m performance. Exam- ples discussed in this section concern stability degradation and noise folding. Tradi- tional techniques for PLL analysis, mostly grounded on continuous-time linear time- invariant feedback theory, fail to predict these phenomena. In most cases, they are over-optimistic with regard to the predicted PLL behavior. This may result in erro- neous design decisions. HTM-based analysis of small-signal PLL behavior does not suffer from this drawback. is exact: there are no hidden approximations or assumptions. The only approxima- tions are the ones explicitly introduced during the analysis. This, however, does not mean that approximations aren't useful. They often help simplifying results, focusing attention to what is really important. For example, traditional (and often useful) PLL models are found to be particular (rank-one) approximations to the exact time-varying models. This provides these traditional models with solid mathematical underpinnings while their shortcomings are clearly identified. In summary, small-signal PLL analysis is an excellent example to illustrate the use of HTMs in analyzing real-life system behavior. It emphasizes the practical relevance of the HTM framework in supporting more accurate and reliable system analysis (and hence design). Automated symbolic LPTV system analysis As holds for all pencil and paper analysis, HTM-based computations, especially sym- bolic ones, can be tedious and error prone. This section therefore introduces an al- gorithm, called SymbolicHTM, for semi-automated HTM-based symbolic analysis of LPTV system behavior. In general, symbolic analysis involves the generation of ex- pressions that describe the behavior of a system (circuit) starting from a topological description stated in terms of the system's (circuit's) design variables [Gie91]. Ex- amples of topological descriptions are circuit netlists and block diagrams. Of course, generating expressions is not a goal by itself. As symbolic analysis often aims to in- crease our understanding on the sy