A simplified hybrid method for calculating the frequency-dependent inductances of transmission lines with rectangular cross section

Abstract

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.

Calculating frequency-dependent inductance of VLSI interconnect by complete multiple reciprocity boundary element method

“…The first category employs the interpolation method [3,4]. For example, paper [4] uses a coupled circuit method to calculate the lowfrequency inductance and the inversion of capacitance matrix for high-frequency inductance, and then forms the full-frequency inductance curve with an interpolation formula.…”

“…The first category employs the interpolation method [3,4]. For example, paper [4] uses a coupled circuit method to calculate the lowfrequency inductance and the inversion of capacitance matrix for high-frequency inductance, and then forms the full-frequency inductance curve with an interpolation formula. Although this category of methods has high computational speed, their reliability and accuracy is very limited because only several interpolation points for very low frequency and very high frequency are computed accurately.…”