Analytical Calculation of Mutual Inductance of Finite-Length Coaxial Helical Filaments and Tape Coils

Xinglong Zhou, Baichao Chen, Yao Luo and Runhang Zhu
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Xinglong Zhou: School of Electrical Engineering, Wuhan University, Wuhan 430072, China
Baichao Chen: School of Electrical Engineering, Wuhan University, Wuhan 430072, China
Yao Luo: School of Electrical Engineering, Wuhan University, Wuhan 430072, China
Runhang Zhu: School of Electrical Engineering, Wuhan University, Wuhan 430072, China

Energies, 2019, vol. 12, issue 3, 1-20

Abstract: Mutual inductance between finite-length coaxial helical filaments and tape coils are presented analytically. In this paper, a mathematical model for finite-length coaxial helical filaments is established, and subsequently, the mutual inductance of the filaments is derived in a series form, containing a one-dimensional integral. The mutual inductance expression of the filaments is then generalized for a tape conductor. When the tape conductor of each coil is closely wound, then the inverse Mellin transform is further utilized for transforming the generalized integral in the mutual inductance expression into a series involving hypergeometric functions, for increasing the calculation speed. Finally, the obtained expressions are compared numerically with the existing analytical solutions and finite-element simulation in order to verify the correctness and general applicability of the results. In this paper, as all the mutual-inductance analytical expressions are concise with fast convergence, it is easy to obtain the numerical results in software, such as Mathematica. The expressions presented in this paper are applicable to any corresponding geometric parameter, and are thereby more advantageous compared to the existing analytical methods. In addition, evaluation by these expressions is considerably more efficient, as compared to finite element simulation.

Keywords: helical coils; modified Bessel functions; mutual inductance; magnetic field; inverse Mellin transform (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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