magnons to propagate over a long distance, it is suitable for SSE observation. SSE measurements are often carried out using YIG prepared in a sintered bulk or a film grown by a physical vapor deposition method, SSE has also been studied using YIG films prepared by metal–organic decomposition (MOD) which is a simple process used for surface coating [3]. We have previously observed SSE in YIG films prepared on a Si substrate by co-precipitation, which consist of densely packed YIG nanoparticles [4]. In order to enhance the SSE voltage, the YIG films are required to have a flat film surface made by a different chemical process, which enables magnons to coherently propagate. In this paper, we report on the longitudinal SSE (LSSE) voltage in YIG films prepared on a Si or gadolinium gallium garnet (GGG) substrate by sol-gel spin-coating to investigate the annealing-temperature dependence of LSSE voltage in the samples. YIG film samples were synthesized by sol-gel and subsequent spin-coating processes, followed by annealing at Ta = 1073-1273 K for 0.5 hour in air. From the XRD spectra of the YIG films, diffraction peaks associated with the garnet phase are readily observed in the spectra of all the annealed samples, proving that they are polycrystalline YIG. Figure 1 shows a surface morphological SEM image from a YIG film made on a Si substrate annealed at 1173 K. The average surface roughness measured by SPM is ~10 nm or less, which is 30% smaller than that of YIG films prepared by co-precipitation. The areal fraction of voids estimated in the film surface by SEM imaging is ~10%, which is 75% smaller than those of YIG films prepared by co-precipitation. The obtained results indicate that the YIG films with a flatter surface can be made by the sol-gel method. To conduct SSE voltage measurements, a 5 nm Pt metal was sputtered on the YIG films. A temperature gradient △T was applied between the top of each sample (Pt side) and the bottom of the substrate to measure the voltage induced by LSSE. Figure 2 shows the variation of the SSE constant S with the annealing temperature Ta. The values of S in each sample are calculated from the △T dependence of the saturation SSE voltage VSSESat. The value of S for YIG/Pt films made on a Si substrate decreases with increasing Ta, showing the same trend as those observed for co-precipitated YIG films, which is attributable to the microstructural evolution of the nanocrystalline YIG films upon annealing. Besides, the magnitude of S is at least 30% smaller than that of co-precipitated YIG films. It is speculated that the observed decrease in the magnitude of S is owing to the increase in the interfacial area between densely packed nanoparticles as the increase in the coercive force of YIG films prepared by sol-gel is observed according to their magnetic measurements by VSM. The values of S in the YIG/Pt films synthesized on a GGG substrate annealed at 1173 K are larger than those made on a Si substrate presumably because a single crystal YIG film is formed on the GGG substrate which yields a high efficiency of magnon excitation.

**References:**

[1] K. Uchida et al, Nature, Vol. 455, p. 778 (2008) [2] K. Uchida et al, Nat. Mater. Vol. 9, p. 894 (2010) [3] A. Kirihara et al, Nat. Mater. Vol. 11, p. 686 (2012) [4] K. Yamada et al, IEEE Trans. Magn. Vol. 55, p. 4500104 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/140878e2be751346f3eeaa41cb7e47b2.jpg)
SEM surface image of a YIG film annealed at 1173 K.

![](https://assets.underline.io/uploads/markdown_image/1/image/fba6a1da143f2ae7c0b37407d6894e1b.jpg)
SSE constants S of Pt(5 nm)/YIG films on a Si or GGG substrate plotted as a function of Ta.

 Annealing temperature dependence of longitudinal spin Seebeck voltage in YIG films prepared by sol-gel spin coating method

Introduction: Biomagnetic measurement systems, such as a magnetoencephalography (MEG), are commonly composed of multi-channel magnetic sensor array more than 100. It is very important to know the positions, orientations, and sensitivities of the magnetic sensors precisely to accurately estimate the neuronal activity. So far, a calibration technique is employed to measure the sensor geometry and sensitivity after assembling or cooling the sensor arrays [1]. This calibration technique is performed by estimating the geometry and sensitivity of the sensors from the measured magnetic field distribution generated by a multi-coil array. However, there is no discussion about the accuracy of the estimation because the coil array itself has not been calibrated and its accuracy has not been evaluated. Therefore, we propose the calibration technique for the coil array based on the three-dimensional (3D) measurement using an X-ray computed tomography (CT). In this paper, we present a calibration result of the coil array and a comparison of the accuracy of the MEG source localization between using the designed and calibrated coil array geometries to measure positions, orientations, and sensitivities of MEG sensors. We fabricated a 18-channel coil array. This coil array was composed of 6 coil modules that have concentric 3 coils orthogonal to each other. The diameter and the distance between each coil were designed 30 mm and about 70 mm, respectively. (1) 3D measurement using X-ray CT The 3D measurement was performed using an X-ray CT machine (inspeXio SMX-225CT FPR HR, Shimazu Corporation). The center position, the orientation of the normal vector, and the radius of each coil were obtained by fitting a circle equation to the 3D data. We call this process “calibration of the coil array”. (2) Measurement of the MEG sensor geometries In this study, we used a whole-head MEG system, which was installed at the Kanazawa Institute of Technology [2]. This MEG system consisted of 160 arrayed SQUID (superconducting quantum interference device) sensors, which had the first-order axial gradiometers. The coil array was placed at the center of the helmet of the MEG cryostat, and the magnetic signals were generated by applying sinusoidal current waveform (80 Hz) to each coil. After measuring the magnetic signals, we estimated the sensor array layout (position, orientation, and sensitivity of each sensor). The sensor array layouts were obtained by solving the inverse problem using (A) designed and (B) 3D measured coil array geometry. (3) MEG source localization In order to confirm that the performance of the MEG system can be improved by employing the 3D-measured coil array geometry, we compared the source localization accuracy using the sensor layouts between (A) and (B). An MEG phantom, which emulates the neuronal activity in human brain as equivalent current dipoles (ECDs) [3], was used to provide the signal sources. The magnetic signals from the ECDs were measured by the MEG sensors, then the sources were localized using the sensor layouts (A) and (B). Results and Discussions: (1) 3D measurement using X-ray CT Figure 1 shows the results of the 3D measurement of the coil array using the X-ray CT. Figure 1 (a) is the entire polygon data converted from the X-ray CT image, and Fig.1 (b) shows the designed geometries of the coils in the module 1 (blue) and the obtained circles based on the X-ray CT measurement (red). The differences between designed and the 3D-measured coil geometries were 0.6±0.3 mm, 0.7±0.4 degrees, and 0.3±0.1 mm (mean±standard deviation of 18 coils) in the center position, the orientation of the normal vector, and the radius, respectively. (2) Measurement of the MEG sensor geometries The sensor array layouts were estimated using the designed and the 3D-measured coil array geometries. The differences of the estimated layouts were 1.2±0.9 mm, 1.0±0.6 degrees, and 0.7±1.9 % (mean±standard deviation of 160 sensors) in position, orientation, and sensitivity, respectively. (3) MEG source localization Figure 2 shows the differences between true value and localized values of the sources in position and orientation, respectively. Both displacements in position and orientation decreased by using the 3D-measured coil array geometry. It was demonstrated that the source localization accuracy was improved by defining the sensor layout using the calibrated coil array geometry. Conclusion: We demonstrated the calibration method of the coil array based on the 3D measurement using the X-ray CT machine. Although the coil array was fabricated preciously, the calibration of the coil array is necessary to bring the best out of the MEG system.

**References:**

[1] T. Yoshida, et al., “Calibration system for multichannel SQUID magnetometer,” in Proc. 16th Annu. Int. Conf. IEEE Eng. Adv. New Opportunities Biomed. Eng., pp.171-172 (1994). [2] H. Kado, et al., “Magnetoencephalogram systems developed at KIT,” IEEE Trans. Appl. Supercond., vol. 9 (2), pp. 4057-4062 (1999). [3] D. Oyama, et al., “Dry phantom for magnetoencephalography － Configuration, calibration, and contribution,” J. Neurosci. Methods, vol. 251, pp. 24-36 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2321ed5ac6ba860c99e1487530a02181.jpg)
Fig. 1 Results of X-ray CT measurements of the coil array. (a) entire polygon data, (b) designed and 3D-measued geometries of the coils on the module 1.

![](https://assets.underline.io/uploads/markdown_image/1/image/bf4370f47df771b814ee17abdf75c1a6.jpg)
Fig. 2 Results of the source localization experiment. This graph shows the differences between the true value and the localized values of the signal sources in position and orientation. The lengths of the squares and the error bars indicate the mean and the standard deviation of 49 signal sources).

 Calibration of a Coil Array Geometry Using an X-ray Computed Tomography

Inrush current is the reason why large power transformers cannot close without load[1]. Controlling the closing phase of circuit breaker can effectively reduce the inrush current when the circuit breaker is closed. However, it is necessary to know the value and direction of residual flux in the transformer core to control the closing phase angle. Therefore, the accurate detection of residual flux has important reference significance for the protection of power transformer. This paper proposes a method of measuring residual flux density in single-phase transformers based on the phase difference between the test voltage and the transient current, and establishes the relationship between the phase difference and residual flux based on the magnetic properties of the iron core. The finite element method is used to model and analyze the measured square transformer core, and the fitting relationship between residual flux and phase difference is obtained according to the calculation result. The experimental results show that the relative error between the finite element calculation results and the experimental results is within 5.93%, which verifies the feasibility of the proposed method and the accuracy of the relation obtained by the finite element calculation. The relationship between different residual flux and phase difference is obtained, which provides effective information for controlling the closing phase of circuit breaker.

**References:**

[1] Y. Wang, Z. Liu and H. Chen, "Research on Residual Flux Prediction of the Transformer," IEEE Transactions on Magnetics, Vol. 53, no. 6, pp. 1-4, June 2017.

**Images:**

 Residual Flux Density Measurement Method of the Single-Phase Transformer Based on Phase Difference

I. Introduction Observation and analysis of magnetic domain structure of magnetic materials with high spatial resolution are essential for understanding and improving the magnetic properties of the materials. In this regards, magnetic force microscopy (MFM) is widely used to observe the magnetic domain structure with high spatial resolution. MFM detects the gradient of magnetic field of which direction is the same as that of MFM tip magnetization. The control of the measuring direction is important to analyze the magnetic domain structure precisely. However, the measuring direction control is not easy especially for hard magnetic materials because the tip magnetization often varies by the strong sample magnetic field at the measuring position. In recent years, we have developed new novel MFM, which enables to fix the measuring field direction on DC magnetic field imaging, based on our developed alternating magnetic force microscopy (A-MFM) [1] and highly sensitive Co-GdOx superparamagnetic tip (SP tip) [2] of which magnetization direction is parallel to the applied magnetic field. A-MFM detects magnetic force gradient near the sample surface with high spatial resolution by using the frequency modulation of cantilever oscillation caused by off-resonant alternating magnetic force [1]. For the imaging of hard magnetic materials, the SP tip, which is magnetized normal to the sample surface by homogeneous AC magnetic field, is used and the SP tip detects the alternating magnetic force between AC tip magnetization and DC magnetic field from the sample and measure the gradient of magnetic field normal to the sample surface [3]. We successfully observed the magnetic domain structure of a very rough fractured Sr ferrite magnet without topographic crosstalk by fixing the measuring direction of DC magnetic field normal to the sample surface [3]. In this study, by using an observed A-MFM image of NdFeB sintered magnet of which measuring direction of magnetic field is normal to the sample surface, we demonstrate three-dimensional magnetic field gradient imaging by measuring field direction transformation, which is based on MFM tip transfer function [4]. A-MFM images, which were measured by SP tip, satisfy the necessary condition of the proposed three-dimensional imaging that the measuring detection of magnetic field for the observed image is fixed. II. Principle of three-dimensional magnetic field gradient imaging Generally, MFM signal of ∂Fz/∂z can be expressed by mx(∂2Hx/∂z2)+my(∂2Hy/∂z2)+mz(∂2Hz/∂z2), where the z direction is normal to the sample surface and m=(mx, my, mz) and H=(Hx, Hy, Hz) are the tip magnetization and the magnetic field from the sample, respectively. Here our used Co-GdOx SP tip is composed of magnetically separated magnetic nanoparticles of which diameter is less than 7 nm and each nanoparticle is thought to behave as a magnetic dipole m. The magnetic field gradient component can be expressed by the transfer function G for sample’s magnetic charge ρm , which is the source of magnetic fields [4]. For examples, gradient of perpendicular magnetic field (∂2Hz/∂z2) is expressed by the following in wave number k space. (∂2Hz/∂z2)(kx, ky, z) =G[∂2Hz/∂z2](kx, ky, z-z0)ρm(kx, ky, z0) ,where the z-z0 is the tip-sample distance. In the case of obtaining the (∂2Hx/∂z2) image from (∂2Hz/∂z2) image, the measuring direction transformation filter G[∂2Hx/∂z2]/G[∂2Hz/∂z2] is used in the following. (∂2Hx/∂z2)(kx, ky, z) =G[∂2Hx/∂z2](kx, ky, z-z0)ρm(kx, ky, z0)=G[∂2Hx/∂z2]/G[∂2Hz/∂z2] (∂2Hz/∂z2)(kx, ky, z) The ∂2Hy/∂z2 image can be obtained in the similar way. The proposed method enables to obtain three magnetic field gradient components from only one component. Various images, such as the amplitude and direction of magnetic field gradient also can be obtained by using these three components. III. Experimental procedure Our A-MFM system was based on a magnetic force microscope with an electromagnet to apply AC magnetic field to the tip for generating off-resonant alternating magnetic force between the AC tip magnetization and DC magnetic field from the sample. A-MFM image was observed at room temperature in air atmosphere using home-made high susceptibility superparamagnetic Co-GdOx granular alloy film [2] coated Si tip. The film thickness was 100 nm. The amplitude and the frequency of the AC magnetic field were 200 Oe and 89 Hz, respectively. A sample of demagnetized NdFeB anisotropic sintered magnet with c-plane was placed over the electromagnet. IV. Results Fig.1(a) shows the∂2Hz/∂z2 image of NdFeB demagnetized sintered magnet. Fig(b) and (c) show the transformed ∂2Hy/∂z2 and ∂2Hy/∂z2 image from the∂2Hz/∂z2 image, respectively. Fig(d), (e) and (f) show the images of the intensity of magnetic field gradient |∂2H/∂z2|, polar angle θ and azimuthal angle Φ of the magnetic field gradient, respectively. As seen in these figures, magnetic field distribution is clearly observed. This method needs only one MFM image of which the measuring detection of magnetic field is fixed, while most methods of three-dimensional magnetic field imaging needs three magnetic field sensors for each three-dimensional direction. The proposed imaging is thought to be useful to obtain the precise information of magnetic field distribution and analyze the magnetic domain structure.

**References:**

[1] H. Saito, H. Ikeya, G. Egawa, S. Ishio, S. Yoshimura, J. Appl. Phys., Vol. 105, p.07D524(2009), [2] Y. Cao, P. Kumar, Y. Zhao, Y. Suzuki, S. Yoshimura, H. Saito, J. Magn. Magn. Mater., Vol. 462, p.119 (2018), [3] Y. Cao, Y. Zhao, P. Kumar, S. Yoshimura, H. Saito, J. Appl. Phys., Vol. 123, p.224503 (2018), [4] H. Saito, J. Chen, S. Ishio, J. Magn. Magn. Mater., Vol. 191, p.153 (1999)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/05cbc7fd1bd1fde3f98a8ae521210af6.jpg)
Fig.1 (a) Measured perpendicular magnetic field gradient image ∂2Hz/∂z2 and its signal transformed images [(b) ∂2Hx/∂z2, (c) ∂2Hy/∂z2, (d) |∂2H/∂z2|, (e) polar angle θ and (f) azimuthal angle Φ ] for a NdFeB sintered magnet.

 Three-dimensional magnetic field gradient imaging of permanent magnet by alternating magnetic force microscopy: Transformation of measuring magnetic field direction based on MFM tip transfer function

INTRODUCTION In recent years, imaging of magnetic nanoparticles (MNPs) has attracted attention as a new diagnostic imaging technique for the imaging of certain targets, such as cancer cells [1]. We previously proposed an MNP imaging method, “magnetic nanoparticle tomography” (MNT), that uses multiple magnetic sensors [2], [3]. In the previous study, an inverse problem analysis was performed to estimate the position of MNPs using the non-negative least squares method (NNLS), which is often used for magnetic particle imaging (MPI). The NNLS method achieves high sensitivity and spatial resolution. However, due to the existence of measurement noise and high sensitivity of NNLS, some MNPs are incorrectly estimated, that is, some artefacts appear. In this study, we apply the minimum variance spatial filter (MV-SF), which is often used in magnetoencephalography (MEG) inverse problem analysis [4], to reduce the artefacts. METHODS The experimental setup is presented in Fig. 1. The Resovist MNP sample was arranged in a sinusoidal magnetic field, which was generated using an excitation coil. The third harmonic magnetic field from MNPs was detected using 16 detection coils. To improve the sensitivity, a cancelation circuit for the fundamental magnetic field was employed. The two-dimensional concentration map of the MNP sample was subsequently obtained by the application of the MV-SF. The distance between the MNP sample and the imaging system (excitation coil and detection coils) was set from 25 mm to 40 mm at intervals of 5 mm. We used two samples with different concentrations of 100 µg-Fe and 500 µg-Fe and estimated the positions for each of them. RESULTS The result of the reconstructed map when the MNP sample was set at are shown in Fig. 2. The white circle in the figure represents the actual sample position. Fig. 2 (a) depicts the result for a sample containing 500 µg-Fe. This result reveals that a sharp signal peak position is observed in the vicinity of the sample position. Fig. 2 (b) exhibits the result for a sample containing 100 µg-Fe. This result indicates that the error between a sharp signal peak position and the actual sample position is within 10 mm. No artefacts appear in both results, contrary to the results using NNLS [3]. From these results, we can conclude that MV-SF is useful for reducing the artefact and estimating the positions of MNPs in magnetic nanoparticle tomography. ACKNOWLEDGMENTS This work was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Young Scientists [grant number JP19K14996], and by a research grant from the Mazda Foundation.

**References:**

[1] T. Knopp and T. M. Buzug, “Magnetic Particle Imaging—An Introduction to Imaging Principles and Scanner Instrumentation,” Springer, 2012. [2] T. Sasayama, T. Yoshida, K. Enpuku, “Two-Dimensional Magnetic Nanoparticle Imaging Using Multiple Magnetic Sensors Based on Amplitude Modulation,” Journal of Magnetism and Magnetic Materials, Vol. 505, 2020, Art. no. 166765. [3]T. Sasayama, N. Okamura, and T. Yoshida, “Sensitivity Improvement of Magnetic Nanoparticle Imaging by Compensation with Digital-to-Analog Converter,” IEEE Trans. Magn. In press. DOI: 10.1109/TMAG.2020.3014375. [4] K. Sekihara and S. S. Nagarajan, “Adaptive Spatial Filters for Electromagnetic Brain Imaging,” New York, USA: Springer-Verlag, 2008.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d77d396ce684c3b306bcd9bb12e3471f.jpg)

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 Inverse Problem Analysis in Magnetic Nanoparticle Tomography with Minimum Variance Spatial Filter

Introduction Magnetocardiography (MCG) is a noninvasive technique that detects the magnetic field generated by the electrical activity of the heart [1]. The estimation of MCG current sources is useful technics for clinical application [2]. Exact low resolution brain electromagnetic tomography (eLORETA) [3] spatial filter is used for visualizing brain activity, as it is a genuine inverse solution with exact, zero error localization in the presence of measurement and structured biological noise. However, it tends to reconstruct a large spatial extension for deep sources due to the decreasing sensitivity of the sensors. In this study, we aim to reduce the influence of the source depth in the reconstructed current sources using multiple spatial filters. Method In order to solve the problem of the large spatial extension for deep sources, in addition to the conventional measurement at the front (chest) of the body, the back is also measured. It is possible to improve the estimation accuracy for a deep signal source. Estimation of MCG current sources was used eLORETA spatial filter. We examined two types of spatial filters for two-side measurement. The first method (128ch method), a spatial filter (128ch) was produced by a read-field matrix using two 64ch sensors as one 128ch sensor. In this method, the regularization parameter λ which determines noise immunity has the same value on the front side and the back side. The second method (2 × 64ch method), two spatial filters (64ch) were separately calculated then one spatial filter (2 × 64ch) was produced from the two spatial filters (64ch). In this method, different λ can be determined on the front side and the back side, and the optimum noise immunity can be given to each. In this study, a spatial filter was created by setting λ as 1% of the maximum eigenvalue in 128ch method, 1% of the maximum eigenvalue on the front side and 5% on the back side in 2 × 64ch method. We estimate MCG current sources within a 175 mm × 175 mm × 995 mm volume. Three thousand two hundred and forty voxels were divided with the size of each voxel being 10 mm × 10 mm × 10 mm. For the forward problem, we calculate the lead-field matrix K using the Biot-Savart Law. For each current source location, K includes two columns that represent X component and Y component, respectively. Results and Discussions We estimated MCG sources at R peak, which indicates the activities of ventricle. Fig.1 (a), (b), and (c) show the estimation results by the conventional 64ch spatial filter, the proposed 128ch spatial filter, and the 2 × 64ch spatial filter, respectively. The upper side is a front view of the heart, and the lower side is a below view of the heart. Each frame represents an analytic space. The estimation result shows voxels with a threshold of 90% or more of the strongest point of the estimated source. Compared to Fig. (a), the estimated sources of Fig. (b) and Fig. (c) are able to suppress the spatial extension of the estimated sources due to the effect of providing the measurement surface on the back side. Moreover, the estimated source of Fig. (b) is not estimated correctly because it appears not only in the ventricle but also in the vicinity of the atrium. It is considered that the estimation is incorrect due to the influence of noise because λ is constant. On the other hand, in Fig. (c), the estimated source appears at the ventricular position, and it is thought that the active position of the heart can be estimated more accurately. Conclusion We proposed two types of spatial filter produced method of eLORETA by two-side measuments of the front and back of the body. By using the back side in addition to the front side, the spatial extension of the estimated source could be suppressed. Among them, the signal source could be estimated at the correct position by produced using a 2 × 64ch spatial filter that can determine the regularization parameter λ on the front side and the back side respectively.

**References:**

 [1] D. Cohen, E.A. Edelsack, J.E. Zimmerman,” Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer”, Applied Physics Letter, Vol. 16, pp. 278-280, 1970. [2] J. S. W. Kwong, B. Leithäuser, J.-W. Park, C.-M. Yu, “Diagnostic value of magnetocardiography in coronary artery disease and cardiac arrhythmias: A review of clinical data,” Int. J. Cardiol., vol. 167, pp. 1835-1842, Sep. 2013. [3] R.D. Pascual-Marqui, “Discrete, 3D distributed, linear imaging methods of electric neuronal activity. Part 1: exact, zero error localization”, Mathmatical Physics, arXiv: 0710. 3341, 2007.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/1c828343ab32aef6e8439143ad174be6.jpg)
Fig. 1. The estimation results by (a) the conventional 64ch spatial filter, (b) the proposed 128ch spatial filter, (c) the 2 × 64ch spatial filter. The upper side is a front view of the heart, the lower side is a below view of the heart. Each frame represents an analytic space. The voxel is the estimated source with a threshold of 90% or more of the strongest source.

 Estimation of Magnetocardiography Current Sources using Multiple Spatial Filters

In rotational ac machines, interlocking is a commonly used manufacturing method to fix the silicon steel laminations. To analyze the range of degradated magnetic properties caused by the interlocking process more accurately, the distribution of magnetic properties around the interlock was investigated and the areas damaged to varying degrees was quantified. This work is meaningful for the accurate modeling and simulation of machines. I. Introduction Electrical steel sheets are usually assembled into core laminations through interlocking, welding or gluing. In comparison, interlocking is suitable for batch production and become the main method of fixing among electrical steel sheets currently. However, the deterioration of the magnetic properties caused by interlocking cannot be ignored. The formation of interlocks is always accompanied by plastic deformation and generation of residual stress, which will change the movement of magnetic domain under magnetization, and the hysteresis characteristics will be significantly influenced. Furthermore, the interlocking process destroys the insulation, resulting in inter-lamination short circuits. At high frequencies, the interlaminar eddy current loss even contributes more to the deterioration of magnetic properties. There have been several magnetic measurements of interlocks on lamination ring cores with primary winding and secondary winding before, and they have investigate the effect of the interlocks number, sizes, and shapes on the overall magnetic properties of lamination ring cores[1-3]. However, the overall magnetic properties of ring cores cannot be served for accurate simulation of the interlocking process. Some preliminary attempts for interlocking localized magnetic measurements are also in progress, but they mainly focus on interlocks with a single size and a single magnetization direction[4]. Therefore, a more comprehensive localized magnetic properties measurement is necessary. II. Experimental and Results A localized magnetic measurement sensor with two B-needle probes and a H-coil have been manufactured. The distance between the B-needle probes is 3.5 mm and the size of the H-coil is 3 mm×3 mm. As is shown in Fig. 1(a), the sensor was connected to a three-axis precision positioning table, and the displacement accuracy of the sensor is 0.1 mm. Then four hollow square shaped samples with interlocks were wound by the exciting coils. The detailed information of samples and interlocks was shown in Fig 1(b). More than three hundred measurement points are taken on the concave and convex surfaces around each interlock to achieve higher resolution measurements of the local vector magnetic properties. Due to the length limitation of the abstract, Fig. 2 shows part of measured results at 50 Hz with 0.5 T sinusoidal excitation. The white rectangle represents the the upper part of the interlocking position. For the single sheet, it can be seen that the loss increases and the magnetic permeability decreases near the interlock. This is attributed to the generation of residual stress during the formation of the interlocks. For the ten-layer laminate, in addition to the residual stress, the insulation between laminations is destroyed near the interlocks and interlaminar short circuits is formed, which will produce extra eddy current loss. The ratio of loss increment and the ratio of permeability decrement of the three interlocks at 50Hz and 0.5T magnetic density will be provided in the whole paper. The damaged areas of varying degrees was quantified. Besides, the size of the interlocks can also cause different influence on the magnetic properties near the interlocks. The measurement were performed with Sample 2 and Sample 4, and the results show that the magnetic properties deterioration area around larger interlocks is bigger. The deterioration area hardly change with different magnetic flux. III. Conclusions In this paper, we concluded the influence of interlocks on the magnetic properties as follows: 1) The size of the interlock and the degree of localized magnetic degradation are positively but not linearly correlated. The requirements for fastened strength should be taken into consideration when selecting a appropriate size. 2) The local magnetic degradation caused by interlocking in the rolling direction is much lower than that in the transverse direction. 3) On the basis of planar distribution of magnetic degradation, different levels of magnetic degradation caused by interlocking can be quatified. Applying these results to the electrical machines can contribute to the improvement in simulations of them.

**References:**

[1] J. Shen, G. Zhou, S. Jin and H. Hao, 2015 International Conference on Sustainable Mobility Applications, Renewables and Technology (SMART) IEEE., p.1-4(2015). [2] K. Senda, H. Toda, and M. Kawano, Ieej Journal of Industry Applications., Vol. 4, p.496-502(2015). [3] S. Imamori, S. Steentjes and K. Hameyer. IEEE Transactions on Magnetics., Vol. 53,(2017). [4] S. Imamori, S. Aihara and H. Shimoji, et al. Journal of Magnetism and Magnetic Materials., Vol. 500, (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8931710e06488033fcd3d967d8528c76.jpg)
Fig 1. (a)The measuring device.(b) The detailed information of samples and interlocks.

![](https://assets.underline.io/uploads/markdown_image/1/image/18b10ed4fde7b21f1354a164e8b2d0a2.jpg)
Fig2. Part of the experimentally measured planar distribution of magnetic properties at 50Hz and 0.5T magnetic density. (a) Upper part of the permeability around the interlock on the convex surfaces of Sample 1. (b) Upper part of the loss around the interlock on the concave suface on the Sample 2.

 Localized Magnetic Properties Measurement of Interlocking Core Laminations

In plane magnetization stripes of soft magnetic alloys have been proposed as magnetic information storage devices. In these kind of systems, regions of uniform magnetization with opposite senses are separated by domain walls (DW), known as head-to-head or tail-to-tail walls, that may have different structures depending on the width and thickness of the stripes. Usually, two types of DW are expected, known as transverse or vortex, depending on stripe width and thickness. The work by Nguyen et al [1] has shown that in stripes thicker than 60 nm, a third type of head-to-head DW may exist, the so called Landau wall, with a significant out-of-plane magnetization core that is not homogenous across the film thickness. These walls have three internal degrees of freedom: chirality, determined by the sense of rotation of the in-plane circulation of the magnetization; polarity, defined by the upwards or downwards normal magnetization; and the sense of the Neel caps.This can result in richer topological configurations than the standard vortex and transverse walls. In particular, the Neel caps modify the shape and position of top and bottom vortices, leading to non-trivial magnetic textures and singularities with possible interest in magnetic transport applications. In this work, we have grown 80 nm -150 nm thick permalloy racetracks by sputtering on Si substrates and on 50 nm thick Si-N membranes in order to study their 3D internal structure by a combination of Magnetic Force Microscopy (MFM), X ray magnetic transmission microscopy (MTXM) and magnetic X-ray tomography [2] at the Mistral Beamline of Alba Synchrotron. Briefly, curved permalloy stripes have been defined by e-beam lithography and lift-off with width in the 200 nm - 5000 nm range and several microns length with different degrees of curvature. These structures have been characterized at remanence after saturating them with an in-plane magnetic field transverse to the average stripe orientation in order to nucleate domain walls and inhomogeneous domain structures. Figure 1(a) shows the MFM image of a 140 nm thick permalloy stripe showing a central domain wall bounded by two half vortex structures, together with a rhomboid transverse domain (diamond state) close to the stripe end. Magnetic transmission X-ray microscopy images (Fig. 1(b)) reveal polarity reversals within the core of the central domain wall and the development of a transverse structure near the right end of the permalloy stripe. Micromagnetic simulations, as shown in Fig. 2 confirm that these walls have indeed a complex 3D magnetic structure across the thickness and can display polarity reversals along their length related with the presence of magnetic singularities such as Bloch points and magnetic antivortices. These 3D magnetic configurations will be resolved in more detail with the aid of angular tilt series of MTXM images around different rotation axes which are the basis for a recently developed magnetic X-ray tomography method. Work supported by Spanish MINECO under grant PID2019-104604RB/AEI/10.13039/501100011033.

**References:**

[1] V. D. Nguyen et al. ,“Third type of domain Wall in soft magnetic nanostrips”; Scientific Reports 5 (2015) 12417 [2] A. Hierro-Rodriguez et al. "Revealing 3D magnetization of thin films with soft X-ray tomography: magnetic singularities and topological charges" Nature Communications 11, 6382 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6fe230b1acfa0d166b7eb628e5631a34.jpg)
Fig. 1.(a) MFM image of 140 nm thick permalloy stripe at transverse remanence. (b) MTXM image at normal incidence of permalloy stripe. Note the polarity reversals at domain wall core. Black dots in this image correspond to 100 nm Au nanoparticles used for alignment.

![](https://assets.underline.io/uploads/markdown_image/1/image/25f7f12d5d4c6cd0ce5f1b860b40bea6.jpg)
Fig. 2. Micromagnetic simulations of the magnetic configuraion of thick permalloy stripes at different sample depths (top/central/bottom slices). Note the subtle changes in magnetization orientation at domain wall cores related with the 3D domain wall configuration.

 3D magnetic structure of domain walls in soft magnetic racetracks by MFM and X-ray microscopy

I. Introduction Wireless power transfer (WPT) system can effectively make up for the shortcomings of traditional electric energy transmission and has a wide range of application prospects in the fields of electric vehicles, biomedicine, and portable equipment [1-3]. There are several ways to realize WPT, among which the WPT based on magnetic coupling resonance has many advantages, such as long transmission distance, high efficiency, simple implementation, and so on, which can meet the requirements of most scenarios. The WPT system needs a stable and efficient high-frequency power supply. The Class E Amplifier, with only one switch component, can realize soft-switching by matching the appropriate bypass capacitor and then get a high efficiency (close to 100%) in MHz [4]. Hence, the Class E Amplifier is extremely suitable for a high-frequency WPT system. At present, the scholars’ research generally focuses on the short-range and high-efficiency WPT systems within 20cm, whose transmission distance is insufficient [5-6]. Silicon MOSFET can not meet the needs of the high-frequency power supplies, GaN components can work at a higher frequency and higher efficiency [7]. Herein, a mid-range high-efficiency wireless power transfer system based on class E power amplifier and Gan components is proposed. This paper optimizes the coupling coil and load in theory and simulation and gives the system parameter design method of ZVS (Zero Voltage Switching) operation of the class E power amplifier. Finally, the Wide Band-gap Semiconductor GaN component is used to build the physical model to verify the accuracy of the design. More detailed results and discussion will be presented in the extended paper. II. Double coil wireless power transmission system based on the class E power amplifier The wireless power transmission system mainly includes three subsystems, class E power amplifier, coupling coil, and load. And the topology is shown in Figure 1. According to the circuit model, the factors that affect the transmission efficiency and power of the system are analyzed, and it is concluded that the mutual inductance of the coils, the load, and the AC resistance of the coils have a great influence on the transmission characteristics. III. Design and optimization of the flat spiral coils for the WPT system The parameters of the coupling coils are closely related to the performance of the WPT system. The design and optimization are carried out through theory and simulation, and the comparison is carried out through experimental measurement. a. Calculation of coil self-inductance and mutual-inductance According to Neumann’s formula [8], the mutual inductance calculation method of the flat spiral coil is derived. The self-inductance and mutual-inductance of the coil are calculated by theory and COMSOL electromagnetic field simulation tool. b. Calculation of the coil AC resistance and determination on the spacing between coil turns To reduce the coil AC resistance as much as possible, the relationship between coil AC resistance and turn spacing is analyzed by COMSOL Multiphysics. And then determines the spacing between coil turns is 2mm. The theoretical calculation, finite element simulation, and experimental measurement results are compared and analyzed, and the results are quite consistent. IV. System circuit simulation calculation and experimental verification Powered by a 24V DC power supply, the optimal load resistance is 10Ω and set the transmission distance to 40cm, then we determine the parameters of the system components. a. Circuit simulation using PSIM Build the system simulation model in PSIM, the circuit realizes soft switching, and the simulation results are shown in Figure 2. The output power of the load is 26.85W and the transmission efficiency is 87.89%. b. System experiment verification In particular, in view of the low on-resistance and small parasitic capacitance of GAN devices, which enable them to maintain high efficiency during high-frequency operation, GaN devices are introduced as switching devices in the experiment. According to the design parameters, we build the experimental model and carry out the relevant measurement. The experimental results are in good agreement with the simulation results. When the distance between coils is 40cm, the output power of the load is 25.99W and the transmission efficiency is 87.34%. V. Conclusions Aiming at the problem of low efficiency of medium and long-distance wireless power transmission, this paper conducts comprehensive efficiency optimization from coil parameter optimization, load, and class E power amplifier. Using new GaN devices, a wireless power transmission system that takes into account the characteristics of mid-range and high efficiency has been developed.

**References:**

[1] Y. Bu, S. Endo, T. Mizuno, IEEE Transactions on Magnetics, vol. 54, pp. 1(2018) [2] F. Benassi, D. Masotti, A. Costanzo, 2019 IEEE International Conference on RFID Technology and Applications (RFID-TA), pp. 306(2019) [3] N. Hasegawa, S. Yoshida, S. Furuta, et al., 2014 IEEE Wireless Power Transfer Conference, pp. 21(2014) [4] F. Tamjid, A. Ghahremani, M. Richardson, et al., 2017 IEEE Topical Conference on RF/Microwave Power Amplifiers for Radio and Wireless Applications (PAWR), pp. 25(2017) [5] L. Kou, J. Lu, P. Di Maso, 2019 IEEE 7th Workshop on Wide Bandgap Power Devices and Applications (WiPDA), pp. 205(2019) [6] H. Li, J. Li, K. Wang, W. Chen, et al., IEEE Transactions on Power Electronics, vol. 30, pp. 3998(2014) [7] J. Song, M. Liu, C. Ma, IEEE Transactions on Industrial Electronics, vol. 67, pp. 8281(2019) [8] H. A. Wheeler, Proceedings of the Institute of Radio Engineers, vol. 16, pp. 1398(1928) [9] H. L. Chan, K. W. E. Cheng, D. Sutanto, 2000 Eighth International Conference on Power Electronics and Variable Speed Drives, pp. 69(2000)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e87a9716c1b30438f50eeea535a90b25.jpg)
Fig. 1 Topology of the WPT system

![](https://assets.underline.io/uploads/markdown_image/1/image/ad2c8f9ba024d557ada47c36613f662c.jpg)
Fig. 2 System circuit simulation results using PSIM

 Research on Mid-distance High-efficiency Wireless Power Transmission System using Class E Amplifier

There were many machine failures caused by the damage of the rolling bearing, for which the main reason was the quality of the steel ball [1]. Many works have been reported on assessing the geometric quality of steel balls, such as shape, size, and surface defects. In contrast, testing the material properties of steel balls is rarely mentioned [2]. As the quality and working life of the bearing depend primarily on the material properties of the steel ball, it is necessary to unambiguously classify the properties of steel balls in making bearings and other applications to ensure the reliability of the mechanical machine system. In this digest, we report on the eddy-current technique for the classification of steel balls based on the amplitude and phase of the eddy-current signal. Three types of 4-mm steel balls, including carbon, chrome, and stainless 304 steel balls, were tested to determine if it had undergone the surface hardening process. Fig. 1 shows the components of the RLC-resonance eddy-current system, which was designed to convert the electromagnetic induction of the steel ball into the phase-sensitive voltage output signals. The pickup coil is mounted statically to detect the eddy-current signal when the steel ball moves back and forth through the pickup coil by the stepping motor translation stage. A microcontroller (Arduino Uno) is used as the main unit to gather and process the data of the stage, such as the position and velocity. The micro-step determined on the driver is set to be 1/32. Fig. 1. The experimental eddy-current system for steel ball sorting. To detect the signal, the reference waveform for the lock-amplifier is synchronized to the excitation signal of the eddy current sensor. The lock-in amplifier receives the output signal from the sensor and generates the analog output voltages in proportion to the in-phase (real) and quadrature-phase (imaginary) components of the signal. The voltages are digitized by the data acquisition (DAQ) device NI USB 6008 from the National Instruments. The translation stage and the DAQ device are both controlled by the computer with the graphic user interface software designed using the Visual Studio C# programming language. The real and imaginary voltage components of the recorded eddy-current signals are subsequently converted into the probability map to show whether the steel balls can be classified by eddy-current sensors. The change in the detected signal should be due to the difference in the electromagnetic properties of the steel balls since the ball diameters are all 4 mm with an error less than 10 μm. Fig. 2. Eddy-current classification of steel balls: (a) determining the resonant frequency, (b) finding out the optimal resistance, and (c) voltage probability map of the steel balls before and after the surface hardening process. The impendence of the pickup coil can be calculated according to Dodd and Deeds method [3]: Zc=[(2πωµn2rm)/(l2-l1)2(r2-r1)2]∫I2[(r2,r1)/α5]{(l2-l1)(1+e-α/α)-1/α}dα (1) where Zc is the impedance of the coil (Ohm), µ is the permeability (Henry/meter), I is the applied current (ampere), α is the separation constant (meter-1), r2 is the outer radius of the coil (meter), r1 is the inner radius of the coil (meter), rm is the average radius of the coil, ω is the angular frequency (rad/second), l2 is the distance from metal testing to top of the coil (meter), l1 is the distance from metal testing to bottom of the coil (meter), n is the number of turns (turns), respectively. Fig. 2(a) shows the voltage amplitude measured at the output terminal when the driving frequency varies from 50 kHz to 200 kHz. The output response is maximized at the resonant frequency of 116 kHz for the RLC circuit. To achieve the higher response, the voltage outputs with various resistors are measured, as shown in Fig.2(b), where the optimal resistance is found to be 20 kΩ. The demodulated eddy-current signals were collected and repeated 100 times for each type of ball, and the result is converted into the voltage probability map in Fig. 2(c). It is found that the steel balls before and after the surface hardening treatment can be classified based on the difference in the eddy-current signal caused by the variation in electrical conductivity and permeability. The result indicates that the proposed method is feasible for application in sorting the material quality of steel balls, which plays a crucial role in mechanical systems. The authors would like to thank Tan Kong Precision Tech Co. Ltd. for providing the steel ball samples. This work is supported by the Ministry of Science and Technology of Taiwan under Grant No. MOST108-2221-E992-083MY2.

**References:**

[1]. H. K. D. H. Bhadeshia, "Steels for bearings", Progress in materials Science, 57(2) 268-435 (2012). [2]. D. Rifai, A. N. Abdalla and K. Ali, "Giant magnetoresistance sensors: A review on structures and non-destructive eddy current testing applications", Sensors, 16(3) 298 (2016). [3]. C. V. Dodd, and W. E. Deeds, "Analytical solutions to eddy-current probe-coil problems", Journal of applied physics, 39(6) 2829-2838 (1968).

**Images:**

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