Fast Methodology for Determining Eye Diagram Characteristics of Lossy Transmission Lines

As the speed of signal through an interconnection increases toward the multigigabit ranges, the effects of lossy transmission lines on the signal quality of printed circuit boards becomes a critical issue. To evaluate the eye diagram and thus the signal integrity in the modern digital systems, this paper proposes a fast methodology that employs only two anti-polarity one-bit data patterns instead of the pseudo-random bit sequence as input sources to simulate the worst-case eye diagram. Analytic expressions are derived for the impulse response of the lossy transmission lines due to the skin-effect loss, while the Kramers-Kronig relations are employed to deal with the noncausal problem related to the dielectric loss. Two design graphs that can be used to rapidly predict the eye diagram characteristics versus the conductive and dielectric losses are then constructed and based on which, the maximally usable length of transmission lines under a certain signal specification can be easily acquired. At last, the time-domain simulations and experiments are implemented to verify the exactitude of proposed concept.