Calculating 2-D Capacitance and Frequency-Dependent Inductance of Rectangular Interconnections in IC by Combined Methods

This paper describes combined methods to calculate the frequency-dependent inductances, which combine cross-section coupled circuit method with boundary element method (BEM) solving just Laplace's equation. It can calculate the inductance in the whole frequency range, and at the same time the capacitance matrix can be obtained. The coupled circuit method is used to calculate inductances in low frequency range; The BEM builds the capacitance matrix, then we invert this matrix, obtain inductance relating to the high frequency at which the current only distributes on the surfaces of conductor. A cubic spline interpolation between inductances at low and high frequency gives a good result over the entire frequency range. It avoids solving Helmholtz's equation, greatly reducing the total calculation. Numerical tests show it is applicable.