A class of optimum digital phase locked loops

This paper presents a class of optimum digital filters for digital phase locked loops, for the important case in which the maximum update rate of the loop filter and numerically controlled oscillator (NCO) is limited. This case is typical when the loop filter is implemented in a microprocessor. In these situations, pure delay is encountered in the loop transfer function and thus the stability and gain margin of the loop are of crucial interest. The optimum filters designed for such situations are evaluated in terms of their gain margin for stability, dynamic error, and steady-state error performance. For situations involving considerably high phase dynamics an adaptive and programmable implementation is also proposed to obtain an overall optimum strategy.