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Nonlinear Analyses of Unsymmetrical Locking Range of Injected Cross-Coupled Oscillator.

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Title: Nonlinear Analyses of Unsymmetrical Locking Range of Injected Cross-Coupled Oscillator.
Authors: Mohammadjany, Armin1 (AUTHOR), Hazeri, Ali Reza2 (AUTHOR) Alireza.Hazeri@iau.ac.ir, Miar-Naimi, Hossein1 (AUTHOR)
Source: Circuits, Systems & Signal Processing. Dec2024, Vol. 43 Issue 12, p7548-7563. 16p.
Subjects: Circuit elements, Tangent function, Differential equations, Inverse functions, Nonlinear analysis
Abstract: In this article, two accurate nonlinear methods are proposed to calculate non-symmetrical locking ranges of the Injected Cross-Coupled Oscillator (ICCO) with the parallel RLC tank and series RL with a parallel C tank for both weak and strong injection levels. By writing governing differential equations of circuit elements of the ICCO, graphical presenting of current vectors, and using the averaging method for solving nonlinear equations, equations of the ICCO are simplified. Then, exact non-symmetrical locking ranges are calculated using the iterative method. Moreover, the describing function of the oscillator's nonlinear part, an inverse tangent function, is applied to the model. The inverse tangent function generates complicated governing differential equations of circuit elements that are accurate. Then, it is solved to ICCO for the first time and has novel results for calculating non-symmetrical locking ranges. There is a good agreement between theoretical and simulation results. The proposed non-symmetrical locking ranges are accurate in both weak and strong injections. The absolute percent of errors for various levels of the injection signal is less than 20%. In the bargain, proposed locking ranges are the most accurate compared to previously published results. [ABSTRACT FROM AUTHOR]
Copyright of Circuits, Systems & Signal Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Nonlinear Analyses of Unsymmetrical Locking Range of Injected Cross-Coupled Oscillator.
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  Data: <searchLink fieldCode="AR" term="%22Mohammadjany%2C+Armin%22">Mohammadjany, Armin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hazeri%2C+Ali+Reza%22">Hazeri, Ali Reza</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> Alireza.Hazeri@iau.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Miar-Naimi%2C+Hossein%22">Miar-Naimi, Hossein</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Circuits%2C+Systems+%26+Signal+Processing%22">Circuits, Systems & Signal Processing</searchLink>. Dec2024, Vol. 43 Issue 12, p7548-7563. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Circuit+elements%22">Circuit elements</searchLink><br /><searchLink fieldCode="DE" term="%22Tangent+function%22">Tangent function</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+functions%22">Inverse functions</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+analysis%22">Nonlinear analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this article, two accurate nonlinear methods are proposed to calculate non-symmetrical locking ranges of the Injected Cross-Coupled Oscillator (ICCO) with the parallel RLC tank and series RL with a parallel C tank for both weak and strong injection levels. By writing governing differential equations of circuit elements of the ICCO, graphical presenting of current vectors, and using the averaging method for solving nonlinear equations, equations of the ICCO are simplified. Then, exact non-symmetrical locking ranges are calculated using the iterative method. Moreover, the describing function of the oscillator's nonlinear part, an inverse tangent function, is applied to the model. The inverse tangent function generates complicated governing differential equations of circuit elements that are accurate. Then, it is solved to ICCO for the first time and has novel results for calculating non-symmetrical locking ranges. There is a good agreement between theoretical and simulation results. The proposed non-symmetrical locking ranges are accurate in both weak and strong injections. The absolute percent of errors for various levels of the injection signal is less than 20%. In the bargain, proposed locking ranges are the most accurate compared to previously published results. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Circuits, Systems & Signal Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00034-024-02834-8
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 7548
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      – SubjectFull: Circuit elements
        Type: general
      – SubjectFull: Tangent function
        Type: general
      – SubjectFull: Differential equations
        Type: general
      – SubjectFull: Inverse functions
        Type: general
      – SubjectFull: Nonlinear analysis
        Type: general
    Titles:
      – TitleFull: Nonlinear Analyses of Unsymmetrical Locking Range of Injected Cross-Coupled Oscillator.
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            NameFull: Hazeri, Ali Reza
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            NameFull: Miar-Naimi, Hossein
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            – D: 01
              M: 12
              Text: Dec2024
              Type: published
              Y: 2024
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            – TitleFull: Circuits, Systems & Signal Processing
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