Thresholds and Tracking Ranges in Phase-Locked Loops

This paper presents a general discussion of phase-locked-loop thresholds and tracking ranges. A typical phase-locked loop and its linear equivalent are introduced, and there is a brief discussion of application of the root locus method and the Bode amplitude plot to this circuit. Calculation of the maximum allowable deviation is considered for both phase and frequency modulation (sinusoidal). The SNR threshold is a function of tracking and modulation, and may vary considerably. Threshold behavior¿with and without limiting¿is discussed, and methods are presented for estimating the threshold in each case. Calculating the tracking range and variation of the tracking range with threshold variation are also discussed. Since an increase in tracking range and a decrease in threshold are obvious design objectives, procedures are given for achieving these goals. After a description of the effects of interference on tracking and the threshold, there is a brief report of a phase-locked-loop intelligibility study conducted by Philco Western Development Laboratories. Appendixes I-IV consider: 1) a phase-locked loop containing an IF amplifier, 2) designing a loop to track Doppler shift only, and 3) improving the SNR by increasing deviation.