Integral and series solutions for inductance of rectangular coils with parallel end faces

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.