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.