Magnetic Coupling between Coplanar Filamentary Coil Antennas with Uniform Current

This letter presents an analytical solution for the mutual inductance of two coplanar filamentary coil antennas. First, the Sommerfeld integral describing the flux linkage between two coplanar turns is converted into a double-integral involving the product of two Bessel functions. Next, analytical integration is performed after replacing the Bessel function that depends on the radii of the coils with its Maclaurin expansion. As a result, the flux linkage between single- or multi-turn pancake coils can be expressed as a combination of spherical Hankel functions. Numerical tests are performed to show the advantages of the proposed approach in terms of accuracy and time cost.