Method for Accurate and Efficient Eye Diagram Prediction of Nonlinear High-Speed Links

Signaling analysis of nonlinear high-speed circuits is challenging because it cannot rely on linear time-invariant principles, whereas an exhaustive nonlinear simulation is computationally prohibitive for low bit error rates. To find the worst-case eye, an exhaustive approach requires nonlinear simulations of <tex-math notation="LaTeX">2ᵐ</tex-math> bit patterns for a channel of <tex-math notation="LaTeX">m</tex-math> -bit memory. In this article, we represent the nonlinear responses to the <tex-math notation="LaTeX">2ᵐ</tex-math> inputs by a rank- <tex-math notation="LaTeX">k</tex-math> matrix, where <tex-math notation="LaTeX">k</tex-math> denotes the number of distinct waveforms in the responses for a prescribed accuracy, which is much smaller than <tex-math notation="LaTeX">2ᵐ</tex-math> . We further develop a fast full cross approximation algorithm to find the rank- <tex-math notation="LaTeX">k</tex-math> model with a low complexity independent of <tex-math notation="LaTeX">2ᵐ</tex-math> . Simulations of large-scale real-world nonlinear circuits with an over 100-bit channel memory demonstrate the accuracy, efficiency, and capacity of the proposed work.