Worst-Case Estimation for Data-Dependent Timing Jitter and Amplitude Noise in High-Speed Differential Link

Differential signaling has been widely used in high-speed interconnects. Signal integrity issues, such as inter-symbol interference (ISI) and crosstalk between the differential pair, however, still cause significant timing jitter and amplitude noise and heavily limit the performance of the differential link. The pre-emphasis filter is commonly used to reduce ISI but may potentially change the crosstalk behavior. In this paper, we first propose formula-based jitter and noise models considering the combined effect of ISI, crosstalk, and pre-emphasis filter. With the same set of input patterns, experiment shows our models achieve within 5% difference compared with SPICE simulation. By utilizing these formula-based models, we then develop algorithms to directly find out the input patterns for worst-case jitter and worst-case amplitude noise through pseudo-Boolean optimization (PBO) and mathematical programming. In addition, a heuristic algorithm is proposed to further reduce runtime. Experiments show our algorithms obtain more reliable worst-case jitter and noise compared with pseudorandom bit sequences simulation and, meanwhile, reduce runtime by 25× when using a general PBO solver and by 150× when using our proposed heuristic algorithm.