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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| Format: | Article |
| Language: | English |
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IEEE
2025-01-01
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| 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. |
| format | Article |
| id | doaj-art-affd81e8c59f4a3fac988bc97f678e87 |
| institution | DOAJ |
| issn | 2644-1225 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Circuits and Systems |
| 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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