Generalized Fully Adjustable Structure for Emulating Fractional-Order Capacitors and Inductors of Orders less than Two

  • Stavroula Kapoulea
  • Georgia Tsirimokou
  • Costas PsychalinosEmail author
  • Ahmed S. Elwakil


A novel scheme suitable for the emulation of fractional-order capacitors and inductors of any order less than 2 is presented in this work. Classically, fractional-order impedances are characterized in the frequency domain by a fractional-order Laplacian of the form \(s^{\pm \alpha }\) with an order \(0<\alpha <1\). The ideal inductor and capacitor correspond, respectively, to setting \(\alpha =\pm 1\). In the range \(1<\alpha <2\), fractional-order impedances can still be obtained before turning into a Frequency- Dependent Negative Resistor (FDNR) at \(\alpha =\pm 2\). Here, we propose an electronically tunable fractional-order impedance emulator with adjustable order in the full range \(0<\alpha <2\). The values of the emulated capacitance/inductance, as well as the bandwidth of operation, are also electronically adjustable. The post- layout simulation results confirm the correct operation of the proposed circuits.


Fractional-order circuits Fractional-order capacitor Constant phase element Fractional-order inductor Operational transconductance amplifiers 



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Authors and Affiliations

  1. 1.Electronics Laboratory, Physics DepartmentUniversity of PatrasRio, PatrasGreece
  2. 2.Department of Electrical and Computer EngineeringUniversity of SharjahSharjahUAE
  3. 3.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityGizaEgypt
  4. 4.Department of Electrical and Computer EngineeringUniversity of CalgaryCalgaryCanada

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