analysis_of_charge-pump_phase-locked_loops_5392IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS―I: REGULAR PAPERS, VOL. 51, NO. 9, SEPTEMBER 2004 1665 Analysis of Charge-Pump Phase-Locked Loops Pavan Kumar Hanumolu, Student Member, IEEE, Merrick Brownlee, Student Member, IEEE, Kartikeya Mayaram, Senior Member, IEEE, and Un-Ku Moon, Senior Member, IEEE Abstract―In this paper, we present an exact analysis for thirdorder charge-pump phase-locked loops using state equations. Both the large-signal lock acquisition process and the small-signal linear tracking behavior are described using this analysis. The nonlinear state equations are linearized for the small-signal condition and the -domain noise transfer functions are derived. A comparison to some of the existing analysis methods such as the impulse-invariant transformation and -domain analys……