Automated nonlinear Macromodelling of output buffers for high-speed digital applications

Abstract

We present applications of a recently developed automated nonlinear macromodelling approach to the important problem of macromodelling high-speed output buffers/drivers. Good nonlinear macromodels of such drivers are essential for fast signal-integrity and timing analysis in high-speed digital design. Unlike traditional black-box modelling techniques, our approach extracts nonlinear macromodels of digital drivers automatically from SPICE-level descriptions. Thus it can naturally capture transistor-level nonlinearities in the macromodels, resulting in far more accurate signal integrity analysis, while retaining significant speedups. We demonstrate the technique by automatically extracting macromodels for two typical digital drivers. Using the macromodel, we obtain about 8× speedup in average with excellent accuracy in capturing different loading effects, crosstalk, simultaneous switching noise (SSN), etc..

Automated Model Generation Approach Using MATLAB

“…Model generators can also be categorized into the black, grey or white box approaches, depending on the level of existing knowledge of the system's structure and parameters. Dong et al (Dong and Roychowdhury 2005) indicates that white-box methods can produce more accurate macromodels than black-box methods. However, this work was only applied to a limited number of digital circuits.…”

“…PWP is further implemented in (Dong and Roychowdhury 2004) for extracting broadly applicable general-purpose macromodels from SPICE netlists such that the generated model is able to capture different loading effects, simultaneous switching noise (SSN), crosstalk noise and so on. Furthermore, a speed up of eight times simulation speed is achieved (Dong and Roychowdhury 2005). However, multiple training data has to be used to cover different operating regions.…”

Fast dynamic simulation of VLSI circuits using reduced order compact macromodel of standard cells

“…It can significantly reduce the simulation time and memory requirements [9], [10], [11]. In this section, implementation of reduced order compact macromodel of standard cells is discussed.…”

Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions

“…System (1) is said to be externally stable if the system's output y(t) can be bounded by a function of the system's input u(t). Specifically, the system is said to be small signal input/output stable if there exist constants r 2 > 0 and γ 2 < ∞ such that ||y|| 2 ≤ γ 2 ||u|| 2 (6) for all t > t 0 given initial state x(0) = 0 and input u(t) such that ||u|| ∞ < r 2 . The external and internal stability of System (1) …”

“…Recently there has been a large amount of interest in piecewise-linear (PWL) model order reduction (MOR) techniques [1], [2], [3], [4], [5], [6], [7], [8]. Currently, PWL methods, such as the Trajectory Piecewise-Linear (TPWL) method [9] are probably the only viable known way to handle strongly nonlinear systems.…”