Digital and analog phase lock loops-analysis and applications to digital communication systems

Digital and analog phase lock loops are analyzed along with their applications to digital communication systems. Digital phase lock loops (DPLL) are characterized by zero-tracking of the incoming signals. The equations of operation for first and second order loops are derived and the analyses are confirmed by numerical results and simulation. The application of DPLL's to the optimum discrete-time demodulation of random angle modulated signals is considered. It is shown that the zero-tracking DPLL is a realizable approximation to the maximum a posteriori discrete-time demodulator. The effects of noise and transmission delays in a class of mutual synchronization systems, which employs analog phase lock loops are investigated. The analytical ideas are developed with respect to a hypothetical one station system which contains a first order phase lock loop and extended to a two station system, containing first or second order loops, and then to a mutual synchronization system of arbitrary size. Preliminary results on the transient behavior of a mutual synchronization system are obtained via an examination of the transient performances of one and two station systems. Results are discussed.