On the Mutual Inductance between Non-Coaxial Coplanar Circular Loops

A simple and efficient explicit solution is derived for the mutual inductance of two non-coaxial coplanar circular loops, which is valid in the quasi-static as well as non-quasi-static frequency ranges. The solution is obtained by rigorously evaluating the Sommerfeld Integral describing the inductance, starting from expanding the integrand into a power series of the loop radius. As a result, a sum of simpler integrals is obtained, and term-by-term analytical integration is straightforwardly performed. The inductance is finally expressed as a series of spherical Hankel functions, with algebraic coefficients depending on the electrical size of the loops. Conducted numerical tests lead to conclude that, accuracy being equal, the proposed expression offers advantages in terms of time cost over conventional numerical integration techniques.