Implementation of the Neumann formula for calculating the mutual inductance between planar PCB inductors

In this paper, a method for estimating the mutual inductance between two planar printed circuit board inductors with straight tracks is presented. The thin copper tracks are first modeled as multiple straight line filaments. The Neumann formula, derived from the magnetic vector potential and Faraday's law of induction, gives an analytical solution of the mutual inductance. Unfortunately, due to the complexity of this formula, it can only be solved analytically for relatively simple geometries. However, by following the procedure presented in this paper, the mutual inductance between two arbitrary-positioned and orientated planar PCB inductors can be estimated with reduced computational effort by solving the Neumann formula using numerical integration. The proposed method is demonstrated at the hand of two experiments; and the measured and estimated mutual inductances show excellent agreement with a maximum absolute error of less than 5%.