Analog Modeling of Fractional-Order Elements: A Classical Circuit Theory Approach

Neven Mijat, Drazen Jurisic, George S. Moschytz

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


In this paper a comprehensive procedure for the analog modeling of Fractional-Order Elements (FOEs) is presented. Unlike most already proposed techniques, a standard approach from classical circuit theory is applied. It includes the realization of a system function by a mathematical approximation of the desired phase response, and the synthesis procedure for the realization of basic fractional-order (FO) one-port models as passive RC Cauer- and Foster-form canonical circuits. Based on the presented one-ports, simple realizations of two-port differentiator and integrator models are derived. Beside the description of the design procedure, illustrative examples, circuit diagrams, simulation results and practical realizations are presented.

Original languageEnglish
Article number9500213
Pages (from-to)110309-110331
Number of pages23
JournalIEEE Access
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2013 IEEE.


This work was fully supported by the Croatian Science Foundation under the project IP-2016-06-1307 ‘‘Fractional Analog and Mixed Systems for Signal Processing’’.

FundersFunder number
Hrvatska Zaklada za ZnanostIP-2016-06-1307


    • Fractional-order element
    • approximation
    • cauer one-port
    • constant-phase element
    • foster one-port
    • fractional immittance
    • fractional-order differentiator and integrator
    • synthesis


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