A physical model for the transient response of capacitively loaded distributed RLC interconnects

Rapid approximation of the transient response of high-speed global interconnects is needed to estimate the time delay, crosstalk, and overshoot in a GSI multilevel wiring network. This paper outlines a rigorous and physical solution for transients in a capacitively-loaded distributed RLC interconnect using a convergent series of modified Bessel functions. Compact models for time delay and repeater insertion are derived. The single-line model is extended to evaluate crosstalk in two-coupled lines. These solutions are validated by HSPICE simulation, and have potential applications to rapid RLC timing analysis, global wire sizing and repeater insertion, signal integrity estimation, and reliability modeling (e.g. voltage overshoot and high current density concerns).