Using a modified Modal Series to analyse weakly nonlinear circuits

In this paper, a modified Modal Series to model and analyse weakly nonlinear circuits is introduced. This method not only provides an analytical expression for the response to input signals, as does Volterra Series, the popular method for the analysis of nonlinear circuits, but also provides the response to initial conditions as well as interaction between the initial conditions and the input signals, which Volterra Series does not. The extension of this method to multi-input circuits is straightforward. The method is applied to analyse three examples: a single-stage amplifier, a typical track and hold sampler, and the Colpitts oscillator. The results are discussed and compared with existing methods.