INDUCTANCE EFFECTS IN RLC TREES

Abstract

A closed form solution for characterizing voltage-based signals in an RLC tree is presented. The closed form solution is used to derive figures of merit to characterize the effects of inductance at a specific node in an RLC tree. The effective damping factor of the signal at a specific node in an RLC tree is shown to be one useful figure of merit. It is shown that as the effective damping factor of a signal increases, an RC model is sufficiently accurate to characterize the waveform. The rise time of the input signal driving an RLC tree is shown to be a second factor that affects the relative significance of inductance. As the rise time of the input signal increases as compared to the effective LC time constant at a specific node within an RLC tree, the signal at this node will no longer exhibit the effects of inductance. It is demonstrated that a single line analysis to determine the importance of including inductance to characterize an interconnect line that is a part of a tree is invalid in many cases and can lead to erroneous conclusions. The error exhibited by single line analysis is due to the large interaction among the branches of the tree.