Worst case timing jitter and amplitude noise in differential signaling

Differential signaling is widely used in high speed data communications. Inter-symbol interference (ISI) and crosstalk between differential pair, however, heavily affect the integrity of differential signaling as measured by timing jitter and amplitude noise in the eye diagram. To reduce the impact of ISI, a pre-emphasis filter is commonly used, but it increases the crosstalk noise. In this paper, we first propose formula-based jitter and noise models considering the combined effect of ISI, crosstalk, and pre-emphasis filter. With given input patterns, our models achieve within 5% difference compared to SPICE simulation. Moreover, using the formula-based models, we develop mathematical programming algorithms to directly find out the input patterns for worst-case jitter and worstcase amplitude noise. Experiments show our algorithms obtain more reliable worst-case jitter and noise compared to Monte Carlo simulation and reduce runtime by 150times.