Entropy 2013, 15(10), 4026-4041; https://doi.org/10.3390/e15104026
Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode
Seconda Università di Napoli, Via Roma 29, Aversa (CE) 81031, Italy
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Received: 12 August 2013 / Revised: 17 September 2013 / Accepted: 18 September 2013 / Published: 25 September 2013
(This article belongs to the Special Issue Dynamical Systems)
Abstract
We study the phenomenon of periodic pulling which occurs in certain integrated microcircuits of relevant interest in applications, namely the injection-locked frequency dividers (ILFDs). They are modelled as second-order driven oscillators working in the subharmonic (secondary) resonance regime, i.e., when the self-oscillating frequency is close (resonant) to an integer submultiple n of the driving frequency. Under the assumption of weak injection, we find the spectrum of the system’s oscillatory response in the unlocked mode through closed-form expressions, showing that such spectrum is double-sided and asymmetric, unlike the single-sided spectrum of systems with primary resonance (n=1). An analytical expression for the amplitude modulation of the oscillatory response is also presented. Numerical results are presented to support theoretical relations derived. View Full-TextKeywords:
Injection pulling; analog frequency dividers; injection-locked frequency dividers (ILFDs); nonlinear oscillators; synchronization; averaging method
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Buonomo, A.; Lo Schiavo, A. Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode. Entropy 2013, 15, 4026-4041.