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Noise analysis of electrical circuits on fractal set.

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Title: Noise analysis of electrical circuits on fractal set.
Authors: Banchuin, Rawid1 (AUTHOR) rawid.ban@siam.edu
Source: COMPEL. 2022, Vol. 41 Issue 5, p1464-1490. 27p.
Subjects: Fractals, Electric circuits, Electric noise, Additive white Gaussian noise, Cantor sets, Fractal analysis
Abstract: Purpose: The purpose of this study is to originally present noise analysis of electrical circuits defined on fractal set. Design/methodology/approach: The fractal integrodifferential equations of resistor-inductor, resistor-capacitor, inductor-capacitor and resistor-inductor-capacitor circuits subjected to zero mean additive white Gaussian noise defined on fractal set have been formulated. The fractal time component has also been considered. The closed form expressions for crucial stochastic parameters of circuit responses have been derived from these equations. Numerical simulations of power spectral densities based on the derived autocorrelation functions have been performed. A comparison with those without fractal time component has been made. Findings: We have found that the Hausdorff dimension of the middle b Cantor set strongly affects the power spectral densities; thus, the average powers of noise induced circuit responses and the inclusion of fractal time component causes significantly different analysis results besides the physical measurability of electrical quantities. Originality/value: For the first time, the noise analysis of electrical circuit on fractal set has been performed. This is also the very first time that the fractal time component has been included in the fractal calculus-based circuit analysis. [ABSTRACT FROM AUTHOR]
Copyright of COMPEL is the property of Emerald Publishing Limited 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.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 158698113
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Noise analysis of electrical circuits on fractal set.
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  Data: <searchLink fieldCode="AR" term="%22Banchuin%2C+Rawid%22">Banchuin, Rawid</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rawid.ban@siam.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22COMPEL%22">COMPEL</searchLink>. 2022, Vol. 41 Issue 5, p1464-1490. 27p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Fractals%22">Fractals</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+circuits%22">Electric circuits</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+noise%22">Electric noise</searchLink><br /><searchLink fieldCode="DE" term="%22Additive+white+Gaussian+noise%22">Additive white Gaussian noise</searchLink><br /><searchLink fieldCode="DE" term="%22Cantor+sets%22">Cantor sets</searchLink><br /><searchLink fieldCode="DE" term="%22Fractal+analysis%22">Fractal analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Purpose: The purpose of this study is to originally present noise analysis of electrical circuits defined on fractal set. Design/methodology/approach: The fractal integrodifferential equations of resistor-inductor, resistor-capacitor, inductor-capacitor and resistor-inductor-capacitor circuits subjected to zero mean additive white Gaussian noise defined on fractal set have been formulated. The fractal time component has also been considered. The closed form expressions for crucial stochastic parameters of circuit responses have been derived from these equations. Numerical simulations of power spectral densities based on the derived autocorrelation functions have been performed. A comparison with those without fractal time component has been made. Findings: We have found that the Hausdorff dimension of the middle b Cantor set strongly affects the power spectral densities; thus, the average powers of noise induced circuit responses and the inclusion of fractal time component causes significantly different analysis results besides the physical measurability of electrical quantities. Originality/value: For the first time, the noise analysis of electrical circuit on fractal set has been performed. This is also the very first time that the fractal time component has been included in the fractal calculus-based circuit analysis. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of COMPEL is the property of Emerald Publishing Limited 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:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1108/COMPEL-08-2021-0269
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 27
        StartPage: 1464
    Subjects:
      – SubjectFull: Fractals
        Type: general
      – SubjectFull: Electric circuits
        Type: general
      – SubjectFull: Electric noise
        Type: general
      – SubjectFull: Additive white Gaussian noise
        Type: general
      – SubjectFull: Cantor sets
        Type: general
      – SubjectFull: Fractal analysis
        Type: general
    Titles:
      – TitleFull: Noise analysis of electrical circuits on fractal set.
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            – D: 01
              M: 09
              Text: 2022
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              Y: 2022
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              Value: 03321649
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              Value: 41
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              Value: 5
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            – TitleFull: COMPEL
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