Interconnection modelling using distributed RLC models

In physical design software, it is often necessary to estimate net, i.e. interconnection delays. Interconnections are typically modelled as lumped RC circuits. This approximation is reasonable in technologies where overall delay is dominated by gate delays. With present sub 130 nm technologies, characteristic signal propagation lengths are comparable to signal wavelengths. Interconnections no longer allow currents to flow through efficiently, resulting in a conspiracy of capacitative, resistive and inductive effects. In recent years, more accurate interconnections models, that approximate an interconnection as n distributed RLC segments, have been devised. In this work, we let the number of segments go to infinity and obtain exact expressions for voltages. In particular, we present a mathematically rigorous time-domain analysis of the Lossy Transmission Line Model.