AbstractThis paper describes a simplified hybrid method to calculate the frequency-dependent inductances of transmission lines, which combines cross-section coupled circuit method with boundary element method (BEM) just solving Laplace's equation. The coupled circuit method is used to calculate inductance in low frequency range; The BEM builds the capacitance matrix, then we invert this matrix (omit the row and column relate to ground plane), we can obtain inductance relating to the high frequency at which the current only distributes on surfaces of conductor. A cubic spline interpolation between inductance at low and very high frequency gives a good result over entire frequency range. Comparing this method with previous hybrid method [3], it avoids solving Helmholtz's equation and obtains the capacitance matrix at the same time, greatly reducing the total burden of calculation. Numerical tests show it is applicable and efficient.

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In this paper, the methods to solve 3-D eddy current problem are reviewed, and the boundary integral equations of minimum order shows many advantages among them. But its formulations in previous papers have some flaws. So, the limit process to obtain a boundary integral equations (BIE) of minimum order is presented, and the errors in the previous equations are corrected.