Transient analysis of lossy interconnects by modified method of characteristics

In this paper, the modified method of characteristics (MMC) is presented to analyze lossy interconnects. The method applies lower order Taylor approximation to model the characteristic admittance, and further applies lower order Pade approximation to model propagation functions of a transmission line. However, different from the single-point or multipoint moment-matching approaches, this method does not generate a reduced-order model of a transmission line prior to constructing the system matrix. Instead, it takes a special expansion and directly incorporates the coefficients of the expansion into the modified nodal admittance (MNA) matrix. On the basis of the specific expansion, a set of time-domain recursive formulae is derived, which concerns only the quantities at the ends of transmission lines. The recursive formulae are similar to those of method of characteristics (MC), with some added modifications. Based on the formulae of MMC, an equivalent time-domain macromodel of a uniform lossy transmission line is obtained. It can be easily implemented within the framework of an existing circuit simulator such as SPICE. The examples indicate that the method gives accurate time-domain simulation of interconnects in high-speed IC systems