We present algorithms for automated macromodeling of nonlinear mixed-signal system blocks. A key feature of our methods is that they automate the generation of general-purpose macromodels that are suitable for a wide range of time- and frequency-domain analyses important in mixed-signal design flows. In our approach, a nonlinear circuit or system is approximated using piecewise-polynomial (PWP) representations. Each polynomial system is reduced to a smaller one via weakly nonlinear polynomial model-reduction methods. Our approach, dubbed PWP, generalizes recent trajectory-based piecewise-linear approaches and ties them with polynomial-based model-order reduction, which inherently captures stronger nonlinearities within each region. PWP-generated macromodels not only reproduce small-signal distortion and intermodulation properties well but also retain fidelity in large-signal transient analyses. The reduced models can be used as drop-in replacements for large subsystems to achieve fast system-level simulation using a variety of time- and frequency-domain analyses (such as dc, ac, transient, harmonic balance, etc.). For the polynomial reduction step within PWP, we also present a novel technique [dubbed multiple pseudoinput (MPI)] that combines concepts from proper orthogonal decomposition with Krylov-subspace projection. We illustrate the use of PWP and MPI with several examples (including op-amps and I/O buffers) and provide important implementation details. Our experiments indicate that it is easy to obtain speedups of about an order of magnitude with push-button nonlinear macromodel-generation algorithms.

We present a fundamentally new approach, ADME, for extracting highly accurate delay models of a wide variety of digital gates. The technique is based on trajectory-piecewise automated nonlinear macromodelling methods adapted from the mixed-signal/RF domain. Advantages over prior current-source models include rapid automated extraction from SPICE-level netlists, transparent retargetability to different design styles and technologies, and the ability to correctly and holistically account for complex input waveform shapes, nonlinear and linear loading, multiple input switching, effects of internal state, multiple I/Os, supply droop and substrate interference. We validate ADME on a variety of digital gates, including multi-input NAND, NOR, XOR gates, a full adder, a multilevel cascade of gates and a sequential latch. Our results confirm excellent model accuracy at the detailed waveform level and testify to the promise of ADME for sustainable gate delay modelling at nanoscale technologies.

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 8x speedup in average with excellent accuracy in capturing different loading effects, crosstalk, simultaneous switching noise (SSN), etc.

We present a novel, general approach towards model-order reduction (MOR) of nonlinear systems that combines good global and local approximation properties. The nonlinear system is first approximated as piecewise polynomials over a number of regions, following which each region is reduced via polynomial model-reduction methods. Our approach, dubbed PWP, generalizes recent piecewise linear approaches and ties them with polynomial-based MOR, thereby combining their advantages. In particular, reduced models obtained by our approach reproduce small-signal distortion and intermodulation properties well, while at the same time retaining fidelity in large-swing and large-signal analyses, e.g., transient simulations. Thus our reduced models can be used as drop-in replacements for time-domain as well as frequency-domain simulations, with small or large excitations. By exploiting sparsity in system polynomial coefficients, we are able to make the polynomial reduction procedure linear in the size of the original system. We provide implementation details and illustrate PWP with an example.