n to PLLs and their applications can be found in [Gard79]. In a lot of applications, PLLs are among those blocks whose performance is crucial in meeting system-level specifications. Hence, adequate and correct analysis of their behavior is of great importance. Traditionally, PLLs are handled as LTI feedback loops [Gard79]. However, the behav- ior of many PLL building blocks exhibits time-varying components. In an LTI model, these components are simply neglected. However, as the PLL feedback loop grows faster, time-varying behavior becomes important as it causes, for example, stability degradation and noise folding. Analyzing these phenomena therefore requires theory and methods to capture a PLL's time-varying behavior. This chapter analyzes PLL time-varying behavior using HTM-based methods. means HTMs, we are able to predict and quantify the aspects of a PLL's behavior that are due to the time-varying nature of its building blocks. The analysis establishes rigorous mathematical underpinnings for PLL small-signal analysis. In doing so, it demarcates the region of validity of traditional PLL models build on LTI theory. The discussion on time-varying PLL behavior is organized as follows. Section 4.2.1 introduces a PLL's basic architecture together with a short discussion on its building blocks. Next, section 4.2.2 reviews prior art on modeling and analysis of PLLs. In section 4.2.3, we provide a brief discussion on the construction of signal models ap- propriate for analyzing PLL behavior. Section 4.2.4 continues with models for the behavior of the PLL building blocks. These models are expressed in terms of HTMs. In section 4.2.5, the building block models are connected in order to obtain the input- output HTM of the overall PLL. Sections 4.2.6 and 4.2.7 show practical results by applying the method to PLLs implemented respectively using a sampling and a mixing PFD. Finally, in section 4.2.8 we come to the conclusions. 4.2.1 PLL architectures and PLL building blocks charge pump loop filter frequency divider input Fi