n order for them to be small, it must hold that both 1/Q << 1 and Cg/2C << 1. All others terms are assigned to the oscillator's core system. Note that this partitioning operation is functional and not physical. For example, in (5.28)-(5.32), the inductive part of the coil is classified as being part of the core system while the inductor losses are labeled as perturbation terms. Physically, however, it is impossible to separate a coil's inductive and resistive behavior. The partitioning operation discussed above is by no means trivial. It is hard to construct a general-purpose algorithm that accomplishes an appropriate partitioning for arbitrary oscillator topologies. In this work, no attempts are made to do SO and all partitionings in the examples are done manually. However, in sections 5.7 and 5.8, we outline parti- tioning strategies that allow us to handle oscillator phase noise analysis and harmonic oscillator behavior. These partitioning strategies basically correspond with the ones in Fig. 5.10. 5.4 Characterizing the oscillator's unperturbed core Next, we characterize the oscillator's unperturbed core system. This core system is described by the equations (5.34) These equations result when the perturbation term ef(x,t) in (5.33) is neglected. Char- acterizing the core system requires us to find all states, i.e. all steady-state solutions XS (t,p) that solve (5.34). In this work, a steady-state solution is defined as being pe- riodic. Furthermore, we assume all periodic steady-state solutions to have the same period T7. Mathematically, this is expressed as (5.35) x,(t+7,p) = x,(t,p) (5.36) Here, p E RP is a constant parameter vector that identifies a particular steady-state solution, i.e. it identifies a particular state of the unperturbed core system. For this reason, p is called the system's state vector. The set of all points in RN that lie on one of the steady-state solutions XS (T,p), i.e. (5.37) is assumed a P-dimensional stable manifold that quickly attracts all other solutions of 7In a more general 