A Study in the Frequency Warping of Time-Domain Methods

This thesis develops a study for the frequency warping introduced by time-domain methods. The work in this study focuses first on the time-domain methods used in the classical SPICE engine, that is the Backward Euler, the Trapezoidal Rule and the Gear's methods. Next, the thesis considers the newly developed high-order method based on the Obreshkov formula. This latter method was proved to have the A-stability and L-stability properties, and is therefore robust in circuit simulation. However, to the best of the author's knowledge, a mathematical study for the frequency warping introduced by this method has not been developed yet. The thesis therefore develops the mathematical derivation for the frequency warping of the Obreshkov-based method. The derivations produced reveal that those methods introduce much smaller warping errors than the traditional methods used by SPICE. In order to take advantage of the small warping error, the thesis develops a shooting method framework based on the Obreshkov-based method to compute the steady-state response of nonlinear circuits excited by periodical sources. The new method demonstrates that the steady-state response can be constructed with much smaller number of time points than what is typically required by the classical methods