NDLI: Generalized nonlinear timing/phase macromodeling: Theory, numerical methods and applications

Content Provider	IEEE Xplore Digital Library
Author	Chenjie Gu Roychowdhury, J.
Copyright Year	2010
Description	Author affiliation: EECS Department, University of California, Berkeley (Chenjie Gu; Roychowdhury, J.)
Abstract	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.
Starting Page	284
Ending Page	291
File Size	17032014
Page Count	8
File Format	PDF
ISBN	9781424481934
ISSN	10923152
e-ISBN	9781424481941
DOI	10.1109/ICCAD.2010.5654174
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-11-07
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Timing Matrix decomposition Orbits Mathematical model Oscillators Equations Approximation methods
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Computer Science Applications Software

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