Mutual Inductance and Force Exerted Between Thick Coils

Progress In Electromagnetics Research, 2009

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.

IEEE Transactions on Magnetics, 2000

We present new and fast procedures for calculating magnetic forces between thin coaxial circular coaxial coils in air. The results are expressed in semianalytical form in terms of the complete elliptical integrals of the first and second kind, Heuman's Lambda function, and a term that must be solved numerically. These expressions are accurate and simple to use for several practical

Journal of Electrical Engineering

The wireless connection distance between the transmission and reception coils of printed circuit boards (PCB) influences the mutual inductance and affects circuit performance. In this study, the mutual inductance M of PCB coils was investigated, and two analytical methods were presented for calculating the mutual inductance between two coaxial rectangular planar PCB coils incorporating magnetic layer. The results were acquired through calculations by using the Neumann integral and Biot-Savart methods. The complete integral calculations and detailed demonstrations of the two methods are presented. The obtained formulas were introduced in some examples of coils with different number of turns. The analytical and experimental results were compared, and a strong agreement between them was observed.

Applied Sciences

The paper describes a new formula for calculating the mutual inductance between a thin conical sheet inductor and a filamentary circular loop, which are coaxial in air. The presented formula is derived semi-analytically using the complete elliptic integrals of the first, second, and third kind, along with the integral term which will be solved numerically. The results are validated using double and single integration methods, as well as the semi-analytical formula. The mutual inductance between a thin cylindrical solenoid and a filamentary circular loop can be obtained using the new formula for the conical coil and circular loop. Presented formulas can be useful in various applications, such as the excitation coil used in electromagnetic-levitation melting, the production of magnetic field homogeneity and broadband RF and wireless power transfer systems that utilize conical inductors. Overall, the paper presents a valuable contribution to the field of inductor design and can be usef...

Progress In Electromagnetics Research B, 2011

Advanced Electromagnetics, 2014

The best analytical formulae for the self-inductance of rectangular coils of circular cross section available in the literature were derived from formulae for the partial inductance of straight wires, which, in turn, are based on the well-known formula for the mutual inductance of parallel current filaments, and on the exact value of the geometric mean distance (GMD) for integrating the mutual inductance formula over the cross section of the wire. But in this way, only one term of the mutual inductance formula is integrated, whereas it contains also other terms. In the formulae found in the literature, these other terms are either completely neglected, or their integral is only coarsely approximated. We prove that these other terms can be accurately integrated by using the arithmetic mean distance (AMD) and the arithmetic mean square distance (AMSD) of the wire cross section. We present general formulae for the partial and mutual inductance of straight wires of any cross section and...

IEEE Transactions on Magnetics, 1992

In conducting media, inductive effects give rise to eddy currents that produce skin effect and proximity effect. In thin wire coils in which the inductive effects are present the current density is forced to remain constant in the coil if the skin depth is larger than the characteristic size of the wire. This paper presents a homogenization technique based on the finite element method, to take into account thin wire coils in twodimensional dynamic magnetic field computations.

IEEE Transactions on Magnetics, 2000

This paper presents an analytical approach for computing the mutual inductance between two air core square coils placed in a flat planar surface. The mutual inductance of the coils is calculated for all possible variations including lateral and angular misalignments in space. In contrast to conventional approximated formulae, the straightforward approach based on Biot-Savart principle is used and their integrals are computed numerically. The results of computed mutual inductance by analytical method are validated by finite element analysis and an experimental setup. Finally, the analysis compares the three mutual inductance calculations: an analytical method, the finite-element model and an experimental results. The values computed by three methods in all cases are in good agreement.

Physics, 2021

In this paper, analytical and semi-analytical formulas are presented for the self- and mutual inductance of thin ordinary disk coils and thin Bitter disk coils. The coils lie concentrically in a plane. The ordinary coils are coils with constant current density. The current density of a current carrying Bitter disc is not uniform across its cross-sectional area, but it is a function of the ratio of the inner diameter of the disk to an arbitrary radius within the disk. In this paper, we show the possibility to calculate the mutual and self-inductance of thin disk coils from the real coils of the cross-sections using some valuable conditions. The formulas for the mutual inductance and the self-inductance were obtained in the semi-analytic form as the combination of the elliptic integral of the second kind and a simple integral for the ordinary disk coils. The mutual inductance and self-inductance were obtained in the analytical form as the elliptic integral of the second kind for the B...

IEEE Transactions on Magnetics, 2000

ABSTRACT This paper presents a synthesis of analytical calculations of magnetic parameters (field, force, torque, stiffness) in cylindrical magnets and coils. By using the equivalence between the amperian current model and the coulombian model of a magnet, we show that a thin coil or a cylindrical magnet axially magnetized have the same mathematical model. Consequently, we present first the analytical expressions of the magnetic field produced by either a thin coil or a ring permanent magnet whose polarization is axial, thus completing similar calculations already published in the scientific literature. Then, this paper deals with the analytical calculation of the force and the stiffness between thin coils or ring permanent magnets axially magnetized. Such configurations can also be modeled with the same mathematical approach. Finally, this paper presents an analytical model of the mutual inductance between two thin coils in air. Throughout this paper, we emphasize why the equivalence between the coulombian and the amperian current models is useful for studying thin coils or ring permanent magnets. All our analytical expressions are based on elliptic integrals but do not require further numerical treatments. These expressions can be implemented in Mathematica or Matlab and are available online. All our models have been compared to previous analytical and semianalytical models. In addition, these models have been compared to the finite-element method. The computational cost of our analytical model is very low, and we find a very good agreement between our analytical model and the other approaches presented in this paper.