nately, the -in principle infinite-dimensional- size of the HTMs tends to make computations unwieldy, hampering their introduction into the circuit design community. This work introduces powerful techniques that render HTM-based analysis useful for design practice. Analysis of up- and downconversion behavior, time-varying noise analysis and stability analysis are made practical. The tehniques allow us to com- pute both numerical results and symbolic expressions. By exploiting the properties of typical LPTV circuits, we obtain compact approximations that cope with the HTM in- versions induced by feedback loops. Furthermore, it is shown that HTMs make up a very natural representation for frequency-domain modeling of LPTV behavior. Their elements have a well-defined physical meaning that is in close agreement with intuition on the matter. All of this establishes HTMs as a powerful and practical framework for capturing time-varying behavior. Theory on HTMs is applied to several examples. Most notable is the HTM-based analysis of PLL behavior. PLLs allow an easy and exact description in terms of HTMs. For slow PLL feedback loops, this xact-time-varying-description reduces to the well-known time-invariant feedback model. For the first time, this time-invariant model is given solid mathematical underpinnings with its shortcomings clearly identi- fied. Finally, it is also shown how a HTM-based analysis unifies the derivation of both continuous-time and discrete-time PLL models. HTMs, together with the methods developed to perform computations with them, are well suited as a framework to teach structured analysis of LPTV system behavior. They extend intuitions on traditional LTI systems to the more general class of LPTV systems. The methods presented to manipulate them can equally be applied to applications as THIS WORK different as mixers and PLLs. They are suited to obtain both symbolic and numerical results. Oscillator behavior: Oscillators are key building blocks in many telecommunica- tion frontends. They are, amongs