Exact and approximated discrete-time non-linear models of voltage switched CP-PLL

The charge-pump phase locked loop (CP-PLL) is a mixed signal system and it is a challenging task for a designer to analyze the exact switching behavior of the PLL using any general concept of feedback systems. As the order of the loop filter (LF) is enhanced to cancel pre-filter noise and spurious signals, the more complexity in analysis is inevitable. The PLL operating with a voltage switched charge-pump (VSCP) is a complicated system, since the system representation is not unique in all switching states of the phase and frequency detector (PFD). Therefore, it is not possible to characterize the system with a unique transfer function. In this paper, an exact discrete-time non-linear model of the VSCP-PLL is presented using efficient Event Driven (ED) modeling. By assuming a constant voltage at control node in the zero-state, the approximation model is demonstrated, which can be sufficient to use without complicating the analysis up to some extent. The ED-simulation of the exact model is validated using an equivalent transistor level model designed in 130nm CMOS process. The ability of both exact and approximation model is mapped applying a ramping reference frequency.