A Discrete-Time Model for the Design of Type-II PLLs With Passive Sampled Loop Filters

are used extensively in electronic systems for frequency synthesis. Recently, a passive sampled loop filter (SLF) has been shown to offer major benefits over the conventional continuous-time loop filter traditionally used in such PLLs. These benefits include greatly enhanced reference spur suppression, elimination of CP pulse-position modulation nonlinearity, and, in the case of phase noise cancelling fractional- PLLs, improved phase noise cancellation. The main disadvantage of the SLF to date has been the lack of a linear time-invariant (LTI) model with which to perform the system-level design of SLF-based PLLs. Without such a model, designers are forced to rely on trial and error iteration supported by lengthy transient simulations. This paper presents an accurate LTI model of SLF-based type-II PLLs that eliminates this disadvantage. Index Terms—Frequency synthesis, phase-locked loop (PLL), PLL linearized model, sampled loop filter (SLF). I