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

Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode

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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)
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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 Injection pulling; analog frequency dividers; injection-locked frequency dividers (ILFDs); nonlinear oscillators; synchronization; averaging method
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.

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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.

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