Piecewise quadratic waveform matching with successive chord iteration

  • Authors:
  • Zhong Wang;Jianwen Zhu

  • Affiliations:
  • University of Toronto, Ontario, Canada;University of Toronto, Ontario, Canada

  • Venue:
  • Proceedings of the 2004 Asia and South Pacific Design Automation Conference
  • Year:
  • 2004

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Abstract

While fast timing analysis methods based on model order reduction have been well established for linear circuits, the timing analysis for non-linear circuits, which are dominant in digital circuits, is usually performed by a SPICE-like, numerical integration-based approach solving differential equations. In this paper, we propose a new technique that leads to the transient so lution of charge/discharge paths with a complexity equivalent to only K DC operating point calculations, where K is the number of transistors along the path. This is accomplished by approximating each nodal voltage as a piecewise quadratic waveform, whose characteristics can be determined by matching the charge/discharge currents calculated by the capacitive components and the resistive components. Successive chord method is then applied to reduce the matrix construction and inversion overhead. Experiments on a wide range of circuits show that an average of 20 times speed-up over HSPICE simulation (transient time only) with 10 picosecond step size can be achieved, while maintaining an average accuracy of 98.03%.