Numerical and analytical investigation of the effects of dimensional parameters on mutual inductance of helical-shaped YBCO superconducting variable inductors

Abstract

High-temperature superconducting coils (HTSCs) have an applied feature in reduction of power air-core inductors losses. This paper presents an analytical method for calculating the mutual inductance of an air-core superconducting variable inductor and investigates the impact of dimensional parameters on the mutual inductance. The proposed method is based on changing the position of a movable inner coil inside an outer coil. A variable inductor may consist of two finite length coaxial helical-shaped coils that their mutual inductance can be changed to achieve a variable inductance. The proposed variable inductor may be further optimized for high-power and high frequency applications and has the potential to be realized in matching circuits technology. To calculate the mutual inductance, a direct and fast method has been employed to solve nonlinear double integration of Neumann’s formula along the current-carrying path that offers two advantages. Firstly, it reduces the computational time comparing to the area-integration methods, especially for complex geometries. Secondly, it can split coil turns accurately as well as other design details that violate axial symmetry. In the end, the Finite Element (FEM) and the loop model methods have been used to verify the results of the analytical method. The analytical and FEM results showed an error of less than 0.064% in the least compatible case.