model without the VCO overload was suggested by M. van Paemel in 1994 and then refined by N. Kuznetsov et al. in 2019. The closed form mathematical model of CP-PLL taking into account the VCO overload is derived in.

These mathematical models of CP-PLL allow to get analytical estimations of the hold-in range (a maximum range of the input signal period such that there exists a locked state at which the VCO is not overloaded) and the pull-in range (a maximum range of the input signal period within the hold-in range such that for any initial