Theory of Periodic Sequence: A Highly-Efficient Signal Integrity Modeling for Ultra-Broadband Transmission Lines

This work introduces and investigates a highly efficient eye diagram model, called the Periodic Eye Diagram (PED), for assessing the performance of ultra-broadband transmission lines from the perspective of signal integrity (SI). The PED model is based on the theory of periodic sequences (TPS), a novel approach for representing the propagation of time-periodic Electromagnetic (EM) waves. Leveraging the parallel nature of EM periodic sequences, the full-wave response of high-speed channels can be rapidly obtained using one-batch multiprocessing. The computational scale remains small due to the inherent frequency-independent property of periodic sequences. Consequently, the PED and its corresponding eye parameters can be derived with both high speed and accuracy. This proposed method holds significant potential for enhancing the analysis and design of emerging ultra-broadband transmission lines with matched loads and manageable discontinuity.