Lock-in range of PLL-based circuits with proportionally-integrating   filter and sinusoidal phase detector characteristic
  In the present work PLL-based circuits with sinusoidal phase detector characteristic and active proportionally-integrating (PI) filter are considered. The notion of lock-in range -- an important characteristic of PLL-based circuits, which corresponds to the synchronization without cycle slipping, is studied. For the lock-in range a rigorous mathematical definition is discussed. Numerical and analytical estimates for the lock-in range are obtained. 
K. D. Aleksandrov, N.V. Kuznetsov, G. A. Leonov, M. V. Yuldashev, R.   V. Yuldashev
math.DS