An LMI-Based Method for Reference Spur Reduction in Charge-Pump Phase-Locked Loops Containing Loop Delay

This paper presents a loop-filter design method for third-order charge-pump phase-locked loops containing the loop delay. This method is derived from a z-domain phase-locked loop model. For a given loop bandwidth, we employ ripple swing control and adjust the filter pole to improve the spur performance. Another dynamic specification, the jitter peaking, is formulated as a H ∞ performance. The loop-filter design is transformed into an H ∞ optimization problem with the ripple swing constraint, which is solved using convex programming skills (linear matrix inequality, LMI). Compared to the conventional method, the method proposed in this study offers greater spur reduction without altering the loop bandwidth.