Piecewise quadratic waveform matching with successive chord iteration

Abstract

While fast timing analysis methods based on model order reduction have been well established for linear circuits, the timing analysis for nonlinear circuits, which are dominant in digital circuits, is usually performed by a SPICE-like, numerical integration-based approach solving differential equations. We propose a new technique that leads to the transient solution 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%.