PRIMA: passive reduced-order interconnect macromodeling algorithm
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
NORM: compact model order reduction of weakly nonlinear systems
Proceedings of the 40th annual Design Automation Conference
Faster, parametric trajectory-based macromodels via localized linear reductions
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
QLMOR: a new projection-based approach for nonlinear model order reduction
Proceedings of the 2009 International Conference on Computer-Aided Design
Bifurcations in Morris-Lecar neuron model
Neurocomputing
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Projection-based approaches for model reduction of weakly nonlinear, time-varying systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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We extend the concept of timing/phase macromodels, previously established rigorously only for oscillators, to apply to general systems, both non-oscillatory and oscillatory. We do so by first establishing a solid foundation for the timing/phase response of any nonlinear dynamical system, then deriving a timing/phase macromodel via nonlinear perturbation analysis. The macromodel that emerges is a scalar, nonlinear time-varying equation that accurately characterizes the system's phase/timing responses. We establish strong links of this technique with projection frameworks for model order reduction. We then present numerical methods to compute the phase model. The computation involves a full Floquet decomposition -- we discuss numerical issues that arise if direct computation of the monodromy matrix is used for Floquet analysis, and propose an alternative method that are numerically superior. The new method has elegant connections to the Jacobian matrix in harmonic balance method (readily available in most RF simulators). We validate the technique on several highly nonlinear systems, including an inverter chain and a firing neuron. We demonstrate that the new scalar nonlinear phase model captures phase responses under various types of input perturbations, achieving accuracies considerably superior to those of reduced models obtained using LTI/LPTV MOR methods. Thus, we establish a powerful new way to extract timing models of combinatorial/sequential systems and memory (e.g., SRAMs/DRAMs), synchronization systems based on oscillator enslaving (e.g., PLLs, injection-locked oscillators, CDR systems, neural processing, energy grids), signal-processing blocks (e.g., ADCs/DACs, FIR/IIR filters), etc..