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A detailed analysis is presented for the inductance calculations of rectangular coils with parallel end faces, with the coils of parallel sides as the special case. Integral solutions are given by the theory of second-order scalar potential. The authors further provide the series solutions for the inductance, which are based on the truncated region eigenfunction expansion method. These series are quite concise and accurate, and with higher computational efficiency by comparison with the integrals. The integral and series solutions are also obtained for the planar rectangular coils. The numerical results of both methods are compared with those of the experimental data, and the proposed methods prove to be accurate and efficient enough for practical applications.

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.

Boundary‐element method (BEM) is applied to the analysis of AC resistance of single‐layer coils. For simplification of the analysis, the coil windings are replaced by a system of parallel straight conductors. Applying the method of images and closed‐form solutions of off‐diagonal matrix elements, and exploiting the symmetry of submatrices, high computational efficiency can be achieved by the proposed approach. As a numerical method, it is suitable for solenoids or pancake coils evenly wound by round or rectangular wires, or other wire shapes with proper symmetry. The proposed method is verified by the numerical results compared with those of finite‐element method (FEM) and measurements, from which it is confirmed that the proposed approach has the same accuracy as the FEM, and the former is much faster and more memory efficient.

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