An RLC interconnect model based on fourier analysis

TLDR

Fourier series analysis is used to model interconnects for periodic signals, noting that aggressor period significantly affects crosstalk noise. The study presents an analytic interconnect model based on Fourier series analysis for periodic signals such as clock signals. The model approximates far‑end waveforms as sums of sinusoids, is applied to RLC interconnect trees with linear computational complexity, and is extended to coupled multi‑interconnect systems for crosstalk analysis, yielding general waveform solutions. Closed‑form expressions for 50% delay and overshoot/undershoot are derived, showing good agreement with SPICE, and the tree model proves effective for clock distribution networks while the extended model accurately captures crosstalk in coupled interconnects.

Abstract

Based on a Fourier series analysis, an analytic interconnect model is presented which is suitable for periodic signals, such as a clock signal. In this model, the far-end time-domain waveform is approximated by the summation of several sinusoids. Closed-form solutions of the 50% delay and overshoots/undershoots are provided when the fifth and higher order harmonics are ignored. Good accuracy is observed between the model and SPICE simulations. The model is applied to resistance-capacitance-inductance interconnect trees and the computational complexity of the model is linear with the size of the tree and the model order. The tree model is shown to be an effective method to analyze clock distribution networks. The single interconnect model is also extended to coupled multi-interconnect systems to analyze crosstalk noise and a general waveform solution is obtained. It is noted that in addition to the transition time, the period of the aggressor signal also has a significant effect on the crosstalk noise.