Nonlinear Analysis of Charge-Pump Phase-Locked Loop: The Hold-In and Pull-In Ranges

In this paper a fairly complete mathematical model of CP-PLL, which reliable enough to serve as tool for credible analysis dynamical properties these circuits, is studied. We refine relevant definitions the hold-in and pull-in ranges related local global stability. Stability steady state charge-pump phase locked loop non-trivial: straight-forward linearization available CP-PLL models may lead incorrect conclusions, because system not smooth near experience overload. work necessary details stability are presented range computed. An upper estimate obtained via limit cycles. The study provided an answer Gardner’s conjecture on similarity transient responses equivalent classical PLL conjectures infinite with proportionally-integrating filter.