Discrete-time Phase and Delay Locked Loops Analyses in Tracking Mode

Abstract — Phase locked loops (PLL) and delay locked loops (DLL) play an important role in establishing coherent references (phase of carrier and symbol timing) in digital communication systems. Fully digital receiver including digital carrier synchronizer and symbol timing synchronizer fulfils the conditions for universal multi-mode communication receiver with option of symbol rate setting over several digit places and long-term stability of requirement parameters. Afterwards it is necessary to realize PLL and DLL in synchronizer in digital form and to approach to these subsystems as a discrete representation of analog template. Analysis of discrete phase locked loop (DPLL) or discrete delay locked loop (DDLL) and technique to determine their characteristics based on analog (continuous-time) template is performed in this posed paper. There are derived transmission response and error function for 1 st order discrete locked loop and resulting equations and graphical representations for 2 nd order one. It is shown that the spectrum translation due to sampling takes effect at frequency characteristics computing for specific values of loop parameters. Keywords—Carrier synchronization, Coherent demodulation, Software defined receiver, Symbol timing