A Comparison of Second, Third, and Fourth Order Phase-Locked Loops

This paper presents data describing various performance characteristics of phase-locked loops, which were obtained for the purpose of determining an optimum selection of system order in view of typical operating conditions. With the functions optimized with respect to particular performance characteristics, calculations of the integrated square error and peak error with polynomial inputs are presented in terms of the noise bandwidth; and the generalized error coefficients are also provided in terms of the bandwidth with consideration for the use of both perfect and imperfect integrators. With specific input functions as provided by signals transmitted from earth satellites, an improved performance is demonstrated with the use of the higher order loops, and experimental results verify the calculations and also demonstrate the feasibility of the fourth order loop design.