On mathematical characterization of a Bessel functions-based passive element in electronic circuits

TL;DR

This paper introduces a new passive circuit element characterized by Bessel functions, offering a physically interpretable and stable alternative for modeling complex media's relaxation phenomena.

Contribution

It presents a novel impedance element based on Bessel functions that maintains physical properties and improves modeling of dispersive biological tissues.

Findings

Accurately models broadband dispersive behavior of biological tissues.

Ensures physical properties like passivity and stability.

Provides a closed-form time-domain expression for simulations.

Abstract

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.