Mutual inductance of two coaxial rectangular PCB coils incorporating magnetic layer

The wireless connection distance between the transmission and reception coils of printed circuit boards (PCB) influences the mutual inductance and affects circuit performance. In this study, the mutual inductance M of PCB coils was investigated, and two analytical methods were presented for calculating the mutual inductance between two coaxial rectangular planar PCB coils incorporating magnetic layer. The results were acquired through calculations by using the Neumann integral and Biot-Savart methods. The complete integral calculations and detailed demonstrations of the two methods are presented. The obtained formulas were introduced in some examples of coils with different number of turns. The analytical and experimental results were compared, and a strong agreement between them was observed.