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L. Ni, S. Pudukotai Dinakarrao, Y. Song, C. Gu, H. Yu:
"A Zonotoped Macromodeling for Eye-Diagram Verification of High-Speed I/O Links With Jitter and Parameter Variations";
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 35 (2016), 6; 1040 - 1051.

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× 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.

Monte Carlo methods;analogue circuits;integrated circuit modelling;parallel processing;reachability analysis;Monte Carlo simulation

http://dx.doi.org/10.1109/TCAD.2015.2481873