This work is aimed at generalizing the design of continuous-time second-order filters to the non-integer-order (fractional-order) domain. In particular, we consider here the case where a filter is constructed using two fractional-order capacitors both of the same order ?. A fractional-order capacitor is one whose impedance is Zc = 1/C(j?) ?, C is the capacitance and ? (0 < ? ? 1) is its order. We generalize the design equations for low-pass, high-pass, band-pass, all-pass and notch filters with stability constraints considered. Several practical active filter design examples are then illustrated supported with numerical and PSpice simulations. Further, we show for the first time experimental results using the fractional capacitive probe described in Ref. 1. © 2009 World Scientific Publishing Company.
First-order filters generalized to the fractional domain
Traditional continuous-time filters are of integer order. However, using fractional calculus, filters may also be represented by the more general fractional-order differential equations in which case integer-order filters are only a tight subset of fractional-order filters. In this work, we show that low-pass, high-pass, band-pass, and all-pass filters can be realized with circuits incorporating a single fractance device. We derive expressions for the pole frequencies, the quality factor, the right-phase frequencies, and the half-power frequencies. Examples of fractional passive filters supported by numerical and PSpice simulations are given. © 2008 World Scientific Publishing Company.
Fractional-Order Equivalent-Circuit Model Identification of Commercial Lithium-Ion Batteries
The precise identification of electrical model parameters of Li-Ion batteries is essential for efficient usage and better prediction of the battery performance. In this work, the model identification performance of two metaheuristic optimization algorithms is compared. The algorithms in comparison are the Marine Predator Algorithm (MPA) and the Partial Reinforcement Optimizer (PRO) to find the optimal model parameter values. Three fractional-order (FO) electrical equivalent circuit models (ECMs) of Li-Ion batteries with different levels of complexity are used to fit the electrochemical impedance spectroscopy (EIS) data operating under different states of charge (SoC) and different operating temperatures. It is found that there is a tradeoff between ECM complexity, identification accuracy, and precision. © 2024 The Electrochemical Society (“ECS”). Published on behalf of ECS by IOP Publishing Limited
Partial fraction expansion–based realizations of fractional-order differentiators and integrators using active filters
Approximations of the fractional-order differentiator and integrator operators s±r are proposed in this work
Editorial note Special Issue on the Design and implementation of fractional-order circuits and systems in real-world applications
The aim of this Special Issue is to present the latest developments, trends, research solutions, and applications of fractional-order circuits and systems with emphasis on real-world applications.
Guest Editorial: Fractional-Order Circuits and Systems: Theory, Design, and Applications
Nowadays, there is a significant research interest in the area of fractional-order circuits.
Programmable constant phase element realization with crossbar arrays
Introduction: Constant Phase Elements (CPEs) have been widely used in many applications due to the extra degree of freedom, which offers new responses and behaviors
Comprehensive comparison based on meta-heuristic algorithms for approximation of the fractional-order Laplacian s ? as a weighted sum of first-order high-pass filters
To implement an approximation of the fractional order Laplacian operator s ? as a weighted sum of high pass filter sections, it is essential to extract the cutoff frequencies and filter gains of each section in order to achieve the lowest error possible
Power and energy analysis of fractional-order electrical energy storage devices
Characterizing and modeling electrical energy storage devices is essential for their proper integration in larger systems
Capacitive behavior and stored energy in supercapacitors at power line frequencies
Supercapacitors are commonly viewed and mainly employed as dc electrical energy storage devices