Advertisement

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
Article
  • 44 Downloads

Abstract

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.

Keywords

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

Notes

References

  1. 1.
    A. Adhikary, S. Choudhary, S. Sen, Optimal design for realizing a grounded fractional order inductor using GIC. IEEE Trans. Circuit Syst. I: Regul. P. 65(8), 2411–2421 (2018)MathSciNetCrossRefGoogle Scholar
  2. 2.
    A. Adhikary, P. Sen, S. Sen, K. Biswas, Design and performance study of dynamic fractors in any of the four quadrants. Circuit Syst. Signal Process. 35(6), 1909–1932 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    A. Adhikary, S. Sen, K. Biswas, Practical realization of tunable fractional order parallel resonator and fractional order filters. IEEE Trans. Circuit Syst. I: Regul. P. 63(8), 1142–1151 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    A. Adhikary, S. Sen, K. Biswas, Design and hardware realization of a tunable fractional-order series resonator with high quality factor. Circuit Syst. Signal Process. 36(9), 3457–3476 (2017)CrossRefGoogle Scholar
  5. 5.
    K. Biswas, G. Bohannan, R. Caponetto, A.M. Lopes, J.A.T. Machado, Fractional-Order Devices (Springer, Berlin, 2017)CrossRefGoogle Scholar
  6. 6.
    G. Carlson, C. Halijak, Approximation of fractional capacitors (1/s)\(^{(1/n)}\) by a regular Newton process. IEEE Trans. Circuit Theory 11(2), 210–213 (1964)CrossRefGoogle Scholar
  7. 7.
    P. Corbishley, E. Rodriguez-Villegas, A nanopower bandpass filter for detection of an acoustic signal in a wearable breathing detector. IEEE Trans. Biomed. Circuit Syst. 1(3), 163–171 (2007)CrossRefGoogle Scholar
  8. 8.
    I. Dimeas, G. Tsirimokou, C. Psychalinos, A.S. Elwakil, Experimental verification of fractional-order filters using a reconfigurable fractional-order impedance emulator. J. Circuit Syst. Comput. 26(09), 1750142 (2017)CrossRefGoogle Scholar
  9. 9.
    R. El-Khazali, On the biquadratic approximation of fractional-order Laplacian operators. Analog Integr. Circuit Signal Process. 82(3), 503–517 (2015)CrossRefGoogle Scholar
  10. 10.
    T.J. Freeborn, B. Maundy, A.S. Elwakil, Field programmable analogue array implementation of fractional step filters. IET Circuit Devices Syst. 4(6), 514–524 (2010)CrossRefGoogle Scholar
  11. 11.
    C. Halijak, An RC impedance approximant to \((1/s)^{1/2}\). IEEE Trans. Circuit Theory 11(4), 494–495 (1964)CrossRefGoogle Scholar
  12. 12.
    Y. Jiang, B. Zhang, High-power fractional-order capacitor with \(1<\alpha <2\) based on power converter. IEEE Trans. Ind. Electron. 85(4), 3157–3164 (2018)CrossRefGoogle Scholar
  13. 13.
    B. Krishna, Studies on fractional-order differentiators and integrators: a survey. Signal Process. 91(3), 386–426 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    K. Matsuda, H. Fujii, H\(\infty \) optimized wave-absorbing control: analytical and experimental result. J. Guidance Control Dyn. 16(6), 1146–1153 (1993)CrossRefzbMATHGoogle Scholar
  15. 15.
    P.A. Mohan, VLSI Analog Filters: Active RC, OTA-C, and SC (Springer, Berlin, 2012)zbMATHGoogle Scholar
  16. 16.
    A. Oustaloup, F. Levron, B. Mathieu, F.M. Nanot, Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circuit Syst. I: Fundam. Theory Appl. 47(1), 25–39 (2000)CrossRefGoogle Scholar
  17. 17.
    D. Pullaguram, S. Mishra, N. Senroy, M. Mukherjee, Design and tuning of robust fractional order controller for autonomous microgrid VSC system. IEEE Trans. Ind. Appl. 54(1), 91–101 (2018)CrossRefGoogle Scholar
  18. 18.
    A.G. Radwan, K.N. Salama, Fractional-order RC and RL circuits. Circuit Syst. Signal Process. 31(6), 1901–1915 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    V.P. Sarathi, G. Uma, M. Umapathy, Realization of fractional order inductive transducer. IEEE Sens. J. 18(21), 8803–8811 (2018)Google Scholar
  20. 20.
    M.C. Tripathy, D. Mondal, K. Biswas, S. Sen, Experimental studies on realization of fractional inductors and fractional-order bandpass filters. Int. J. Circuit Theory Appl. 43(9), 1183–1196 (2015)CrossRefGoogle Scholar
  21. 21.
    G. Tsirimokou, A. Kartci, J. Koton, N. Herencsar, C. Psychalinos, Comparative study of discrete component realizations of fractional-order capacitor and inductor active emulators. J. Circuit Syst. Comput. 27(11), 1850170 (2018)CrossRefGoogle Scholar
  22. 22.
    G. Tsirimokou, C. Psychalinos, A. Elwakil, Design of CMOS Analog Integrated Fractional-Order Circuits: Applications in Medicine and Biology (Springer, Berlin, 2017).  https://doi.org/10.1007/978-3-319-55633-8 CrossRefGoogle Scholar
  23. 23.
    G. Tsirimokou, C. Psychalinos, A.S. Elwakil, K.N. Salama, Experimental behavior evaluation of series and parallel connected constant phase elements. Int. J. Electron. Commun. (AEÜ) 74, 5–12 (2017)CrossRefGoogle Scholar
  24. 24.
    G. Tsirimokou, C. Psychalinos, A.S. Elwakil, K.N. Salama, Electronically tunable fully integrated fractional-order resonator. IEEE Trans. Circuit Syst. II Express Briefs 65(2), 166–170 (2018)CrossRefGoogle Scholar
  25. 25.
    J. Valsa, J. Vlach, RC models of a constant phase element. Int. J. Circuit Theory Appl. 41(1), 59–67 (2013)Google Scholar
  26. 26.
    P. Veeraian, U. Gandhi, U. Mangalanathan, Analysis of fractional order inductive transducers. Eur. Phys. J. Spec. Top. 226(16–18), 3851–3873 (2017)CrossRefGoogle Scholar
  27. 27.
    R. Verma, N. Pandey, R. Pandey, Realization of a higher fractional order element based on novel OTA based IIMC and its application in filter. Analog Integr. Circuit Sig. Process 97(1), 177–191 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

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

Personalised recommendations