A Frequency Estimation Insight for Analyzing Synchronization Stability of Frequency-Locked Loop

Frequency-locked loop (FLL) has a lower computational cost than the phase-locked loop (PLL) in solving dc offset, unbalanced components, and harmonics. For the synchronization stability analysis, the FLL is usually regarded as an equivalent PLL with an amplitude-filtered normalization unit, introducing the time-variant amplitude coefficient involved in the nonlinear phase dynamics. If the conventional linearization model is used by approximating the phase nonlinearity and omitting the time-variant coefficient, the obtained stabilizing condition is not accurate enough. This work analyzes the FLL from a frequency estimation insight to avoid analyzing the phase dynamics. This insight utilizes inherently smoother frequency estimation dynamics than the equivalent frequency of the synchronized phase. Thus, a frequency-oriented linearization model is developed without involving the phase states. This model provides a more accurate dynamic prediction and a stronger stabilization condition than the conventional linearization analysis. Also, the obtained conditions are concise without depending on the phase states, which differ from the large-signal synchronization stability analysis. More importantly, the proposed insight is feasible for the highly-popular second-order generalized integrator-based FLL. Simulation and experimental validated the above claims.