Large time-step integration method for modeling of oscillating circuits

Abstract

A new integration method for highly oscillating circuits is developed. At every integration step, nonlinear transformation is applied to the driving signal represented as the sum of constant and harmonic waveforms in the phase space. Components of the output waveform that consist of higher harmonics in the phase space are transformed back into time space using universal Chebyshev transformation that does not depend upon the nonlinearity of the component. To enable different values of waveform at the end of the time interval, half-frequency components are inserted into signals. The integration step can be equal to, part of, or a multiple of the oscillation period. The method may use a time step that is hundreds of times larger than in plain transient analysis, for example, in Spice simulation. The time step can be fixed or variable to determine the exact length of the oscillation period.