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

In contrast to the existing approaches, 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. One advantage of the proposed method is that it allows one to specify the Alter poles in advance. The loop Alter design problem is formulated as an H-infinity optimization problem for which a recently developed convex programming skill (i.e., LMI) is used. Behavior-level simulation, which takes account of the charge-pump current mismatch and the phase frequency detector timing error, is performed.