t others, needed for channel selection and clock and data recovery, etc. Their behavior is often characterized by the presence of signal com- ponents that vary at widely different rates. This causes simulation times to soar when using traditional algorithms, e.g. SPICE. This poses a problem, especially when run- ning repetitive or lengthy system-level simulations. A second part of this work presents methods to extract compact models that capture an oscillator's dynamics. To do so, these methods exploit the widely spaced time con- stants that characterize the oscillator's behavior. While these time constants often poses a bottleneck to traditional simulation algorithms, they enable the methods here pre- sented to explicitly separate the oscillator's slow- and fast-varying signal components. This results in models that are readily solved using multi-rate simulation techniques whichallows us to greatly boost simulation speed. The modeling strategy is solidly grounded on the theory of dynamical systems, perturbation analysis and averaging. It yields clear insights into the mechanisms that govern oscillator dynamic behavior. Applications of the theory involve oscillator phase noise analysis and modeling the set- tling behavior of harmonic oscillators. As phase noise analysis is concerned, theory is greatly simplified as compared to the current approach based on stochastic differential equations. The harmonic oscillator models provide a means for efficient simulation. The theoretical foundations presented in this work provide a sound basis for under- standing oscillator dynamics. It can be used to teach analysis of oscillator stability, settling and noise behavior. The algorithms for harmonic oscillator behavioral model- ing are readily implemented on top of existing harmonic balance or shooting algorithms as found in commercial simulators. 1.2.2 Math, it's a language Formalizing knowledge requires a language that is accurate enough to describe that knowledge. We must be able to express conditions, perform analyses and