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Generalized Analytical Equations for Injected Ring Oscillator With $RC$ -Load.

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Title: Generalized Analytical Equations for Injected Ring Oscillator With $RC$ -Load.
Authors: Hazeri, Ali Reza1, Miar-Naimi, Hossein1
Source: IEEE Transactions on Circuits & Systems. Part I: Regular Papers. Jan2018, Vol. 65 Issue 1, p223-234. 12p.
Subjects: Injection locked oscillators, Load forecasting (Electric power systems), Differential equations
Abstract: In this paper, a new efficient circuit level analysis is introduced considering the effect of all harmonics and multi-injection for locking and pulling phenomena in $N$ -stage differential and single-ended ring oscillators with the $RC$ -load. Analytical equations are derived for the locking range in both single- and multi-injection cases. At the beginning, using a nonlinear approach, the voltage amplitude and frequency of $RC$ -load free running ring oscillators are derived as simple closed-form equations. Then, to analyze the mentioned phenomena, differential equations describing the circuit behavior are derived by circuit level equations. Furthermore, analyses are extended for general multi-injections with arbitrary amplitude and excess phase for different output nodes. The simplest and most accurate analytical equation is achieved for the locking range. In contrary to few previous works, the proposed analysis is derived directly from equations governing ring oscillators so that we can expect results with more accuracy without any tedious and time-consuming pre-processing like perturbation projection vector. To evaluate the analysis, many simulations have been performed. Simulation results validate presented analytical equations, which provide useful design insights. Absolute percent error of all proposed equations in comparison with simulation results is better than 20%. [ABSTRACT FROM PUBLISHER]
Copyright of IEEE Transactions on Circuits & Systems. Part I: Regular Papers is the property of IEEE 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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DbLabel: Engineering Source
An: 127252310
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  Data: Generalized Analytical Equations for Injected Ring Oscillator With $RC$ -Load.
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  Data: <searchLink fieldCode="AR" term="%22Hazeri%2C+Ali+Reza%22">Hazeri, Ali Reza</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Miar-Naimi%2C+Hossein%22">Miar-Naimi, Hossein</searchLink><relatesTo>1</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22IEEE+Transactions+on+Circuits+%26+Systems%2E+Part+I%3A+Regular+Papers%22">IEEE Transactions on Circuits & Systems. Part I: Regular Papers</searchLink>. Jan2018, Vol. 65 Issue 1, p223-234. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Injection+locked+oscillators%22">Injection locked oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Load+forecasting+%28Electric+power+systems%29%22">Load forecasting (Electric power systems)</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, a new efficient circuit level analysis is introduced considering the effect of all harmonics and multi-injection for locking and pulling phenomena in $N$ -stage differential and single-ended ring oscillators with the $RC$ -load. Analytical equations are derived for the locking range in both single- and multi-injection cases. At the beginning, using a nonlinear approach, the voltage amplitude and frequency of $RC$ -load free running ring oscillators are derived as simple closed-form equations. Then, to analyze the mentioned phenomena, differential equations describing the circuit behavior are derived by circuit level equations. Furthermore, analyses are extended for general multi-injections with arbitrary amplitude and excess phase for different output nodes. The simplest and most accurate analytical equation is achieved for the locking range. In contrary to few previous works, the proposed analysis is derived directly from equations governing ring oscillators so that we can expect results with more accuracy without any tedious and time-consuming pre-processing like perturbation projection vector. To evaluate the analysis, many simulations have been performed. Simulation results validate presented analytical equations, which provide useful design insights. Absolute percent error of all proposed equations in comparison with simulation results is better than 20%. [ABSTRACT FROM PUBLISHER]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IEEE Transactions on Circuits & Systems. Part I: Regular Papers is the property of IEEE 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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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1109/TCSI.2017.2726100
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 12
        StartPage: 223
    Subjects:
      – SubjectFull: Injection locked oscillators
        Type: general
      – SubjectFull: Load forecasting (Electric power systems)
        Type: general
      – SubjectFull: Differential equations
        Type: general
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      – TitleFull: Generalized Analytical Equations for Injected Ring Oscillator With $RC$ -Load.
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            NameFull: Hazeri, Ali Reza
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            NameFull: Miar-Naimi, Hossein
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              Text: Jan2018
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              Y: 2018
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            – TitleFull: IEEE Transactions on Circuits & Systems. Part I: Regular Papers
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