Efficient Analytical Evaluation of Inductive Coupling Strength in Wireless Power Transfer Systems

The evaluation of inductive coupling between coils of wire is a classic problem of electrical engineering. The accurate modeling of coupled coils has received renewed interest with the spread of wireless power transfer (WPT) systems. This problem has been quite well addressed for coplanar or perfectly coaxial coils but it is known the misalignment conditions easily lead to a sharp decrease of the efficiency. Hence, it is crucial to take misalignment into account in order to properly design the overall WPT system. The aim of this work is to develop an analytical procedure for the efficient calculation of the magnetic flux linkage between parallel flat pancake coils with lateral misalignment. The procedure consists of converting the original integral expression describing the flux into a sum of simpler finite integrals, which may be easily expressed in explicit form. Next, the flux linkage is given as a sum of elementary functions, that is as a combination of powers of geometrical parameters of the problem. The analytical method proves advantageous over numerical techniques in terms of computational speed, often reducing computation time significantly. For instance, analytical methods can achieve results in just a few milliseconds, as opposed to several seconds required by numerical methods like finite element analysis (FEA).