Oscillator-AC: restoring rigour to linearized small-signal analysis of oscillators

Standard small-signal analysis methods for circuits break down for oscillators because small input perturbations result in arbitrarily large output changes, thus invalidating fundamental assumptions for small-signal analysis. In this paper, we propose a novel oscillator-AC (OAC) approach remedying this situation, thus restoring validity and rigour to small-signal analysis of oscillators. Our approach centers around a novel, general equation formulation for circuits that we term the GeMPDE. A key feature of our approach is to solve for bivariate frequency variables with the help of novel augmenting phase condition equations. Our GeMPDE-based small-signal analysis provides both amplitude and frequency characteristics in a unified manner and is applicable to any kind of oscillator described by differential equations. We obtain speedups of 1-2 orders of magnitude over the transient simulation approach commonly used today by designers for oscillator perturbation analysis. We also demonstrate and explain how our linearization approach captures the inherently nonlinear phenomenon of injection locking in oscillators.