The high frequency resistance and inductance of the 3-D complex interconnect structures can be calculated by solving an eddy current electromagnetic problem. In this paper, a model for charactering such a 3-D eddy current problem is proposed, in which the electromagnetic fields in both the conducting and non-conducting regions are described in terms of the magnetic vector potential, and a set of the indirect boundary integral equations (IBIE) is obtained. The IBIEs can be solved by boundary element method, so this method avoids discretizing the domain of the conductors. As an indirect boundary element method, it is of minimum order. It does not restrict the direction of the current in conductors, and hence it can consider the mutual impedance between two perpendicular conductors. The numerical results can well meet the analytical solution of a 2-D problem. The mutual impedance of two perpendicular conductors is also shown under the different gaps between conductors and different frequencies.

A virtual 3-D extractor of the single dielectric is presented in this paper. In the indirect boundary integral equations, the plane charge distribution on the surface of conductors is replaced with mesh charge distribution, and we use the multipole-accelerated algorithm to further depress the computational complexity. Numerical results show that its computational complexity is about O(n), where n is the number of the discrete variables. Within the comparable accuracy, it runs several times faster than the Fastcap, which is a very advanced multipole-accelerated parasitic capacitance extractor now.

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. I.