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

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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.

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References

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  5. K. Biswas, G. Bohannan, R. Caponetto, A.M. Lopes, J.A.T. Machado, Fractional-Order Devices (Springer, Berlin, 2017)

    Book  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  9. R. El-Khazali, On the biquadratic approximation of fractional-order Laplacian operators. Analog Integr. Circuit Signal Process. 82(3), 503–517 (2015)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  11. C. Halijak, An RC impedance approximant to \((1/s)^{1/2}\). IEEE Trans. Circuit Theory 11(4), 494–495 (1964)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  13. B. Krishna, Studies on fractional-order differentiators and integrators: a survey. Signal Process. 91(3), 386–426 (2011)

    Article  MathSciNet  Google Scholar 

  14. K. Matsuda, H. Fujii, H\(\infty \) optimized wave-absorbing control: analytical and experimental result. J. Guidance Control Dyn. 16(6), 1146–1153 (1993)

    Article  Google Scholar 

  15. P.A. Mohan, VLSI Analog Filters: Active RC, OTA-C, and SC (Springer, Berlin, 2012)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  18. A.G. Radwan, K.N. Salama, Fractional-order RC and RL circuits. Circuit Syst. Signal Process. 31(6), 1901–1915 (2012)

    Article  MathSciNet  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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

    Book  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. P. Veeraian, U. Gandhi, U. Mangalanathan, Analysis of fractional order inductive transducers. Eur. Phys. J. Spec. Top. 226(16–18), 3851–3873 (2017)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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Authors and Affiliations

  1. Electronics Laboratory, Physics Department, University of Patras, Rio, Patras, 26504, Greece

    Stavroula Kapoulea, Georgia Tsirimokou & Costas Psychalinos

  2. Department of Electrical and Computer Engineering, University of Sharjah, P. O. Box 27272, Sharjah, UAE

    Ahmed S. Elwakil

  3. Nanoelectronics Integrated Systems Center (NISC), Nile University, Giza, Egypt

    Ahmed S. Elwakil

  4. Department of Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, Canada

    Ahmed S. Elwakil

Authors
  1. Stavroula Kapoulea
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  2. Georgia Tsirimokou
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  3. Costas Psychalinos
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  4. Ahmed S. Elwakil
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Corresponding author

Correspondence to Costas Psychalinos.

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This research is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme “Human Resources Development, Education and Lifelong Learning” in the context of the project “Strengthening Human Resources Research Potential via Doctorate Research-2nd Cycle” (MIS-5000432), implemented by the State Scholarships Foundation (IKY).

This article is based upon work from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology.

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Kapoulea, S., Tsirimokou, G., Psychalinos, C. et al. Generalized Fully Adjustable Structure for Emulating Fractional-Order Capacitors and Inductors of Orders less than Two. Circuits Syst Signal Process 39, 1797–1814 (2020). https://doi.org/10.1007/s00034-019-01252-5

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  • DOI: https://doi.org/10.1007/s00034-019-01252-5

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