Calculation of the Mutual Inductance and the Magnetic Force Between a Thick Circular Coil of the Rectangular Cross Section and a Thin Wall Solenoid (Integro-Differential Approach)

Abstract

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.

Simple Method to Calculate the Force Between Thin Walled Solenoids

“…Yang and Hull present expressions to obtain force and torque between square loops [7]. Babic et al present formulas for the calculation of magnetic forces between: coaxial cylindrical magnets and thin coils [8], thick rectangular coils and thin walled solenoids [9], inclined circular coils [10], and misaligned thick coils with parallel axes [11]. Shiri and Shoulaie present a method that is useful to calculate the force between planar spiral coils [12], and also calculates the electromagnetic force distribution on a coil [13].…”

Mutual Inductance Calculation Between Misalignment Coils for Wireless Power Transfer of Energy

“…The mutual inductance of such configurations has been obtained over series expressed by Legendre polynomials [1][2][3]. Recently, a considerable work has been done in the calculation of the mutual inductance between circular coils with parallel and inclined axes using improved Grover's formulas elliptic integrals, Bessel and Strouve functions [5][6][7][8][9][10][11][12][13]. The problem can be directly tackled using purely numerical methods such as finite and boundary element methods.…”

THE EQUIVALENT SELF-INDUCTANCE OF <I>N</I> COUPLED PARALLEL COILS

“…The problem of coupled coils and their application, in parallel or in series, is one of the most important subjects and permanent topics in the fields of electromagnetism and electro-technology [1][2][3][4][5]. In recent years, renewed attention has been aroused [4,5].…”

“…In recent years, renewed attention has been aroused [4,5]. The equivalent self-inductance of N uncoupled coils, whether for the series or the parallel case, can be calculated by using the corresponding formula for the complex impedance of alternating current.…”