Computation of the lock-in ranges of phase-locked loops with PI filter

In the present work the lock-in range of PLL-based circuits with proportionally-integrating filter and sinusoidal phase-detector characteristics are studied. Considered circuits have sinusoidal phase detector characteristics. Analytical approach based on the methods of phase plane analysis is applied to estimate the lock-in ranges of the circuits under consideration. Obtained analytical results are compared with simulation results.