<P> The terms hold - in range, pull - in range (acquisition range), and lock - in range are widely used by engineers for the concepts of frequency deviation ranges within which phase - locked loop - based circuits can achieve lock under various additional conditions . </P> <P> In the classic books on phase - locked loops, published in 1966, such concepts as hold - in, pull - in, lock - in, and other frequency ranges for which PLL can achieve lock, were introduced . They are widely used nowadays (see, e.g. contemporary engineering literature and other publications). Usually in engineering literature only non-strict definitions are given for these concepts . F. Gardner in 1979 in the 2nd edition of his well - known work, Phaselock Techniques, formulated the following problem (p. 70) (see also the 3rd edition (p. 187 - 188)): "There is no natural way to define exactly any unique lock - in frequency". The lack of rigorous explanations led to the paradox: "despite its vague reality, lock - in range is a useful concept" (p. 70). Many years of using definitions based on the above concepts has led to the advice given in a handbook on synchronization and communications, namely to check the definitions carefully before using them . First rigorous mathematical definitions were given in . </P>

Phase locked loop capture range and lock range