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Fractal Calculus Analysis of a Non-ideal Operational Amplifier Bandpass Filter.

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Title: Fractal Calculus Analysis of a Non-ideal Operational Amplifier Bandpass Filter.
Authors: Banchuin, Rawid1 (AUTHOR) rawid.ban@siam.edu, Golmankhaneh, Alireza Khalili2,3 (AUTHOR) alirezakhalili2002@yahoo.co.in
Source: Circuits, Systems & Signal Processing. Jul2026, Vol. 45 Issue 7, p5140-5162. 23p.
Subjects: Operational amplifiers, Bandpass filters, Fractal analysis, Frequency-domain analysis, Analog circuits, Transfer functions, Power law (Mathematics), Imperfection
Abstract: Fractal calculus is a new branch of calculus that has been widely applied in many scientific disciplines, e.g., sub-diffusion, super-diffusion, spatial analysis, and electrical engineering. In the area of electrical engineering, the fractal calculus has been applied to the analysis of many electrical circuits and the modeling of memelement and inverse memelement under the effect of fractal time. However, to the best of our knowledge, there exists no application of the fractal calculus to the active electrical circuit. Therefore, for the first time, we apply the fractal calculus to the analysis of an active circuit under the effect of fractal time in this work. The operational amplifier (OPAMP)-based bandpass (BP) filter has been chosen as our candidate active circuit. For a complete analysis, the nonidealities of the OPAMP have been taken into account. It has been found that the filter exhibits a power law dynamic in the frequency domain due to the effect of fractal time without any usage of the fractional order circuit element. The influences of the OPAMP's nonidealities on both magnitude and phase of the nondifferentiable (ND) transfer function are comprehensively analyzed. [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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DbLabel: Engineering Source
An: 194867717
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  Data: Fractal Calculus Analysis of a Non-ideal Operational Amplifier Bandpass Filter.
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  Data: <searchLink fieldCode="JN" term="%22Circuits%2C+Systems+%26+Signal+Processing%22">Circuits, Systems & Signal Processing</searchLink>. Jul2026, Vol. 45 Issue 7, p5140-5162. 23p.
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  Data: <searchLink fieldCode="DE" term="%22Operational+amplifiers%22">Operational amplifiers</searchLink><br /><searchLink fieldCode="DE" term="%22Bandpass+filters%22">Bandpass filters</searchLink><br /><searchLink fieldCode="DE" term="%22Fractal+analysis%22">Fractal analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Frequency-domain+analysis%22">Frequency-domain analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Analog+circuits%22">Analog circuits</searchLink><br /><searchLink fieldCode="DE" term="%22Transfer+functions%22">Transfer functions</searchLink><br /><searchLink fieldCode="DE" term="%22Power+law+%28Mathematics%29%22">Power law (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Imperfection%22">Imperfection</searchLink>
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  Data: Fractal calculus is a new branch of calculus that has been widely applied in many scientific disciplines, e.g., sub-diffusion, super-diffusion, spatial analysis, and electrical engineering. In the area of electrical engineering, the fractal calculus has been applied to the analysis of many electrical circuits and the modeling of memelement and inverse memelement under the effect of fractal time. However, to the best of our knowledge, there exists no application of the fractal calculus to the active electrical circuit. Therefore, for the first time, we apply the fractal calculus to the analysis of an active circuit under the effect of fractal time in this work. The operational amplifier (OPAMP)-based bandpass (BP) filter has been chosen as our candidate active circuit. For a complete analysis, the nonidealities of the OPAMP have been taken into account. It has been found that the filter exhibits a power law dynamic in the frequency domain due to the effect of fractal time without any usage of the fractional order circuit element. The influences of the OPAMP's nonidealities on both magnitude and phase of the nondifferentiable (ND) transfer function are comprehensively analyzed. [ABSTRACT FROM AUTHOR]
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  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/s00034-025-03459-1
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        Text: English
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      – SubjectFull: Operational amplifiers
        Type: general
      – SubjectFull: Bandpass filters
        Type: general
      – SubjectFull: Fractal analysis
        Type: general
      – SubjectFull: Frequency-domain analysis
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      – SubjectFull: Analog circuits
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      – SubjectFull: Power law (Mathematics)
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      – SubjectFull: Imperfection
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      – TitleFull: Fractal Calculus Analysis of a Non-ideal Operational Amplifier Bandpass Filter.
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              Text: Jul2026
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              Y: 2026
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