Loop filter design for third-order charge-pump PLL using linearized discrete-time model

A new loop filter design for third-order charge-pump phase locked loops is presented. The design is based on a discrete-time model with loop delay. In addition to the closed-loop stability, this method deals with the practical considerations: ripple swing, reference spur, and stability margin. Some of which are derived in terms of linear matrix inequalities (LMIs). Trade-off among the conflicting objectives is made via recently developed convex programming tools. System-level simulation, which takes into account the charge-pump current mismatch and the phase frequency detector timing error, is performed.