Loop Filter Design for Phase-Locked Loops with Delay: A Multi-objective Control Approach

Abstract—Two loop filter design methods for phase-locked loops (PLLs) with loop delay are presented, which employs multi-objective control technique to deal with the various design objectives: small noise bandwidth and large gain and phase margins, etc. Trade-off among the conflicting objectives is made via recently developed convex optimization skill in conjunction with appropriate adjustment of certain design parameters. By applying first-order Padé approximation for the delay term, one of the design methods has the advantage that almost all except one of the filter poles can be assigned a priori. On the other hand, through applying a special coordinate transformation technique, a new PI form loop filter design is also presented. It is noted that both of the proposed methods are applicable to PLL of any order. Numerical simulation on nonlinear PLL model is performed which demonstrates the effectiveness of the proposed methods. Index Terms—PLL, time delay, PI form filter, multi-objectiv