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Journal of Electrical and Computer Engineering
Volume 2013 (2013), Article ID 246742, 9 pages
Research Article

Investigation on Locking and Pulling Modes in Analog Frequency Dividers

Seconda Università degli Studi di Napoli, Via Roma 29, 81031 Aversa, Italy

Received 3 April 2013; Accepted 10 July 2013

Academic Editor: Mohamad Sawan

Copyright © 2013 Antonio Buonomo and Alessandro Lo Schiavo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We compare the main analytical results available to estimate the locking range, which is the key figure-of-merit of LC frequency dividers based on the injection locking phenomenon. Starting from the classical result by Adler concerning injection-locked oscillators, we elucidate the merits and the shortcomings of the different approaches to study injection-locked frequency dividers, with particular emphasis on divider-by-2. In particular, we show the potential of a perturbation approach which enables a more complete analysis of frequency dividers, making it possible to calculate not only the amplitude and the phase of the locked oscillation, but also the region where it exists and is stable, which defines the locking region. Finally, we analyze the dynamical behaviour of the dividers in the vicinity of the boundary of the locking region, showing that there exists a border region where the occurrence of the locking or the pulling operation mode is possible, depending on the initial conditions of the system.