Fast and Precise Method for Inductance Calculation of Coaxial Circular Coils With Rectangular Cross Section Using the One-Dimensional Integration of Elementary Functions Applicable to Superconducting Magnets

Analysis of Inductance Calculation of Coaxial Circular Coils With Rectangular Cross Section Using Inverse Hyperbolic Functions

“…According to the works in [7] and [11], the mutual inductance of coils 1 and 2 in Fig. 1 can be calculated by…”

“…2) Evaluation of G 0 and G π : When evaluating G 0 and G π , the work in [11] claimed that the L'Hopital rule could be applied to F in (4), but an examination of F shows that F has infinite limits at ϕ = 0 and ϕ = π; hence, the L'Hopital rule cannot be applied to F . In fact, it is the combination of F in (3) that has finite limits at ϕ = 0 and ϕ = π, where the infinite limits of F cancel out.…”

“…I 4 and I 5 in (10) can be independently replaced by any expression in Table I with their expressions of X listed in Table II, and Y = Y 0 in (11). To be consistent, I 4 and I 5 are usually replaced by the same branch.…”

“…Later, this method was improved by Luo and Chen for the case of self-inductance calculation [10]. Recently,Zupan et al presented a fast and precise method as an alternative to the method in [7], which was demonstrated to be the fastest method among the aforementioned methods [11]. However, a close inspection reveals minor errors in the reasoning of the method, and the method can be further improved if inverse hyperbolic functions are utilized.…”

“…However, a close inspection reveals minor errors in the reasoning of the method, and the method can be further improved if inverse hyperbolic functions are utilized. This paper presents the improved version, along with related topics, such as the treatment of singularities and the reason why the expression in [11] is relatively complex.…”