Calculating Mutual Inductance Between Circular Coils With Inclined Axes in Air

Abstract

In this paper we present a lucid, easy, and accurate approach for calculation of the mutual inductance between all inclined circular coils with either rectangular cross section or negligible section. We use Grover's formula for the mutual inductance between two filamentary circular coils with inclined axes that lie in the same plane. Their centers are either displaced along the axis of one coil or displaced along one axis of the first coil and then displaced sideways in addition. We apply the filament method for coil combinations comprising circular coils of rectangular cross section, thin wall solenoids, thin disk coils (pancakes), and filamentary circular coils. In this approach we clarify how Grover's formulas have to be used for different coil combinations in the filament treatment. Thus, two well-known methods (Grover's formulas and the filament method) can be easily used to calculate the mutual inductance between all inclined circular coils, even though the problem is purely three-dimensional.Index Terms-Circular coil of rectangular cross section, filament method, filamentary circular coil, mutual inductance, thin disk coil (pancakes), thin wall solenoid.

Planar Transformers Excited by Square Waves

“…Using results of [39][40][41]43] the self inductances of the coils may be calculated, and using results of [42] the parasitic capacitances of the coils are evaluated. In the case of the coils with the turn number greater than 200, in which the wires are presented with more than one layer, the evaluation of the parasitic capacitances is verified based on frequency of the oscillatory response to step voltage and calculated selfinductance.…”

“…The values in Table 2 referring to transformers in opposite turn number (e.g., 10 × 20 and 20 × 10) are due to the relations of the radius of each one, in accordance to [39][40][41]43].…”

“…These applications may be seen in several researches on electromagnetics fields [33][34][35][36][37][38], considering analysis of their characteristics as self and mutual inductances [39][40][41] or parasitic capacitances [42]. With these feasible applications, an analysis about transformers built with planar coils is presented in this paper, considering the case of square wave excitation, comparing this analysis with the related problems of [19][20][21].…”

A novel dumbbell-shaped coil featured with cross coupling suppression for long distance relay wireless power transfer applications

“…Where mutual inductance M ab can be calculated via Neumann equation [23,24]. The M ab value is affected by the shape, size, and relative position of the coil and the surrounding magnetic medium; it is in inverse proportion to the relative distance d ab between the coil of L a and L b .…”

Mutual Inductance and Force Exerted Between Thick Coils

“…The calculation of mutual inductance for circular coils has been studied by many authors [3][4][5][6][7][8][9][10][11][12]. These papers are generally based on the application of Maxwell's formula, Neumann's formula and the Biot Savart law.…”