Pull-in range of phase-lock circuits with arbitrary feedback filter

Existing methods for the theoretical determination of the capture range of selected automatic phase control loops, using a sin (¿-phase comparator, are analysed. From the results of this analysis, an equivalent method to the one used by Goldstein in his treatment of loops with sawtooth comparator is developed that can be applied to a wider variety of interesting loop filters. The method is based on the experimentally suggested hypothesis that all non-synchronized states of loops of most interest are asymptotically periodic. A function is derived which allows quick determination of the capture range of most stable a.p.c. loops containing one large integration time-constant in their filter branch. The method is directly applied to a few technically interesting cases, and very good agreement with experimental results is found.