Design of a Low-pass Filter from Fractional Chebyshev Polynomials

2021Abdelaty A.M.Amgad A.Attia H.A.Elbarawy M.T.M.M.Radwan A.G.

This paper introduces a novel magnitude approximation for the fractional-order Chebyshev low-pass filter. The proposed magnitude response is constructed from the fractional Chebyshev polynomials originating from the series solution of fractional-order Chebyshev differential equation. The transfer function of the fractional-order Sallen-Key biquad is used as a prototype for the approximation. To identify the coefficients of the Sallen-Key topology, the flower pollination algorithm (FPA) is used to minimize an objective function representing the sum of relative magnitude error. The optimization problem is executed in MATLAB, and stable solutions are chosen for the implementation. Two different cases are investigated corresponding to filter orders 1.8 and 2.7. LT-Spice is used for circuit simulations, and the Valsa approach is used for fractional-order capacitor approximation. The original magnitude response is compared with the optimized one and the circuit simulation results, and this comparison shows a magnitude error less than 2%. © 2021 IEEE.

Optimal Charging and Discharging of Supercapacitors

2020Abdelaty A.M.Elbarawy M.T.M.M.Fouda M.E.JournalRadwan A.G.

In this paper, we discuss the optimal charging and discharging of supercapacitors to maximize the delivered energy by deploying the fractional and multivariate calculus of variations. We prove mathematically that the constant current is the optimal charging and discharging method under R s -CPE model of supercapacitors. The charging and round-trip efficiencies have been mathematically analyzed for constant current charging and discharging. © 2020 The Electrochemical Society (“ECS”). Published on behalf of ECS by IOP Publishing Limited.