Entropy 2013, 15(10), 4026-4041; doi:10.3390/e15104026
Article

Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode

Seconda Università di Napoli, Via Roma 29, Aversa (CE) 81031, Italy
* Author to whom correspondence should be addressed.
Received: 12 August 2013; in revised form: 17 September 2013 / Accepted: 18 September 2013 / Published: 25 September 2013
(This article belongs to the Special Issue Dynamical Systems)
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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.
Keywords: Injection pulling; analog frequency dividers; injection-locked frequency dividers (ILFDs); nonlinear oscillators; synchronization; averaging method

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MDPI and ACS Style

Buonomo, A.; Lo Schiavo, A. Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode. Entropy 2013, 15, 4026-4041.

AMA Style

Buonomo A, Lo Schiavo A. Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode. Entropy. 2013; 15(10):4026-4041.

Chicago/Turabian Style

Buonomo, Antonio; Lo Schiavo, Alessandro. 2013. "Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode." Entropy 15, no. 10: 4026-4041.

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