IMS Fast Method for Large-Scale Signaling Analysis of Nonlinear Circuits Including Worst-Case Eye and Bit Error Rate Analysis

Signaling analysis of nonlinear circuits is challenging because it cannot rely on linear time invariant principles, while an exhaustive nonlinear simulation is computationally prohibitive for low bit error rates (BER). To find the worst-case eye as well as BER, an exhaustive approach requires nonlinear simulations of 2
^m
bit patterns for a channel of m-bit memory, where
$m$
can be larger than 100 in today's high-speed and high-performance design. In this work, we develop fast and accurate algorithms for large-scale signaling analysis of nonlinear circuits, including both worst-case eye and BER analysis. In the proposed algorithms, only O(k) nonlinear simulations are required, with
$k$
much less than 2
^m
and independent of 2
^m
. While performing
$k$
nonlinear simulations only, we find an accurate and efficient method to determine the probability density function of the nonlinear responses, from which accurate BER results can be obtained. Simulations of large-scale real-world nonlinear circuits demonstrate the accuracy, efficiency, and capacity of the proposed method.