On the Flux Linkage between Pancake Coils in Resonance-Type Wireless Power Transfer Systems

This work presents a series representation for the mutual inductance of two coaxial pancake coils which remains accurate in non-quasi-static regime under the hypothesis that the current in the source coil is uniformly distributed. Making use of Gegenbauer's addition theorem and a term-by-term analytical integration, the mutual inductance between two generic turns belonging to distinct coils is expressed as a sum of spherical Hankel functions with algebraic coefficients. The accuracy and efficiency of the resulting expression is proved through pertinent numerical examples.