Calculating mutual inductance between circular coils with inclined axes in air

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.