Synthesis and Optimization of Fractional-Order Elements Using a Genetic Algorithm

Aslihan Kartci, Agamyrat Agambayev, Mohamed Farhat, Norbert Herencsar, Lubomir Brancik, Hakan Bagci, Khaled N. Salama

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


This study proposes a new approach for the optimization of phase and magnitude responses of fractional-order capacitive and inductive elements based on the mixed integer-order genetic algorithm (GA), over a bandwidth of four decade, and operating up to 1 GHz with low phase error of approximately ±1°. It provides a phase optimization in the desired bandwidth with minimal branch number, and avoids use of negative component values, and any complex mathematical analysis. Standardized, IEC 60063 compliant commercially available passive component values are used; hence, no correction on passive elements is required. To the best knowledge of the authors, this approach is proposed for the first time in the literature. As validation, we present numerical simulations using MATLAB® and experimental measurement results, in particular the Foster-II and Valsa structures with five branches for precise and/or high-frequency applications. Indeed, the results demonstrate excellent performance and significant improvements over the Oustaloup approximation, the Valsa recursive algorithm, and the continued fraction expansion as well as the adaptability of the GA-based design with five different types of distributed RC/RL network.
Original languageEnglish (US)
Pages (from-to)80233-80246
Number of pages14
JournalIEEE Access
StatePublished - 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: For the research, infrastructure of the SIX Center was used. (Aslihan Kartci and Agamyrat Agambayev contributed equally to this work.)


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