Efficient analysis of slow-varying oscillator dynamics

This paper presents a new method to characterize the behavior of an oscillator´s slow-varying modes, e.g., amplitude and phase. Key to the method is the projection of the original set of circuit equations onto the slow manifold defined by the oscillator´s core system. The core system corresponds to the terms of the circuit equations that generate the fast-varying oscillations. The corresponding slow manifold is made up by the core system´s steady-state solutions. By means of perturbation and averaging techniques, we then extract the equations that govern the oscillator´s motion over the slow manifold. These equations correspond to the (slow-varying) dynamics of, for instance, the oscillator´s amplitude, phase or common-mode level. In many cases, they capture that part of the oscillator´s behavior that is of greatest interest. Moreover, since the method here presented explicitly separates the analysis of an oscillator´s fast- and slow-varying behavior, it can be used to improve simulation efficiency or for behavioral model extraction.