Exact lock-in range for a second-order PLL with discontinuous sawtooth phase detector characteristic

In the present work, we show how the development of the theory of differential equations with discontinuous right-hand sides allows to analyze a modern electronic system used for synchronization of signals. An exact solution to the Gardner problem on the lock-in range is obtained for a second-order type 2 phase-locked loop (PLL) with a sawtooth phase detector characteristic for the first time.