dealt with are: Linear periodically time-varying (LPTV) systems: LPTV system behavior comes into play when system or circuit behavior is linearized in the neigh- borhood of a periodic (time-varying) operating point. This work has devel- oped methods that allow us to manipulate LPTV systems in the frequency do- main [Vana02a, Vana02c]. The methods build on the Harmonic Transfer Matrix (HTM) representation of an LPTV system [Maas88, Molloo, Vana02c, Were91a]. HTMs allow us to handle LPTV systems in a manner that is similar to dealing with LTI systems by means of (Laplace- or frequency-domain) transfer func- tions. This work has elaborated the theory of HTMs in full detail, including the frequency-domain characterization of signal transfers, LPTV stability analy- sis and LPTV noise analysis. The HTM framework has been applied to capture mixer and PLL behavior [Vana02a, Vana02c, Vana03a]. With regard to PLLs, our exact time-varying analysis gives solid mathematical underpinnings to a number of traditional (time-invariant) models while identifying their shortcomings. 6.1 MAIN ACHIEVEMENTS Oscillator dynamics: Oscillator behavior is often characterized by the pres- ence of widely spaced time constants. While this often poses a bottleneck to traditional simulation algorithms, it enables the methods presented in this work to explicitly separate the oscillator's slow- and fast-varying signal components. This results in compact models that can be solved very efficiently using a large simulation time step The modeling strategy is solidly grounded on the the- ory of dynamical systems, perturbation analysis and averaging [Bogo61, Kev81, Vana03b]. Applications of the theory involve oscillator phase noise analysis [Vana02d, Vana03c], injection locking behavior [Vana02d] and the construction of behavioral harmonic oscillator models [Vana01c, Vana02b, Vana03b]. More- over, the theory here developed yields clear insights into the basic mechanisms that govern oscillator dynamic behavior (e.g. start-up behavior, etc.). 6.1.1 HTM-bas