  In this article, we present a new analytical formulation for calculation of
the mutual inductance between two circular filaments arbitrarily oriented with
respect to each other, as an alternative to Grover [1] and Babic [2]
expressions reported in 1944 and 2010, respectively. The formula is derived via
a generalisation of the Kalantarov-Zeitlin method, which showed that the
calculation of mutual inductance between a circular primary filament and any
other secondary filament having an arbitrary shape and any desired position
with respect to the primary filament is reduced to a line integral. In
particular, the obtained formula provides a solution for the singularity issue
arising in the Grover and Babic formulas for the case when the planes of the
primary and secondary circular filaments are mutually perpendicular. The
efficiency and flexibility of the Kalantarov-Zeitlin method allow us to extend
immediately the application of the obtained result to a case of the calculation
of the mutual inductance between a primary circular filament and its projection
on a tilted plane. Newly developed formulas have been successfully validated
through a number of examples available in the literature, and by a direct
comparison with the results of calculation performed by the FastHenry software.
