scillator's fast- and slow-varying signal components. This allows us to use a much larger simulation time step than possible when solving the original set of circuit equations. This in turn results in shorter simulation times. On a related issue, the averaged equations can be used to construct compact be- havioral models. These models can be solved efficiently using a large simulation time step. They are readily implemented in almost any environment for system- level simulation (Matlab/Simulink, VHDL-AMS, etc.) and are especially useful for running lengthy or repetitive system-level simulations. The method provides a powerful framework to handle often complex nonlinear behavior. Besides for numerical analysis, it can also be used to obtain symbolic expressions that describe the oscillator's dynamics. These expressions are of great help during those stages of a design when not all parameters have been given a suitable value yet. This chapter presents examples on how to derive symbolic expressions that characterize an oscillator's injection locking behavior and the settling behavior of an harmonic (LC-based) oscillator. From a theoretical point of view, the averaging methods here presented yield a simplification of the proof of existing results on oscillator phase noise analysis. This part of the work culminated in a semi-analytic method for the computation of an oscillator's entire phase noise spectrum [Vana03c]. In short, this method shows quite some good and novel results with regard to the (sym- bolic and numerical) analysis of an oscillator's dynamic behavior. 5.3 OSCILLATOR CIRCUIT EQUATIONS control IM(Vgate>Ydrain) Figure 5.9: Harmonic oscillator circuit topology. Here, the resistors with val- ues R/2 model the inductor losses, IM (Vgate, Vdrain) denotes the drain-source current of a MOS transistor and the capacitors Cg capture some small (tran- sistor) capacitances. 5.3 Oscillator circuit equations The behavior of an oscillator circuit is described by the system of differential-algebraic equations (DAEs) co