8. Main synchronization

Abstract

In the present chapter the main synchronization of the second order type-I loop is treated. At first, the local stability analysis is presented and closed expressions for the limits of the hold-in range are obtained. From these expressions it becomes evident that, except for time delay, the parameters ξ and ρ of the LPF also affect the width of the hold-in range. This fact is not predicted by the conventional PLL theory which accepts that the holdin range is a function only of the open loop gain [4]-[5]. Then, global stability analysis follows and, except for the interpretation of the capture effect, approximate closed form expressions for the width of the capture range result. After that, the dynamic behaviour of the loop is investigated, and particularly the fast capture (lock-in) process. Closed expressions result for the lock-in time and the beat-note frequency. In addition, the loop tracking capabilities and the effect of noise and disturbances on loop behaviour are examined. Finally, new design criteria for the second order type-I PLL are suggested.