Passivity Enforcement for Method of Characteristics-based Multiconductor Transmission Line Macromodels

In the recent past, method of characteristics (MoC) has emerged as an efficient macromodeling and simulation technique for long high-speed transmission lines with low loss. However, one of the major limitations of this technique is that, the resulting interconnect macromodels are not guaranteed to be passive, which can lead to non-physical unstable transient responses during simulation. In order to address this problem, we present a new passivity compensation algorithm for non-passive MoC-based multiconductor transmission line (MTL) macromodels. The algorithm is based on the first-order perturbation of the non-passive macromodel and can handle single as well as coupled interconnects. A sample numerical example is presented to validate the efficiency of the algorithm.