Optimization of Phase-Locked Loops With Guaranteed Stability

Phase-locked loops (PLL) have found applications in many industrial applications such as communication and control systems. The key requirements are stability and loop performance in terms of signal-to-noise ratio and tracking errors. Here we present a two-step approach to PLL design. First, we present a Lyapunov approach to analyze the loop stability. The parameter range that can guarantee stability can be easily derived in the process. Second, we present a multi-objective optimization method that can search a set of values within the above range of parameters to achieve an optimal trade-off between loop bandwidth, transient and steady-state performance. Simulation results are contained to illustrate the performance of our procedure.