r by CT-LTI analysis. They model the noise folding caused by the sampling nature of the PFD. High-frequency input noise components, e.g. spurs, are downconverted to baseband. Note that all extra terms are positive. Hence, the resulting baseband noise is, therefore, always worse than the one predicted by LTI techniques. Fig. 4.18 illustrates the impact of noise folding for a white input noise process n(t), i.e. Snn(jw) = Nnoise. Fig. 4.18(a) plots Soooo (joo)/SLT1(j0), the ratio of the PLL's (baseband) phase noise PSD predicted by respectively time-varying and time-invariant 13 The baseband phase noise component is characterized by the element Soooo (jw) of the HPSD matrix See (jw), i.e. the element with indices (0,0). See section 3.5.3 in chapter 3 for notational conventions concerning the elements of HPSD matrices. 4.2.7 Example 2: PLL with mixing PFD analysis. Here, (4.77) This ratio is drawn for several values of WUG/WO. Fig. 4.18(b) shows the output phase noise contributions coming from high-frequency noise components folding into base- band. This corresponds to the lower terms in (4.76). Observing Fig. 4.18(a), it is seen that, for WUG/WO growing large, the PSD predicted by time-varying analysis starts to deviate from the one predicted by time-invariant analysis. This especially holds true for frequencies near zero. Fig. 4.18(b) clarifies the reason for this. While (4.77) pre- dicts the noise PSD to be 0 near W = 0, time-varying analysis predicts a non-zero noise level due to high-frequency components folding into baseband. These components are (silently) neglected when using traditional time-invariant techniques. 4.2.7 Example 2: PLL with mixing PFD The time-varying behavior of a mixing PFD turns out to have less of an impact on a PLL's small-signal performance than that of a sampling PFD. For the setup in Fig. 4.7 and with the mixing PFD HTMs specified by (4.29)-(4.31), the most important HTM elements characterizing the transfers from Oin(t) to the baseband component of ((t) are found to equal Ho,o(s) (4.7