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## Volume 12, Issue 3 Metrics 0

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Energies 2019, 12(3), 566; https://doi.org/10.3390/en12030566

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

School of Electrical Engineering, Wuhan University, Wuhan 430072, China
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Received: 30 December 2018 / Revised: 3 February 2019 / Accepted: 4 February 2019 / Published: 12 February 2019
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# 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. View Full-Text
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0). MDPI and ACS Style

Zhou, X.; Chen, B.; Luo, Y.; Zhu, R. Analytical Calculation of Mutual Inductance of Finite-Length Coaxial Helical Filaments and Tape Coils. Energies 2019, 12, 566.

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