An Analytic RLC Model for Coupled Interconnects Which Uses a Numerical Inverse Laplace Transform

In this article, a numerical inverse Laplace transform (NILT)-based algorithm is used to efficiently approximate key characteristics of coupled high-speed VLSI interconnects, such as 50% delay, overshoot, and peak crosstalk. Through the use of a variable (LC or RC) modal decoupling technique, matrix inversion at each time point and pole of the numerical inverse Laplace formula is computed on a diagonal matrix, allowing for minimal computation times at the cost of a slight reduction in accuracy. The proposed methodology independently solves the modal voltage response at each time point, pole, and line allowing for parallel computation resulting in further speed up. In addition, the order of the NILT approximation can be modified depending on the speed and accuracy needed. Four numerical examples of coupled interconnects are presented to evaluate the accuracy and computational efficiency of the proposed methodology. Overall, the NILT-based algorithm provides useful approximations of the time-domain response, while being significantly faster than SPICE.