Nonlinear Analysis of Differential <italic>LC</italic> Oscillators and Injection Locked Frequency Dividers

A comprehensive nonlinear analysis of autonomous and periodically forced fully-differential, negative-resistor LC oscillators is presented. Through nonlinear transformations in the state space, it is shown that oscillators within this class exhibit qualitatively similar dynamical behavior in terms o...

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Main Authors: Konstantinos Metaxas, Vassilis Alimisis, Costas Oustoglou, Yannis Kominis, Paul P. Sotiriadis
Format: Article
Language:English
Published: IEEE 2025-01-01
Series:IEEE Open Journal of Circuits and Systems
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Online Access:https://ieeexplore.ieee.org/document/10904493/
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author Konstantinos Metaxas
Vassilis Alimisis
Costas Oustoglou
Yannis Kominis
Paul P. Sotiriadis
author_facet Konstantinos Metaxas
Vassilis Alimisis
Costas Oustoglou
Yannis Kominis
Paul P. Sotiriadis
author_sort Konstantinos Metaxas
collection DOAJ
description A comprehensive nonlinear analysis of autonomous and periodically forced fully-differential, negative-resistor LC oscillators is presented. Through nonlinear transformations in the state space, it is shown that oscillators within this class exhibit qualitatively similar dynamical behavior in terms of their limit cycles and bifurcation curves, at least within an open region containing the origin. The case of autonomous, complementary BJT oscillators is used to validate the qualitative analysis and demonstrate a general approach of how to numerically extend the bifurcation curves away from the equilibrium point and determine the oscillatory conditions. When external periodic force is present, we focus on the special case of periodically multiplicatively-forced fully-differential, negative-resistor, LC oscillators and use Harmonic Balance techniques to derive analytical expressions estimating the locking range in the weak injection regime. The results are used to calculate the locking range of a harmonically forced complementary BJT oscillator yielding explicit expressions closely aligned with experimental measurements, thus verifying the validity of the analysis.
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spelling doaj-art-affd81e8c59f4a3fac988bc97f678e872025-08-20T02:55:53ZengIEEEIEEE Open Journal of Circuits and Systems2644-12252025-01-01610010910.1109/OJCAS.2025.354590410904493Nonlinear Analysis of Differential <italic>LC</italic> Oscillators and Injection Locked Frequency DividersKonstantinos Metaxas0https://orcid.org/0009-0006-6569-1860Vassilis Alimisis1https://orcid.org/0000-0002-2090-1493Costas Oustoglou2https://orcid.org/0000-0003-0915-8886Yannis Kominis3https://orcid.org/0000-0002-5992-7674Paul P. Sotiriadis4https://orcid.org/0000-0001-6030-4645School of Electrical and Computer Engineering, National Technical University of Athens, Athens, GreeceSchool of Electrical and Computer Engineering, National Technical University of Athens, Athens, GreeceSchool of Electrical and Computer Engineering, National Technical University of Athens, Athens, GreeceSchool of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, GreeceSchool of Electrical and Computer Engineering, National Technical University of Athens, Athens, GreeceA comprehensive nonlinear analysis of autonomous and periodically forced fully-differential, negative-resistor LC oscillators is presented. Through nonlinear transformations in the state space, it is shown that oscillators within this class exhibit qualitatively similar dynamical behavior in terms of their limit cycles and bifurcation curves, at least within an open region containing the origin. The case of autonomous, complementary BJT oscillators is used to validate the qualitative analysis and demonstrate a general approach of how to numerically extend the bifurcation curves away from the equilibrium point and determine the oscillatory conditions. When external periodic force is present, we focus on the special case of periodically multiplicatively-forced fully-differential, negative-resistor, LC oscillators and use Harmonic Balance techniques to derive analytical expressions estimating the locking range in the weak injection regime. The results are used to calculate the locking range of a harmonically forced complementary BJT oscillator yielding explicit expressions closely aligned with experimental measurements, thus verifying the validity of the analysis.https://ieeexplore.ieee.org/document/10904493/Bifurcation analysisinjection-locked frequency dividers (ILFDs)locking range (LR)nonlinear oscillatorsharmonic balancesynchronization
spellingShingle Konstantinos Metaxas
Vassilis Alimisis
Costas Oustoglou
Yannis Kominis
Paul P. Sotiriadis
Nonlinear Analysis of Differential <italic>LC</italic> Oscillators and Injection Locked Frequency Dividers
IEEE Open Journal of Circuits and Systems
Bifurcation analysis
injection-locked frequency dividers (ILFDs)
locking range (LR)
nonlinear oscillators
harmonic balance
synchronization
title Nonlinear Analysis of Differential <italic>LC</italic> Oscillators and Injection Locked Frequency Dividers
title_full Nonlinear Analysis of Differential <italic>LC</italic> Oscillators and Injection Locked Frequency Dividers
title_fullStr Nonlinear Analysis of Differential <italic>LC</italic> Oscillators and Injection Locked Frequency Dividers
title_full_unstemmed Nonlinear Analysis of Differential <italic>LC</italic> Oscillators and Injection Locked Frequency Dividers
title_short Nonlinear Analysis of Differential <italic>LC</italic> Oscillators and Injection Locked Frequency Dividers
title_sort nonlinear analysis of differential italic lc italic oscillators and injection locked frequency dividers
topic Bifurcation analysis
injection-locked frequency dividers (ILFDs)
locking range (LR)
nonlinear oscillators
harmonic balance
synchronization
url https://ieeexplore.ieee.org/document/10904493/
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AT costasoustoglou nonlinearanalysisofdifferentialitaliclcitalicoscillatorsandinjectionlockedfrequencydividers
AT yanniskominis nonlinearanalysisofdifferentialitaliclcitalicoscillatorsandinjectionlockedfrequencydividers
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