Analytical study of mutual inductance of hexagonal and octagonal spiral planer coils

This paper presents a closed form formula for the mutual inductance of coaxial hexagonal and octagonal planar spiral coils. For analysis, spiral coils are assumed to be composed of concentric filaments and Biot-Savart law has been utilized to scrutinize the mutual inductance between two filaments. Two planar spiral coils of seven turns is simulated in Ansys Maxwell software and fabricated on FR4 substrate to demonstrate the validity of the proposed formulas. Calculation results also have been confirmed by Grover formula for the mutual inductance of two identical hexagonal and octagonal filaments. The measurement and simulation results are in very good agreement with calculation that indicates the feasibility of theoretical formulas.