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Evaluating the spectrum of periodic pulling in subharmonic resonant LC circuits
Author(s) -
Buonomo Antonio,
Lo Schiavo Alessandro
Publication year - 2015
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2047
Subject(s) - inductor , subharmonic , rlc circuit , capacitor , electronic circuit , lc circuit , spectrum (functional analysis) , resonance (particle physics) , frequency divider , topology (electrical circuits) , describing function , signal (programming language) , physics , equivalent circuit , voltage , control theory (sociology) , mathematics , computer science , engineering , electrical engineering , nonlinear system , quantum mechanics , control (management) , optoelectronics , cmos , artificial intelligence , programming language
Summary We analyze the features of the oscillations arising in forced inductor–capacitor (LC) oscillators when they operate in the periodic pulling mode, under the action of a weak injection signal. In radio frequency integrated circuits, both voltage‐controlled oscillators subject to undesired couplings and injection‐locked frequency dividers behave like forced LC oscillators. These are modeled as second‐order driven oscillators working in the subharmonic (secondary) resonance regime. The analysis is based on the generalized Adler's equation, which we introduce to describe the phase dynamics of dividers of any division ratio and to derive closed‐form expressions for the spectrum components of the system's oscillatory response. We show that the spectrum is double‐sided and asymmetric, unlike the single‐sided spectrum of systems with primary resonance. Numerical and experimental results are given to validate the presented results, which significantly generalize those available in the literature. Copyright © 2014 John Wiley & Sons, Ltd.