ior. After a brief reminder on HTM basics in section 4.1, section 4.2 addresses frequency- domain modeling and analysis of PLL small-signal behavior, including the time-varying aspects. Using the HTM formalism, the well-known continuous-time, linear time- invariant (LTI) approximation is extended to take the impact of a PLL's time-varying behavior into account. The main source of this time-varying behavior lies in the nature of the sampling/mixing phase-frequency detector (PFD). Especially for PLLs with a fast feedback loop, this time-varying behavior has severe impact on, for example, loop stability. Hence, it cannot be neglected. Contrary to traditional LTI analysis, HTM- based analysis is able to predict and quantify these effects. As holds for all pencil and paper analysis, HTM-based computations, especially sym- bolic ones, can be tedious and error prone. Section 4.3 therefore introduces an al- gorithm for automated HTM-based symbolic analysis of LPTV system behavior. It demonstrates that traditional techniques for automated symbolic analysis of LTI sys- tems [Fern98, Gie91, Lin91] can be extended to handle LPTV behavior as well. The algorithm is applied to a number of different downconversion stages. 4.1 HTMs in a nutshell The previous chapter elaborated the HTM framework in full mathematical detail. This may have left the impression that it requires an enormous amount of knowledge to 4.1 HTMS IN A NUTSHELL apply HTMs in practice. This is not the case! Anyone mastering frequency-domain LTI system analysis can, with limited effort, get sufficient grasp on HTMs to put them to use in practice. This section summarizes the basic knowledge that is needed to get started. Of course, the better one masters the complete theory on HTMs, the easier it becomes to handle more complex systems. Note that this section can be skipped by readers who feel sufficiently familiar with basic HTM theory. A HTM-based representation of LPTV system behavior relies on the observation that LPTV systems transfer signal content from one f