-62.76 dB -54.47 dB Table 5.1: Harmonic content of the steady-state common-mode waveform respectively obtained from first-order averaging results and SPICE-like sim- ulation results. Due to higher-order perturbation components, results start to deviate significantly from the 6th harmonic on. In summary, averaging is a powerful method for the analysis and modeling of an os- cillator's dynamic behavior. It allows us to obtain numerical results as well as sym- bolic expressions. In the sections to come, we demonstrate its practical use for both the analysis of oscillator phase behavior and for behavioral model extraction. Furthermore, it is shown that averaging not only simplifies the analysis of an oscillator's determin- istic dynamics, e.g. settling and stability, but also that of its stochastic behavior, e.g. phase noise. 5.7 Oscillator phase (noise) analysis The methods outlined above can be used to model an oscillator's phase (noise) behav- ior [Dem00a, Dem00b, Dem02, Kae90, Haji98, Vana02d]. For this particular applica- tion, the perturbation analysis presented in section 5.5 reduces to the one in [Dem00a, Dem00b]. Hence, this work embeds existing theories on oscillator phase behavior within a more global framework. Phase (noise) behavior concerns the prediction of oscillator phase shifts induced by the injection of small (noise) currents and/or voltages into the circuit. With regard to this particular application, Fig. 5.22(a) illustrates how to partition the oscillator circuit. The core system corresponds to the input-free oscillator while the perturbation terms are associated with the injected currents and/or voltages, e.g. noise. For a single exter- nal input u(T) E R, the (normalized) circuit equations corresponding to this setup are written as (5.102) Here, X E RN contains the circuit's state variables. The injected signal u(T) can be either a deterministic signal or a noise process. The strength (standard deviation) of this signal (random process) is assumed to be well below that of the current and volt