e treated as perturbation terms. Here, X E RN represents the circuit's normalized state variables. The first and second term in (5.33) represent a system of autonomous DAEs that capture the oscillator's unperturbed core behavior. The term ef (x, t) represents the perturbation components. Here, E is called a perturbation variable. It labels the corresponding term as small with respect to the other ones. Note that the perturbation term may depend explicitly on the (normalized) time variable T. This is, for example, caused by the presence of a vector of non-zero input sources b(t) = b(t/wo) in (5.6). Since, in this text, these inputs are assumed to be weak , they can be treated as part of the perturbation term ef (x, T). As such, they introduce an explicit dependence on time. Example (Harmonic oscillator): Fig. 5.10 shows two ways to partition an harmonic oscillator with the parts encircled by the dashed lines corresponding to the perturba- tion terms. The choice between both depends on the kind of behavior in which one is interested. In Fig. 5.10(a), one is interested in the oscillator's phase noise behavior, i.e. the oscillator phase shifts induced by noise sources. In that case, the core system corresponds to the noise-free oscillator. Only the noise sources are treated as perturba- tions. In Fig. 5.10(b), we target the harmonic oscillator's settling behavior. Here, the resonant tank -excluding tank losses- corresponds to the oscillator's core system. The feedback transistor currents and the tank losses are treated as perturbation terms. In order for them to be small compared to the current circulating in the resonant tank, the tank's Q-factor must be sufficiently large (about 10 in order of magnitude). Example (Voltage-controlled harmonic oscillator): For the voltage-controlled har- monic oscillator topology in Fig. 5.9, it is indicated in (5.28)-(5.32) how to perform CHARACTERIZING THE OSCILLATOR'S UNPERTURBED CORE the partitioning operation. Here, the terms in the square brackets mark the perturbation terms. I