With higher operating frequencies, transmission lines are required to model global on-chip interconnects. In this paper, an accurate and efficient solution for the transient response at the far end of a transmission line based on a direct pole extraction of the system is proposed. Closed form expressions of the poles are developed for two special interconnect systems: an RC interconnect and an RLC interconnect with zero driver resistance. By performing a system conversion, the poles of an interconnect system with general circuit parameters are solved. The Newton–Raphson method is used to further improve the accuracy of the poles. Based on these poles, closed form expressions for the step and ramp response are determined. Higher accuracy can be obtained with additional pairs of poles. The computational complexity of the model is proportional to the number of pole pairs. With two pairs of poles, the average error of the 50% delay is 1% as compared with Spectre simulations. With ten pairs of poles, the average error of the 10%-to-90% rise time and the overshoots is 2% and 1.9%, respectively. Frequency dependent effects are also successfully included in the proposed method and excellent match is observed between the proposed model and Spectre simulations.
Full On-chip low dropout voltage regulator with an enhanced transient response for low power systems
