Inductance calculation of planar multi-layer and multi-wire coils: An analytical approach

This paper describes for the first time an analytical algorithm for calculating the inductance of planar multi-wire coils with arbitrary number of parallel wires and layers. The special topology of multi-wire coils, with many parallel wires connected at both endings, allows efficient telemetric energy transfer and low Joule losses due to a reduced DC resistance. The algorithm is based on an integral solution starting from Biot–Savart's law and allows a fast calculation of the coil inductance.The algorithm is verified with a large number of fabricated and measured coils with inductance values ranging from 45 nH to 10 μH. The small coils are microfabricated on a polyimide foil with electroplated gold wires. The larger coils are realized on a printed circuit board. The coils have up to seven parallel wires and two layers. The inductance is measured at 1 MHz and shows good agreement to the calculation results. The error between calculation and measurement is less than 10% and proves the correctness of the presented algorithm.