Second-Order Limit-Switched Loop

Abstract

<p>Time Division Multiple Access (TDMA) or burst mode operation of a communication system requires that synchronization be achieved within an alloted preamble time or else the entire data burst may be lost. A conventional phase-locked loop occasionally exhibits a prolonged lock-up time known as hangup, especially when the initial phase error falls within the neighbourhood of 180 degrees, and is therefore not suitable for synchronization of this type of system. The main purpose of this work is to extend the investigation of a modified phase-locked loop which is termed a limit-switched loop (LSL). The LSL offers a faster lock-up time and lower probability of hangup. The transient probability density function (pdf) of the phase error for a first-order LSL and the steady-state pdf of the phase error for the second-order LSL have been obtained, using Fokker-Planck techniques. Simulations and experimental methods have been used to obtain the probability of hangup on a low frequency model which also reveals the optimum range for the switching time.</p>