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A Phasor-Based Analysis of Sinusoidal Injection Locking in LC and Ring Oscillators.

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Title: A Phasor-Based Analysis of Sinusoidal Injection Locking in LC and Ring Oscillators.
Authors: Hong, Brian, Hajimiri, Ali
Source: IEEE Transactions on Circuits & Systems. Part I: Regular Papers. Jan2019, Vol. 66 Issue 1, p355-368. 14p.
Subjects: Phasor measurement, Injection locked oscillators, Integrated circuits
Abstract: A new perspective into the locking behavior of LC and ring oscillators is presented. By decomposing a sinusoidal injection current into in-phase and quadrature-phase components, exact expressions for the amplitude and phase of an injection-locked LC oscillator which hold for any injection strength and frequency are derived and confirmed by simulation. The analysis, which can be naturally extended to an arbitrary LC resonator topology, leads to a rigorous understanding of the fundamental physics underlying the locking phenomenon. Furthermore, an investigation of the different necessary and sufficient conditions for injection locking to occur is carried out, leading to a more precise notion of the lock range. The ring oscillator is also analyzed in an analogous fashion, resulting in simple yet accurate closed-form expressions for the fractional lock range in the small-injection and long-ring regimes; the expressions are validated by simulations of single-ended inverter-based ring oscillators in 65-nm CMOS. The mathematics behind how the injection modifies the phase delay contributed by each stage in the ring is discussed. A corollary that generalizes the small-injection lock range to any feedback-based oscillator topology is established. Conceptual and analytical connections to the existing literature are reviewed. [ABSTRACT FROM AUTHOR]
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
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  Data: A Phasor-Based Analysis of Sinusoidal Injection Locking in LC and Ring Oscillators.
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  Data: <searchLink fieldCode="AR" term="%22Hong%2C+Brian%22">Hong, Brian</searchLink><br /><searchLink fieldCode="AR" term="%22Hajimiri%2C+Ali%22">Hajimiri, Ali</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Phasor+measurement%22">Phasor measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Injection+locked+oscillators%22">Injection locked oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Integrated+circuits%22">Integrated circuits</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: A new perspective into the locking behavior of LC and ring oscillators is presented. By decomposing a sinusoidal injection current into in-phase and quadrature-phase components, exact expressions for the amplitude and phase of an injection-locked LC oscillator which hold for any injection strength and frequency are derived and confirmed by simulation. The analysis, which can be naturally extended to an arbitrary LC resonator topology, leads to a rigorous understanding of the fundamental physics underlying the locking phenomenon. Furthermore, an investigation of the different necessary and sufficient conditions for injection locking to occur is carried out, leading to a more precise notion of the lock range. The ring oscillator is also analyzed in an analogous fashion, resulting in simple yet accurate closed-form expressions for the fractional lock range in the small-injection and long-ring regimes; the expressions are validated by simulations of single-ended inverter-based ring oscillators in 65-nm CMOS. The mathematics behind how the injection modifies the phase delay contributed by each stage in the ring is discussed. A corollary that generalizes the small-injection lock range to any feedback-based oscillator topology is established. Conceptual and analytical connections to the existing literature are reviewed. [ABSTRACT FROM AUTHOR]
– 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.2018.2860045
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      – Code: eng
        Text: English
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        PageCount: 14
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    Subjects:
      – SubjectFull: Phasor measurement
        Type: general
      – SubjectFull: Injection locked oscillators
        Type: general
      – SubjectFull: Integrated circuits
        Type: general
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      – TitleFull: A Phasor-Based Analysis of Sinusoidal Injection Locking in LC and Ring Oscillators.
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            NameFull: Hong, Brian
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              Text: Jan2019
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