Series-, Parallel-, and Inter-Connection of Solid-State Arbitrary Fractional-Order Capacitors: Theoretical Study and Experimental Verification

Aslihan Kartci*, Agamyrat Agambayev, Norbert Herencsar, Khaled N. Salama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


In this paper, general analytical formulas are introduced for the determination of equivalent impedance, magnitude, and phase, i.e., order, for n arbitrary fractional-order capacitors (FoCs) connected in series, parallel, and their interconnection. The approach presented helps to evaluate these relevant quantities in the fractional domain, since the order of each element has a significant effect on the impedance of each FoC and their equivalent capacitance cannot be considered. Three types of solid-state fractional-order passive capacitors of different orders, using ferroelectric polymer and reduced graphene oxide-percolated P(VDF-TrFE-CFE) composite structures, are fabricated and characterized. Using an impedance analyzer, the behavior of the devices was found to be stable in the frequency range 0.2 - 20 MHz, with a phase angle deviation of ±4°. Multiple numerical and experimental case studies are given, in particular for two and three connected FoCs. The fundamental issues of the measurement units of the FoCs connected in series and parallel are derived. A MATLAB open-access source code is given in the Appendix for easy calculation of the equivalent FoC magnitude and phase. The experimental results are in good agreement with the theoretical assumptions.

Original languageEnglish (US)
Pages (from-to)10933-10943
Number of pages11
JournalIEEE Access
StatePublished - Feb 24 2018

Bibliographical note

Funding Information:
This work was supported in part by COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology), in part by the National Sustainability Program under Grant LO1401, and in part by the Czech Science Foundation under Grant 16-06175S. For the research, infrastructure of the SIX Center was used.

Publisher Copyright:
© 2013 IEEE.


  • Arbitrary-order FoC
  • FoC
  • MATLAB open access source code
  • fractional calculus
  • fractional-order capacitor
  • interconnection
  • parallel connection
  • series connection
  • solid-state device

ASJC Scopus subject areas

  • Computer Science(all)
  • Materials Science(all)
  • Engineering(all)


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