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Journal of Electrical and Computer Engineering
Volume 2013, Article ID 145314, 9 pages
Research Article

Divide-by-Three Injection-Locked Frequency Dividers with Direct Forcing Signal

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

Received 9 April 2013; Accepted 14 June 2013

Academic Editor: Jose Silva-Martinez

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.


Divide-by-three frequency dividers with direct forcing signal are analyzed, and the actual locking mechanism underlying their operation is highlighted. In particular, it is shown that the locking mechanism cannot be explained with the mixing between signals, as commonly made in the literature. An analytical procedure based on the averaging method is developed for solving the equation describing such dividers, and the first approximation to the oscillation in the locked states is predicted. The amplitude and phase of the output voltage in steady state as well as the locking range are derived in terms of the circuit parameters, obtaining useful design guidelines. The derived results are shown to be very close to SPICE simulations for a 0.13 um RF-CMOS process.