Abstract:
The Method of Edge Currents (MEC) proposed in our previous paper [1] is applied herein for calculating the mutual external inductance associated with fringing magnetic fields that wrap ground planes of a stripline structure. This method employs a quasi-static approach, image theory, and direct magnetic field integration. The resultant mutual external inductance is frequency-independent. The approach has been applied to estimating mutual inductance for both symmetrical and asymmetrical stripline structures. Offset of the signal trace from the centered position both in horizontal and vertical directions is taken into account in asymmetrical structures. The results are compared with numerical simulations using the CST Microwave Studio Software.

Abstract:
Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly finite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an integral of a single analytical expression. Sample numerical results are given for some representative cases and the approach to the limit where the turns are considered to be smeared out over the solenoid windings is explored.

Abstract:
We present exact three-dimensional semi-analytical expressions of the force exerted between two coaxial thick coils with rectangular cross-sections. Then, we present a semi-analytical formulation of their mutual inductance. For this purpose, we have to calculate six and seven integrations for calculating the force and the mutual inductance respectively. After mathematical manipulations, we can obtain semi-analytical formulations based on only two integrations. It is to be noted that such integrals can be evaluated numerically as they are smooth and derivable. Then, we compare our results with the filament and the finite element methods. All the results are in excellent agreement.

Abstract:
Systems that employ stimulating and implantable monitoring devices utilize inductive links, such as external and implanted coils. The calculation of the mutual inductance and the magnetic force between these coils is important for optimizing power transfer. This paper deals with an efficient and new approach for determining the mutual inductance and the magnetic force between two coaxial coils in air. The setup is comprised of a thick circular coil of the rectangular cross section and a thin wall solenoid. We use an integro-differential approach to calculate these electrical parameters. The mutual inductance and the magnetic force are obtained using the complete elliptic integrals of the first and second kind, Heuman's Lambda function and one term that has to be solved numerically. All possible regular and singular cases were solved. The results of the presented work have been verified with the filament method and previously published data. The advantage of these proposed formulas for mutual inductance or for the magnetic force is that they give the solution in the analytical and the semi-analytical form either for regular cases or singular cases. It is not case with already known methods in which it is necessary to take particular care of these cases of consideration.

Abstract:
Mutual external inductance (MEI) associated with fringing magnetic fields in planar transmission lines is a cause of socalled "ground plane noise", which leads to radiation from printed circuit boards in high-speed electronic equipment. Herein, a Method of Edge Currents (MEC) is proposed for calculating the MEI associated with fringing magnetic fields that wrap the ground plane of a microstrip line. This method employs a quasi-magnetostatic approach and direct magnetic field integration, so the resultant MEI is frequencyindependent. It is shown that when infinitely wide ground planes are cut to form ground planes of finite width, the residual surface currents on the tails that are cut off may be redistributed on the edges of the ground planes of finite thickness, forming edge currents. These edge currents shrink to filament currents when the thickness of the ground plane becomes negligible. It is shown that the mutual external inductance is determined by the magnetic flux produced by these edge currents, while the contributions to the magnetic flux by the currents from the signal trace and the finite-size ground plane completely compensate each other. This approach has been applied to estimating the mutual inductance for symmetrical and asymmetrical microstrip lines.

Abstract:
For two LC circuits with mutual-inductance, we introduce a new quantization scheme in the context of number-phase quantization through the standard Lagrangian formalism. The commutative relation between the charge operator and the magnetic flux operator is derived. Then we use the Heisenbergequation of motion to obtain the current and voltage equation across the inductance and capacity. The results clearly show how the current and voltage in a single LC circuit are affected by the circuit parameters and inductance coupling coefficient. In addition, adopting invariant eigen-operator method the energy-level gap of the dynamic Hamiltonian which describes two LC circuits with mutual-inductance is obtained.

Abstract:
We present a practical and simple method for calculating the mutual inductance between two non-coaxial circular coils with parallel axes. All possible circular coils such as coils of rectangular cross section, thin wall solenoids, thin disk coils (pancakes) and circular filamentary coils are taken into consideration. We use Grover's formula for the mutual inductance between two filamentary circular coils with parallel axes. The filament method is applied for all coil combinations, for coils of the rectangular cross section and for thin coils. We consider that the proposed method is very simple, accurate and practical for engineering applications. Computed mutual inductance values obtained by the proposed method have been verified by previously published data and the software Fast-Henry. All results are in a very good agreement. This method can be used in various electromagnetic applications such as coil guns, tubular linear motors, transducers, actuators and biomedical implanted sensors.

Abstract:
A live line measurement method for the zero sequence parameters of transmission lines with mutual inductance is introduced. The mathematical models of the measurement method are given. Global Positioning System (GPS) is used as the synchronous signal for the measurement carried out at different substations simultaneously. The measurement system and digital simulation results are given. Finally, the live line measurement results of two 220 kV transmission lines with mutual inductance in Hainangrid are given. Results from both simulation and on-site measurement show that the live line measurement method is feasible, and its measurement accuracy can satisfactorily meet the requirements of engineering measurement.

Abstract:
A toroidal field coil (TFC) is composed of several individual toroidal coils (ITCs), which are connected in a series and distributed in a toroidal and symmetrical form. Cross section of ITCs is rectangular or negligible. This paper presents analytical equations for mutual inductance of two ITCs applicable to Tokamak reactors using the filament method. These equations are based on those formulated by Neumann. The numerical analysis of the integrations resulting from these equations is solved using the extended three-point Gaussian algorithm. The finite element method (FEM) is employed to verify the mutual inductance equations of ITCs. The results obtained using the FEM, when dimensional parameters of ITCs are changed, confirm the analytical and empirical results showing an error of less than 0.2043% in the worst case. This indicates the reliability of the presented equations.

Abstract:
Although matching effects in superconducting anti-dot arrays have been studied extensively through magneto-resistance oscillations, these investigations have been restricted to a very narrow temperature window close to the superconducting transition. Here we report a "two coil" mutual inductance technique, which allows the study of this phenomenon deep in the superconducting state, through a direct measurement of the magnetic field variation of the shielding response. We demonstrate how this technique can be used to resolve outstanding issues on the origin of matching effects in superconducting thin films with periodic array of holes grown on anodized alumina membranes.