Mathematical Modeling of Phase-Locking Systems with Pulse Modulation

The paper presents a mathematical description of pulse systems and phase synchronization devices using the state variable method. The generalized structural diagram of a pulse system with phase control is analyzed. A mathematical description of the processes occurring in the system in the following operating modes – the number of pulses from the feedback circuit and the number of pulses from the device input are equal, the output signal frequency is less than the specified one is proposed, as well as the frequency detection mode with a significant excess of the feedback circuit signal frequency. The considered mathematical models of the studied class of devices take into account the nonlinear nature of systems operating in the frequency phase detection mode, and significantly reduce the calculation time when modeling processes on a computer.