 of the averaged state-changing dynamics. This allows us to analyze, for instance, an oscillator's settling behavior and its phase noise behavior. This concludes our overview of the basic concepts underlying the oscillator analysis presented in this chapter. In what follows, we discuss each of the steps in greater depth. Firstly, however, we review previous art on the matter. 5.1.6 Modeling oscillator behavior Earth Electronic oscillator Rloss ef(r,t) Vunperturbed(t) Asin(wot+0) 0.32%/century state changing state changing state changing state changing Figure 5.7: The behavior of both the earth and an electronic oscillator is gov- erned by the same mechanisms. Both can be partitioned in a core system and a set of perturbation terms (encircled by the dashed line). Next, the core sys- tem's behavior is characterized by identifying all of its states (steady-state solutions). The perturbation terms slowly drive the system from one state to another. This causes slow-varying transient dynamics. Finally, averaging helps us to identify the relevant part of the equations that govern the oscilla- tor's state-changing behavior. 5.2 PRIOR ART Prior art In what follows, we briefly review general autonomous system theory, oscillator phase noise theory and methods for numerical simulation. 5.2.1 General theory Over the centuries, the analysis of nonlinear oscillators and their behavior has been subject to many publications. Historically among the first are the treatments on ce- lestial mechanics [Hest87, Suz96]. With the advent of the industrial revolution and its machines, the theory of mechanical vibrations [Kry147, Rand03, Sto50] became a popular area of research. Also, the abstract study of autonomous differential equa- tions resulted in many useful techniques. Here, the work of Krylov, Bogoliubov and Mitropolsky [Bogo61] offers one of the most concise discussions on the matter. They introduce both singular perturbation theory and averaging. Other treatments in this area [Kev81, Murd88, Verhu96] build on similar ideas. With 