Melnikov’s method applied to accidental phase modulation phenomenon

The performance of clock recovery phase-locked loop (PLL) can be severely degraded by unwanted spurious phase modulation, due to noise and nonlinearities associated with the transmission medium. Consequently, choosing appropriate circuit parameters to avoid or at least reduce these undesirable effects plays a crucial role in achieving a successful PLL circuit. This paper demonstrates that Melnikov’s method, originally proposed to identify chaos in dynamic systems, can be successfully used to establish the appropriate circuit parameters by determining the regions that ensure the correct operation under conditions of noise and nonlinearities, represented by periodic perturbations. This study considers the use of one of the most commonly adopted configurations for clock recovery, the second-order PLL with lag-lead filter, and provides a valuable tool for circuit dimensioning and design of clock distribution networks