Approximate time-domain models of three-dimensional interconnects

Abstract

The time-domain modeling of the connections in a high-speed computer is such of a complexity that practical problems can only be solved using suitable approximations. Presented are the results of a time-domain modeling work where a novel and faster representation of the capacitances has been developed. Instead of a circuit with O(n2) capacitances (where n is the number of conductors), an equivalent circuit of n pseudo-capacitances and n dependent voltage sources is used. Due to the increased sparsity of the simulation matrix, the method considerably speeds up the SPICE or ASTAP compute time. In addition, pseudo-capacitances and voltage sources can be calculated from the coefficient of potential matrix, thus making the calculation of the capacitance matrix unnecessary. This reduces the computational complexity of the capacitance extraction O(n3) to O(n2) resulting in another major speed-up.