avior is also worse than predicted by CT-LTI analysis. This is due to noise folding: high-frequency noise components are downconverted, contributing to the low-frequency phase noise content. Noise folding is illustrated in Fig. 4.17 and is caused by the time-varying behavior of the PLL building blocks. Noise folding is responsible for high-frequency spurs appearing in the PLL's close-in phase noise spectrum. Noise folding is readily analyzed by means of the HTM-based noise analysis tech- niques outlined in section 3.5.3 of the previous chapter. Consider, for instance, the VCO noise process n(t) (capturing its phase-noise behavior) injected at the position 4.2.6 Example 1: PLL with sampling PFD Figure 4.17: Noise folding: high-frequency noise components, e.g. spurs, are downconverted, contributing to the PLL's low-frequency phase noise content. indicated in Fig. 4.11. The HTM Anoise(s) that characterizes the transfer of noise to the output phase O(t) can be shown to equal -17-1(a) A(s+jwo) s-jwo (4.74) s+jwo The PLL's output phase noise (at least the part due to the action of the VCO noise) is now characterized by (4.75) Here, Snn (jw) and See(jw) represent harmonic power spectral density (HPSD) matri- ces respectively that correspond to the noise at the VCO's input and the (phase) noise at the VCO's output. If n(t) is stationary and characterized by the power spectral density (PSD) function Snn(jw), then, by evaluating (4.75), it can be shown that the PLL's baseband phase 4.2 PHASE-LOCKED LOOP ANALYSIS W/WUG Figure 4.18: Baseband noise PSD for PLLs using sampling PFDs. (a) Ratio Soooo (ja))/SLT1(jw) between the noise PSD predicted by respectively time- varying and time-invariant analysis. (b) Normalized contributions due to high-frequency noise components folding into baseband. noise content¹³ is characterized by Seooo(jw) = A(jw) (4.76) Here, the first term captures that part of the phase noise as it is (approximately) obtained by means of traditional CT-LTI analysis. The lower terms, however, are unaccounted fo