Analysis of first and second order binary quantized digital phase-locked loops for ideal and white Gaussian noise

Specific configurations of first and second order all digital phase locked loops were analyzed for both ideal and additive white Gaussian noise inputs. A design for a hardware digital phase locked loop capable of either first or second order operation was examined along with appropriate data obtained from testing of the hardware loop. All parameters chosen for the analysis and the design of the digital phase locked loop were consistent with an application to an Omega navigation receiver although neither the analysis nor the design were limited to this application. Ideal inputs were considered for both first and second order digital phase locked loops with the objective of classifying the time response of the loops. For both loops it was found that the phase error response was given by a nonlinear difference equation for which no direct solution was found. Partial response characteristics of the phase error were determined for both the first and second order loops when the frequency of the input signal is identical to that of the loop's quiescent frequency.