Emulation of Fractional-Order Capacitors (CPEs) and Inductors (FOIs)

  • Georgia Tsirimokou
  • Costas Psychalinos
  • Ahmed Elwakil
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)


The design of fractional-order capacitors and inductor emulators is introduced in a systematic way procedure, where the second-order approximation of the CFE is utilized in order to approximate the variable s α of fractional calculus. OTAs are employed as building blocks, using MOS transistors biased in subthreshold region, offering the advantage of operating in a low voltage environment. The emulation schemes that have been proposed are voltage excited, as well as current excited in order to be available for different types of applications based on potentiostatic and galvanostatic measurements, respectively. Both emulators (capacitor and inductor) are fabricated in AMS 0.35 μm CMOS technology, the efficiency of which is verified through experimental results. As a design example, a fractional-order resonator is presented.


Fractional-order capacitors Fractional-order inductors Fractional-order resonator Low-voltage circuits 


  1. 1.
    Elwakil, A.S.: Fractional-order circuits and systems: an emerging interdisciplinary research area. IEEE Circ. Syst. Mag. 10(4), 40–50 (2010)CrossRefGoogle Scholar
  2. 2.
    Oldham, K.B.: The Fractional Calculus. Elsevier, London (1974)MATHGoogle Scholar
  3. 3.
    Westerlund, S., Ekstam, L.: Capacitor theory. IEEE Trans. Dielectr. Electr. Insul. 1(5), 826–839 (1994)CrossRefGoogle Scholar
  4. 4.
    Yufera, A., Rueda, A., Munoz, J.M., Doldan, R., Leger, G., Rodriguez-Villegas, E.O.: A tissue impedance measurement chip for myocardial ischemia detection. IEEE Trans. Circ. Syst. I: Regul. Pap. 2(12), 2620–2628 (2005)CrossRefGoogle Scholar
  5. 5.
    Rodriguez, S., Ollmar, S., Waqar, M., Rusu, A.: A battery sensor ASIC for implantable bio-impedance applications. IEEE Trans. Biomed. Circ. Syst. 10(3), 533–544 (2016)CrossRefGoogle Scholar
  6. 6.
    Tripathy, M., Mondal, D., Biswas, K., Sen, S.: Experimental studies on realization of fractional inductors and fractional-order bandpass filters. Int. J. Circ. Theory Appl. 2014, 98 (2014)Google Scholar
  7. 7.
    Freeborn, T.J., Maundy, B., Elwakil, A.S.: Field programmable analogue array implementation of fractional step filters. IET Circ. Dev. Syst. 4(6), 514–524 (2010)CrossRefGoogle Scholar
  8. 8.
    Adhikary, A., Sen, S., Biswas, K.: Practical realization of tunable fractional order parallel resonator and fractional order filters. IEEE Trans. Circ. Syst. I: Fundam. Theory. Appl. 63(8), 1142–1151 (2016)MathSciNetGoogle Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Georgia Tsirimokou
    • 1
  • Costas Psychalinos
    • 1
  • Ahmed Elwakil
    • 2
    • 3
  1. 1.Physics Department Electronics LaboratoryUniversity of PatrasRio PatrasGreece
  2. 2.Department of Electrical and Computer EngineeringUniversity of SharjahSharjahUnited Arab Emirates
  3. 3.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityCairoEgypt

Personalised recommendations