| As operating frequencies increase and device sizes decrease, the complexity of modern circuits are putting enormous pressures on computer aided design tools. In the VLSI area, interconnect effects such as signal delay, cross-talk, ringing, reflections and distortion can severely effect the signal integrity of designs. In addition, susceptibility of high-speed circuits to incident fields can also influence the signal integrity of networks. Consequently, circuit designers must consider interconnect analysis to ensure circuit performance and reliability. However, the modeling of high-speed interconnects using conventional circuit simulators such as SPICE can become prohibitively CPU expensive.; In this thesis, efficient algorithms for the simulation of high-speed interconnects are presented. The methods are based on a matrix rational approximation (MRA) of an exponential function used to describe the solution of Telegrapher's equation. The transmission line parameters of the macromodel can be lossy, coupled and frequency-dependent. An advantage of the MRA algorithm is that the macromodel can be formulated analytically in terms of predetermined coefficients and the per-unit-length parameters. In addition the proposed algorithm is passive. Passivity is an important property to satisfy to ensure stability of the overall network. The MRA algorithm is also compatible with passive model order reduction techniques based on congruence transformations. In addition, the MRA algorithm can be used to perform sensitivity analysis and to predict the effect of incident fields on interconnects. |
