Analytical Solutions for Distributed Interconnect Models—Part II: Arbitrary Input Response and Multicoupled Lines

Analytical Solutions for Distributed Interconnect Models—Part II: Arbitrary Input Response and Multicoupled Lines In this paper, a new method is presented to calculate the exact analytical solution of distributed RC, LC, and RLC interconnects with a random input at an arbitrary point through the line. The proposed method, based on a modified Duhamel theorem, is used to calculate the time-domain transient response of the initially conditioned interconnects. This method is applied to a line driven by ramp and exponential inputs. The new analytical solutions are expressed as an infinite summation of sinusoidal terms. However, a negligible worst case error of <1% is observed for the expressions compared with HSPICE simulations for Fourier series with tens of terms. In addition, from these results a new model for transient response of a line considering the driver output resistance and capacitance is presented. Good accuracy is observed between the model and HSPICE simulations for various distributed interconnects and drivers. Furthermore, the developed solution is extended to include signal transient and crosstalk noise in multicoupled inductive-effect-prominent lines. In addition, arbitrary switching patterns for identical and nonidentical lines are investigated employing the new method and evaluated with HSPICE simulations.