On mathematical characterization of a Bessel functions-based passive element in electronic circuits
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914505812869120 |
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| author | Colombaro, Ivano Tudela-Pi, Marc |
| author_facet | Colombaro, Ivano Tudela-Pi, Marc |
| contents | Modeling relaxation phenomena in complex media is central to understanding multiscale dynamics in materials science, bioengineering and condensed matter physics. Existing fractional-order models, while flexible, sometimes lack physical interpretability, closed-form time-domain expressions, and compatibility with physically realizable architectures. In this work, we propose a novel passive element whose impedance and admittance are defined analytically via modified Bessel functions of first kind, through the electro-mechanical analogy. This approach preserves key physical properties such as analyticity, passivity, BIBO (bounded-input, bounded-output) stability and monotonicity, while enabling the direct use of its time-domain representation in simulations and system modeling. As an application, we demonstrate that this model accurately captures the broadband dispersive behavior of biological tissues, offering a physically grounded and tractable alternative to fractional-order formulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22798 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On mathematical characterization of a Bessel functions-based passive element in electronic circuits Colombaro, Ivano Tudela-Pi, Marc Computational Physics Modeling relaxation phenomena in complex media is central to understanding multiscale dynamics in materials science, bioengineering and condensed matter physics. Existing fractional-order models, while flexible, sometimes lack physical interpretability, closed-form time-domain expressions, and compatibility with physically realizable architectures. In this work, we propose a novel passive element whose impedance and admittance are defined analytically via modified Bessel functions of first kind, through the electro-mechanical analogy. This approach preserves key physical properties such as analyticity, passivity, BIBO (bounded-input, bounded-output) stability and monotonicity, while enabling the direct use of its time-domain representation in simulations and system modeling. As an application, we demonstrate that this model accurately captures the broadband dispersive behavior of biological tissues, offering a physically grounded and tractable alternative to fractional-order formulations. |
| title | On mathematical characterization of a Bessel functions-based passive element in electronic circuits |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2604.22798 |