A Closed-Form Transient Response of Coupled Transmission Lines

There is a growing interest in analysis of crosstalk noise and delay in coupled transmission lines in various fields. Due to the large number of interconnections and associated compression, this analysis is particularly significant in large integrated circuits. There are various ways to analyze crosstalk noise and delay considering the compromise between accuracy and complexity. This article presents closed-form expressions in the Laplace domain based on transmission line theory to obtain crosstalk noise and delay of identical and nonidentical coupled interconnections. To this end, a simple model is proposed, which encompasses both capacitive and inductive coupling features in coupled interconnections. Moreover, it serves to handle both functional and dynamic crosstalk. The crosstalk noise voltage and propagation delay at the far-end of coupled lines are observed. The transient response of coupled transmission lines is demonstrated for various case studies. The obtained results are compared with Advanced Design System simulations indicating that the proposed model computes crosstalk noise and captures waveform shapes with desired accuracy. Moreover, the derived form is scalable for the analysis of N coupled multiconductors, opening new horizons to analyze the complex integrated circuit interconnections with decent accuracy and high computation speed.