Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Minimization of Spread of Time-Constants and Scaling Factors in Fractional-Order Differentiator and Integrator Realizations

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

The approximations of fractional-order differentiator/integrator transfer functions are currently performed using integer-order rational functions, which are in general implemented through appropriate multi-feedback topologies. The spreading in the values of time-constants and scaling factors, needed to implement these topologies, increases as the order of the differentiator/integrator and/or the order of the approximation increases. This leads to non-practical values of capacitances and resistances/transconductances in the implementation. A solution to overcome this obstacle is introduced in this paper, based on the employment of a combination of fractional-order and integer-order integrators and differentiators for implementing the desired function. The performance of the proposed scheme is verified through post-layout simulations using Cadence and the Design Kit provided by the Austria Mikro Systeme \(0.35~\upmu \mathrm{m}\) CMOS technology process.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. A. Agambayev, S.P. Patole, M. Farhat, A. Elwakil, H. Bagci, K.N. Salama, Ferroelectric fractional-order capacitors. ChemElectroChem 4(11), 2807–2813 (2017)

    Article  Google Scholar 

  2. P. Bertsias, F. Khateb, D. Kubanek, F.A. Khanday, C. Psychalinos, Capacitorless digitally programmable fractional-order filters. AEU Int. J. Electron. Commun. 78, 228–237 (2017)

    Article  Google Scholar 

  3. P. Bertsias, C. Psychalinos, A. Elwakil, B. Maundy, Current-mode capacitorless integrators and differentiators for implementing emulators of fractional-order elements. AEU Int. J. Electron. Commun. 80, 94–103 (2017)

    Article  Google Scholar 

  4. P. Bertsias, C. Psychalinos, A.G. Radwan, A.S. Elwakil, High-frequency capacitorless fractional-order CPE and FI emulator. Circuits Syst. Signal Process. (2017). https://doi.org/10.1007/s00034-017-0697-0

    Article  MathSciNet  Google Scholar 

  5. R. Caponetto, G. Dongola, G. Maione, A. Pisano, Integrated technology fractional order proportional–integral-derivative design. J. Vib. Control 20(7), 1066–1075 (2014)

    Article  MathSciNet  Google Scholar 

  6. R. Caponetto, S. Graziani, F.L. Pappalardo, F. Sapuppo, Experimental characterization of ionic polymer metal composite as a novel fractional order element. Adv. Math. Phys. 1–10, 2013 (2013)

    MATH  Google Scholar 

  7. 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 

  8. P. Corbishley, E. Rodriguez-Villegas, A nanopower bandpass filter for detection of an acoustic signal in a wearable breathing detector. IEEE Trans. Biomed. Circuits Syst. 1(3), 163–171 (2007)

    Article  Google Scholar 

  9. I. Dimeas, I. Petraš, C. Psychalinos, New analog implementation technique for fractional-order controller: a DC motor control. AEU Int. J. Electron. Commun. 78, 192–200 (2017)

    Article  Google Scholar 

  10. I. Dimeas, G. Tsirimokou, C. Psychalinos, A.S. Elwakil, Experimental verification of fractional-order filters using a reconfigurable fractional-order impedance emulator. J Circuits Syst Comput 26(09), 1750142 (2017)

    Article  Google Scholar 

  11. T.J. Freeborn, A.S. Elwakil, B. Maundy, Approximated fractional-order inverse Chebyshev lowpass filters. Circuits Syst Signal Process 35(6), 1973–1982 (2016)

    Article  MathSciNet  Google Scholar 

  12. T.J. Freeborn, B. Maundy, A.S. Elwakil, Field programmable analogue array implementation of fractional step filters. IET Circuits Devices Syst. 4(6), 514–524 (2010)

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. J. Jerabek, R. Sotner, J. Dvorak, J. Polak, D. Kubanek, N. Herencsar, J. Koton, Reconfigurable fractional-order filter with electronically controllable slope of attenuation, pole frequency and type of approximation. J. Circuits Syst. Comput. 26(10), 1750157 (2017)

    Article  Google Scholar 

  15. I.S. Jesus, J.T. Machado, Development of fractional order capacitors based on electrolyte processes. Nonlinear Dyn. 56(1–2), 45–55 (2009)

    Article  Google Scholar 

  16. D.A. John, S. Banerjee, G.W. Bohannan, K. Biswas, Solid-state fractional capacitor using MWCNT-epoxy nanocomposite. Appl. Phys. Lett. 110(16), 163504 (2017)

    Article  Google Scholar 

  17. N.A. Kant, M.R. Dar, F.A. Khanday, C. Psychalinos, Ultra-low-voltage integrable electronic realization of integer-and fractional-order Liao’s chaotic delayed neuron model. Circuits Syst. Signal Process. 36(12), 4844–4868 (2017)

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. D. Kubánek, F. Khateb, G. Tsirimokou, C. Psychalinos, Practical design and evaluation of fractional-order oscillator using differential voltage current conveyors. Circuits Syst. Signal Process. 35(6), 2003–2016 (2016)

    Article  MathSciNet  Google Scholar 

  20. P.A. Mohan, OTA-C filters, in VLSI Analog Filters, ed. by P.A. Mohan (Springer, Berlin, 2013), pp. 147–249

    Chapter  Google Scholar 

  21. A. Oustaloup, F. Levron, B. Mathieu, F.M. Nanot, Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47(1), 25–39 (2000)

    Article  Google Scholar 

  22. I. Podlubny, I. Petraš, B.M. Vinagre, P. O’leary, L. Dorčák, Analogue realizations of fractional-order controllers. Nonlinear Dyn. 29(1), 281–296 (2002)

    Article  MathSciNet  Google Scholar 

  23. A.G. Radwan, Resonance and quality factor of the \({{RL}}_{\beta } {{C}}_{\alpha }\) circuit. IEEE J. Emerg. Sel. Top. Circuits Syst. 3(3), 377–385 (2013)

    Article  Google Scholar 

  24. A.G. Radwan, M.E. Fouda, Optimization of fractional-order RLC filters. Circuits Syst. Signal Process. 32(5), 2097–2118 (2013)

    Article  MathSciNet  Google Scholar 

  25. A.G. Radwan, K.N. Salama, Passive and active elements using fractional \({{L}}_{\beta } {{C}}_{\alpha }\) circuit. IEEE Trans. Circuits Syst. I Regul. Pap. 58(10), 2388–2397 (2011)

    Article  MathSciNet  Google Scholar 

  26. S. Roy, On the realization of a constant-argument immittance or fractional operator. IEEE Trans. Circuit Theory 14(3), 264–274 (1967)

    Article  Google Scholar 

  27. L.A. Said, A.G. Radwan, A.H. Madian, A.M. Soliman, Fractional order oscillator design based on two-port network. Circuits Syst. Signal Process. 35(9), 3086–3112 (2016)

    Article  MathSciNet  Google Scholar 

  28. A. Soltan, A.G. Radwan, A.M. Soliman, Fractional order Sallen–Key and KHN filters: stability and poles allocation. Circuits Syst. Signal Process. 34(5), 1461–1480 (2015)

    Article  Google Scholar 

  29. 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 

  30. 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. Circuits Syst. Comput. 27(11), 1850170 (2018)

    Article  Google Scholar 

  31. G. Tsirimokou, C. Psychalinos, Ultra-low voltage fractional-order differentiator and integrator topologies: an application for handling noisy ECGs. Analog Integr. Circ. Sig. Process 81(2), 393–405 (2014)

    Article  Google Scholar 

  32. G. Tsirimokou, C. Psychalinos, Ultra-low voltage fractional-order circuits using current mirrors. Int. J. Circuit Theory Appl. 44(1), 109–126 (2016)

    Article  Google Scholar 

  33. G. Tsirimokou, C. Psychalinos, A.S. Elwakil, K.N. Salama, Electronically tunable fully integrated fractional-order resonator. IEEE Trans. Circuits Syst. II Express Briefs 65(2), 166–170 (2018)

    Article  Google Scholar 

  34. J. Valsa, J. Vlach, RC models of a constant phase element. Int. J. Circuit Theory Appl. 41(1), 59–67 (2013)

    Google Scholar 

  35. C. Vastarouchas, G. Tsirimokou, T.J. Freeborn, C. Psychalinos, Emulation of an electrical-analogue of a fractional-order human respiratory mechanical impedance model using OTA topologies. AEU Int. J. Electron. Commun. 78, 201–208 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Stavroula Kapoulea & Costas Psychalinos

  2. Department of Electrical and Computer Engineering, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates

    Ahmed S. Elwakil

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

    Ahmed S. Elwakil

Authors
  1. Stavroula Kapoulea
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Costas Psychalinos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ahmed S. Elwakil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Costas Psychalinos.

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kapoulea, S., Psychalinos, C. & Elwakil, A.S. Minimization of Spread of Time-Constants and Scaling Factors in Fractional-Order Differentiator and Integrator Realizations. Circuits Syst Signal Process 37, 5647–5663 (2018). https://doi.org/10.1007/s00034-018-0840-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-018-0840-6

Keywords

Search

Navigation