Mathematical model of the phase-locked loop with a current detector

The mathematical model of the pulses phase-locked loop (PLL) with a frequency-phase detector and a current pump, which is represented as a set of difference and transcendental equations and relies on the dynamics of the given deterministic system (in the general case, an arbitrary-order loop filter) described by an automation with a finite number of components and combined differential equations, is examined. An algorithm describing the operation of the in-lock indicator of the given PLL is proposed. The particular cases of the first- and second-order loop filters are discussed. PLL simulation is performed under transient conditions.