Mutual-Inductance Computation between Coaxial Thin Conical Sheet Inductor and the Circular Loop in Air

Abstract

The paper describes a new formula for calculating the mutual inductance between a thin conical sheet inductor and a filamentary circular loop, which are coaxial in air. The presented formula is derived semi-analytically using the complete elliptic integrals of the first, second, and third kind, along with the integral term which will be solved numerically. The results are validated using double and single integration methods, as well as the semi-analytical formula. The mutual inductance between a thin cylindrical solenoid and a filamentary circular loop can be obtained using the new formula for the conical coil and circular loop. Presented formulas can be useful in various applications, such as the excitation coil used in electromagnetic-levitation melting, the production of magnetic field homogeneity and broadband RF and wireless power transfer systems that utilize conical inductors. Overall, the paper presents a valuable contribution to the field of inductor design and can be useful in various applications involving conical inductors.