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The tensor complex permeability of a multi-turn coil with elliptic cross-section is analytically expressed. In field analysis, a multi-turn coil can be modeled by the uniform material that has the present tensor complex permeability. It is shown that the frequency characteristic of the present tensor complex permeability is in good agreement with that evaluated by finite element method applied to a unit cell of the multi-turn coil region.

The authors introduce a new method to evaluate the complex permeability of a multi-turn rectangular coil. To obtain the complex permeability of a rectangular coil in a closed form, it is approximated as an elliptic coil. Because the rectangular coil has different complex permeabilities in the vertical and horizontal directions, the complex permeability have to be defined in a tensor form. It suffices to discretize the coil region into rather coarse finite elements without considering the skin depth in contrast to the conventional finite element method.

The proposed method is shown to give the impedance of multi-turn coils which is in good agreement with results obtained by the conventional finite element (FE) analysis. By extending the proposed approach, the authors can easily perform 3D FE analysis without difficulty in discretization of the coil region with fairly fine finite elements. Moreover, they found that the approximation of rectangular coils as the elliptic coils is valid for analysis of quasi-static fields using this homogenization method.

The novelty of this study is in the approximation of the rectangular coils with elliptic coils, and the complex permeability for them is formulated here in a closed form. The proposed formula includes that for the round coils. Using the present method, the authors analyze the rectangular coils without fine discretization.

The purpose of this paper is to analyze the characteristics of the factors influencing the effect of magnetic levitation, including the impedance angle of the levitated coil, number of turns, material parameter, frequency of excitation and geometric parameters. The final purpose is to provide approaches to increasing the levitation effect.

Some design principles and strategies for levitation systems are suggested, such as selecting the number of turns of the levitated coil, choosing the frequency of excitation considering the saturation phenomenon of levitation force against frequency and deciding the section area of the excitation coil and its ratio of height and thickness.

The magnetic force is not always repulsive in a cycle. Therefore, the key approach to increasing the levitation is to increase the period when the force is repulsive and decrease the time when attractive. The impedance angle of the equivalent circuit of the levitated coil determines the ratio of the two periods, and the larger the angle, the longer the repulsion period. A valuable finding is that a saturation situation exists between the levitation force and frequency; that is, when the frequency increases to a certain value, the increasing degree of force tends to decrease as the frequency increases.

Some influential characteristics were found in some factors against the effect of the levitation system, which is beneficial for improving the efficiency of systems. For example, owing to the saturation phenomenon of the frequency, it is useless to continue increasing the frequency and the copper-levitated coil does not bring much greater force effectiveness than the aluminum coil.

The purpose of this paper is to evaluate the response of the spinal cord, the transmembrane potential, during lumbar magnetic stimulation, using a figure of eight coil.

In order to obtain a precise stimulation of the spinal cord and not the nearby nervous fibres, the coil from the electric circuit of the magnetic stimulator is optimized. The new proposed design is based on the turns’ placement inside the coil, the number of turns required to produce activation. Once the coil configuration is established, the paper addresses other issues that need to be solved: reducing power consumption (the low efficiency of power transfer from the coil to the tissue is a major drawback) and reducing coil heating.

The traditional commercial coils, used for magnetic stimulation in some preliminary experiments, had proved their inability to specifically stimulate the target tissue, without activating the surrounding areas and the low efficiency of power transfer from the coil to the nervous tissue. A more realistic modelling of the stimulating coil, based on the distribution of turns inside the coil can lead to directly stimulation of the spinal cord, during lumbar magnetic stimulation.

If the electrical circuit of the magnetic stimulator is improved, the direct stimulation of the spinal cord is obtained; so, this technique could facilitate functional motor activities, including standing and stepping in paralyzed people, without requiring implantation of electrodes like in electrical stimulation.

The authors underlined that the spinal cord stimulation can be achieved by magnetic stimulation, only if the parameters of the stimulator circuit are optimized. Therefore an original and realistic modelling of the inductive coil was proposed based on number and turns’ distribution within the coil. The coil is designed so that reducing the excessive heating makes it difficult in obtaining a more frequent repetition of stimulus.

Gradient coils designed by conventional target field methods usually have a complex physical structure and these methods are not convergent for complex routing area problems. This study aims to design a multi-coil (MC) gradient system arranged on a complex routing area including two cylindrical surfaces with different radii for a head magnetic resonance imaging scanner.

A MC system model is established. In this model, the sub-coils are evenly distributed on two cylindrical wiring surfaces, and the radii of coils are the same on one cylindrical surface. With the target magnetic field set, the currents in every individual coil are solved by constrained least-squares fitting based on the Levenberg–Marquardt method.

The magnetic field nonlinearity generated by designed coils is validated as 4.50% and 3.57% for X-gradient coil and Z-gradient coil, respectively, which satisfy the mainstream nonlinearity standards. The analysis of the optimization results indicates that hardware requirements can be considerably reduced by connecting coils with the same currents in series.

High-linearity gradient magnetic fields are generated on complex routing areas by adopting the MC structure. In addition, the requirements for current sources and amplifiers are considerably reduced.

Industry growth in the field of coil coatings has been impressive as several of the articles abstracted below attest. The advantages inherent in coil coatings from the points of view of economy, adaptability to automation, and adaptability of the final product to fabrication are impressive ones that industry is taking full advantage of. There are, to be sure, some problems associated with the use of precoated steel, such as destruction of the coating during weldability, but techniques have been devised, including mechanical fastening, to circumvent such problems.

This paper aims to find an approach that achieves constant output power and transfer efficiency in an open space, such as charging pads.

In this study, a topology of the five-coil system including two transmitting coils is presented. Also, in a fixed-frequency mode and an open space, this study focuses on the two transmitting coils to achieve the uniform magnetic field and ultimately, attain the constant output power and transfer efficiency.

In a fixed-frequency mode and an open space, the constant output power and transfer efficiency is then achieved in experiments by inserting the relay loop into the uniform magnetic field.

An approach that achieves constant output power and transfer efficiency in an open space. The topology of the five-coil magnetically coupled resonant-wireless power transfer (MCR-WPT) system shows prospective value for various applications, which could be used at designing of wireless battery charger dedicated for cars or mobile phones.

By comparing the simulation and experimental results, the topology can be optimized in the transmission performance by itself. By doing so, the constant output power and transfer ef?ciency are achieved in the constant frequency mode.

Recent advances in nano and picosatellite missions and future such missions require three axis attitude control system hardware for attitude control purposes. A simple, cost effective, yet an efficient devise that is used for active attitude control is magnetic torquer coil. The purpose of this paper is to describe the design and fabrication of a template to manufacture magnetic torquer coils of varying sizes and shapes.

Details about the development of the template design, analysis, and fabrication are discussed. The development status of the system is outlined and the working prototype of the device is described and some preliminary test results are given.

A fully functional prototype of the template has been developed and testing has been conducted that demonstrated the effectiveness of the device. Magnetic torquer coils of varying sizes were fabricated and tested. A finite element analysis was performed by modeling the characteristics of the fabricated coils to determine thermally induced stresses and deformations during its space operations.

The paper illustrates and demonstrates an effective application of torquer coil template in the satellite fabrication industry. The benefits from the approach are generally applicable to any future university and industry missions using picosatellite technology.

The designed template satisfied all the constraints and requirements. Furthermore, its advantages include scalability, modularity, and its capability to fabricate magnetic torquer coils of varying sizes and shapes.

The purpose of this paper is to present an accurate and efficient hybrid method for the calculation of the inductance of a coil and its inductance change due to deformed turns using numerical methods.

The paper opted for finite element method coupled with analytical method (FCA) to accurately calculate the inductance of a coil, which is used as reference value. An algorithm with a power function is presented to approximate the partial inductance matrix with the purpose of obtaining the percentage change of the inductance due to deformed turns by using the partial element equivalent circuit (PEEC) with an approximated model and an optimization process. The presented method is successfully validated by the numerical results.

The paper provides a systematic investigation of the inductance of an arbitrary shaped coil and shows how to accurately and efficiently evaluate the inductance change of a coil due to its deformed turns. It suggests that the inductance of a coil can be accurately calculated by using FCA and its percentage change due to deformed turns can be efficiently calculated by using the PEEC_Approximation.

As this research is for the magnetostatics, the skin- and proximity-effects have not been taken into account.

The paper includes implication for the worst-case analysis of the coil’s inductance due to mechanical damage or manufacturing tolerance.

This paper fulfills an identified need to study how the inductance change of a coil can be obtained accurately and efficiently.

The impedance compensation approaches have been adopted to achieve the maximum output power and transfer efficiency in many magnetic coupling resonance wireless power transfer projects. However, it remains a challenge to obtain the constant output power and transfer efficiency in a fixed-frequency mode during variations in transfer distance and orientation of the coils. In this paper, using two series transmitting coils to achieve the constant output power and transfer efficiency is used.

First, the circuit model is established and transfer characteristics are studied. Second, using the two series transmitting coils to achieve the constant output power and transfer efficiency is investigated. Finally, the experimental system is designed; it can optimize the transfer performances by itself; the constant output power and transfer efficiency are achieved in the fixed-frequency mode.

When the receiving coil moves between the two series transmitting coils, the tolerance of the output power and transfer efficiency is less than 5 per cent.

When a receiving coil is placed between the two series transmitting coils, there are space limits. The receiving coil only shifts between the two transmitting coils.

However, the rail guide vehicle may achieve constant output power and transfer efficiency when it moves on the rail guide. So, this topology may provide a practical solution.

In this research, the three-coil MCR-WPT system including two series transmitting coils is presented. In a fixed-frequency mode, the constant output power and transfer efficiency is achieved in experiments during variations in transfer distance and orientation of the coils. The fluctuation of the output power and transfer efficiency is less than 5 per cent.

In eddy current nondestructive testing, ferrite-cored probes are usually used to detect and locate defects such as cracks and corrosion in conductive materials. However, the generic analytical model for evaluating corrosion in layered conductor using ferrite-cored probe has not yet been developed. The purpose of this paper is to propose and verify the analytical model of an E-cored probe for evaluating corrosion in layered conductive materials.

A cylindrical coordinate system is adopted and the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived first, and then the expansion coefficients of the solution are obtained by matching the boundary and interface conditions between the regions and the subregions. Finally the closed-form expression of the impedance of the multi-turn coil is derived by using the truncated region eigenfunction expansion (TREE) method, and the impedance calculation is carried out in Mathematica. In the frequency range of 100 Hz to 10 kHz, the impedance changes of the E-cored coil and air-cored coil due to the layered conductor containing corrosion are calculated, respectively, and the influences of corrosion on the coil impedance change are investigated.

An analytical model for the detection and evaluating of corrosion in layered conductive materials using E-cored probe is proposed. The model can quickly and accurately calculate the impedance change of E-cored coil due to corrosion in layered conductor. The correctness of the analytical model is verified by finite element method and experiments.

An accurate theoretical model of E-cored probe for evaluating corrosion of multilayer conductor is presented. The analytical model can be used to detect the inhomogeneity of layered conductor, design ferrite-cored probe or directly evaluate the corrosion defects of layered conductors.