Linear Time-Variant Modeling and Analysis of All-Digital Phase-Locked Loops

All-digital phase-locked loops (ADPLL) are inherently multirate systems with time-varying behavior. In support of this statement linear time-variant (LTV) models of ADPLL are presented that capture spectral aliasing effects that are not captured by linear time-invariant (LTI) models. It is analytically shown that the latter are subset of the former. The high-speed ΣΔ modulator that improves the frequency resolution of the digitally-controlled oscillator (DCO) is included, too. It realizes fractional resampling and interpolation of the tuning data of the DCO. The noise transfer from all three operating clock domains of the ADPLL (reference, ΣΔ, and DCO) to its output phase is accurately predicted and design metrics are derived with regard to its folded close-in and far-out phase noise performance. The analytical results are validated via simulations using measured event-driven modeling techniques for a CMOS RF ADPLL.