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In this article, we present a new analytical formulation for calculation ofthe mutual inductance between two circular filaments arbitrarily oriented withrespect to each other, as an alternative to Grover [1] and Babic [2]expressions reported in 1944 and 2010, respectively. The formula is derived viaa generalisation of the Kalantarov-Zeitlin method, which showed that thecalculation of mutual inductance between a circular primary filament and anyother secondary filament having an arbitrary shape and any desired positionwith respect to the primary filament is reduced to a line integral. Inparticular, the obtained formula provides a solution for the singularity issuearising in the Grover and Babic formulas for the case when the planes of theprimary and secondary circular filaments are mutually perpendicular. Theefficiency and flexibility of the Kalantarov-Zeitlin method allow us to extendimmediately the application of the obtained result to a case of the calculationof the mutual inductance between a primary circular filament and its projectionon a tilted plane. Newly developed formulas have been successfully validatedthrough a number of examples available in the literature, and by a directcomparison with the results of calculation performed by the FastHenry software.

Efficient calculation of the mutual inductance of arbitrarily oriented circular filaments via a generalisation of the Kalantarov-Zeitlin method