A Modified Analytical Calculation Model for Mutual Inductance Between Arbitrarily Oriented Solenoid Coils

Accurate calculation of mutual inductance (MI) between solenoid coils is essential for system design, but complex geometries and spatial arrangements make it challenging. This paper presents a modified analytical method for calculating the MI between two circular-wound air-core solenoid coils arbitrarily oriented in three-dimensional (3D) space. The analytical model used to calculate the MI between two solenoid coils is based on the use of magnetic vector potential (MVP). The helical structure of the solenoid coils is represented by successive coaxial circular filaments arranged along their central axes. Each filament is represented by an equivalent regular polygon with a sufficient number of sides. The proposed approach allows the MI between two solenoid coils to be calculated using a single analytical formula, without imposing restrictions on the relative positions of the coils, while taking lateral and angular misalignments into account. The modified analytical model is validated for accuracy and applicability by comparing its results with experimental measurements and FEM-based simulation results for coil systems with different diameters, turn numbers, and turn pitches. The MI results for various angular and lateral misalignments are in good agreement with experimental measurements and FEM results. The MI calculation model proposed in this work provides a fast and reliable tool for analyzing the electromagnetic behavior of coupled coil systems, designing inductive power transfer systems, and assessing electromagnetic compatibility.