4. Main synchronization

Abstract

In this chapter the main synchronization of the first order PLL is discussed. At first, we perform the local stability analysis of the main synchronization, which results in closed mathematical expressions for the limits of the synchronization (hold-in) region. Next, the ability of the VCO to follow phase and frequency variations of the reference signal is investigated and closed expressions for the tracking limits are obtained. After that, the global dynamical behaviour of the first order loop is examined and the limits of the capture region are concluded. The analysis confirms the coincidence of the hold-in and capture ranges in the first order PLL. In addition, closed expressions for the settling time of the synchronization process (lock-in time) and the frequency of the beat-note during detuning are derived.