PULL-IN PERFORMANCE OF FIRST-ORDER PHASELOCKED LOOPS
MITRE CORP BEDFORD MA
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A phase-locked loop is briefly described, together with the derivation of the basic differential equation which governs the dynamic behavior of the loop during the pull-in process. The special case of the pull-in process of the first-order loop when a sine wave of constant frequency is applied to the input of the loop is also described. The relationship between the frequency mistuning of the loop, the initial starting phase angle of the input sine wave, and the time required for the loop to pull in is discussed. The statistical parameters associated with the pull-in time is reviewed. In particular, expressions are given for the probability density function of the pull-in time and the cumulative distribution of the pull-in time.
- Statistics and Probability