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