Development of mutual inductance formula for misaligned planar circular spiral coils

The mutual inductance, M, is a key figure of merit in all magnetically coupled systems, but it plays an especially crucial role in the design of loosely coupled coils used in inductive power transfer (IPT) systems. This paper presents a new closed form expression for the mutual inductance of planar circular spiral coils also known as Archimedean coils. This new expression, which is derived using the magnetic vector potential, accounts for both coil-to-coil separation and axial misalignment distances. In what follows, the analytical formulation is first presented. Next, MATLAB is used to evaluate the resulting expression over a wide range of separation and misalignment distances and corresponding plots are obtained. Finally, a physical prototype is built, tested, and its measured mutual inductance is compared against the previously obtained analytical results.