A Zonotoped Macromodeling for Eye-Diagram Verification of High-Speed I/O Links With Jitter and Parameter Variations

Abstract

It is challenging to efficiently evaluate the performance bound of high-precision analog circuits with input and parameter variations at nano-scale. With the use of zonotope to model uncertainty of input data pattern (or jitter) and multiple parameters, a reachability-based verification is developed in this paper to compute the worst-case eye-diagram. The proposed zonotope-based reachability analysis can consider both spatial and temporal variations in one-time simulation. Moreover, a nonlinear zonotoped macromodeling is further developed to reduce the computational complexity. Performance bound for I/O links considering the parameter variations are evaluated. In addition, the eye-diagrams are generated by the proposed zonotoped macromodel for performance evaluation considering both temporal and spatial variations. As shown by experiments, the zonotoped macromodel achieves up to $450 {\times }$ speedup compared to the Monte Carlo simulation of the original model within small error under specified macromodel order for high-speed I/O links eye-diagram verification.