Skip to main content
SpringerLink
Log in

Practical Design and Evaluation of Fractional-Order Oscillator Using Differential Voltage Current Conveyors

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

Abstract

This paper deals with the design, analysis, computer simulation, and experimental measurement of fractional-order sinusoidal oscillator with two current conveyors, two resistors, and two fractional immittance elements. The used conveyor is based on the bulk-driven quasi-floating-gate technique in order to offer high threshold-to-supply voltage ratio and maximum input-to-supply voltage ratio. The supply voltage of the oscillator is 1 V, and the power consumption is \(74\,\upmu \hbox {W}\), and hence the proposed oscillator can be suitable for biomedical, portable, battery-powered, and other applications where the low-power consumption is critical. A number of equations along with graphs describing the theoretical properties of the oscillator are presented. The unique features of fractional-order oscillator are highlighted considering practical utilization, element computation, tuning, phase shift of output signals, sensitivities, etc. The simulations performed in the Cadence environment and the measurements of a real chip confirm the attractive features of the proposed oscillator.

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

Access this article

Log in via an institution

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. G. Carlson, C. Halijak, Approximation of fractional capacitors \((\text{1/s })^{\wedge }(\text{1/n })\) by a regular Newton process. IEEE Trans. Circuits Syst. 11, 210–213 (1964)

    Google Scholar 

  2. A.M. Elshurafa, M.N. Almadhoun, K.N. Salama, H.N. Alshareef, Microscale electrostatic fractional capacitors using reduced graphene oxide percolated polymer composites. Appl. Phys. Lett. 102, 232,901 (2013)

    Article  Google Scholar 

  3. A.S. Elwakil, Fractional-order circuits and systems: an emerging interdisciplinary research area. IEEE Circuits Syst. Mag. 10, 40–50 (2010)

    Article  Google Scholar 

  4. H.O. Elwan, A.M. Soliman, Novel CMOS differential voltage current conveyor and its applications. Circuits Devices Syst. IEE Proc. 144, 3 (1997)

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. A.K. Gil’mutdinov, N.V. Porivaev, P.A. Ushakov, Active RC-filter on parametric RC-EDP for adaptive communication systems. Nelineynyy Mir 11, 740–746 (2011)

    Google Scholar 

  7. F. Khateb, Bulk-driven floating-gate and bulk-driven quasi-floating-gate techniques for low-voltage, low-power analog circuits design. Int. J. Electron. Commun. (AEU) 68, 64–72 (2014)

    Article  Google Scholar 

  8. F. Khateb, The experimental results of the bulk-driven quasi-floating-gate MOS transistor. Int. J. Electron. Commun. (AEU) 69, 462–466 (2015)

    Article  Google Scholar 

  9. M.S. Krishna, S. Das, K. Biswas, B. Goswami, Fabrication of a fractional order capacitor with desired specifications: a study on process identification and characterization. IEEE Trans. Electron Devices 58, 4067–4073 (2011)

    Article  Google Scholar 

  10. B. Maundy, A.S. Elwakil, T. Freeborn, On the practical realization of higher-order filters with fractional stepping. Signal Process. 91, 484–491 (2011)

    Article  MATH  Google Scholar 

  11. B. Maundy, A.S. Elwakil, S. Gift, On the realization of multi-phase oscillators using fractional-order allpass filters. Circuits Syst. Signal Process. 31, 3–17 (2012)

    Article  MathSciNet  Google Scholar 

  12. D. Mondal, K. Biswas, Performance study of fractional order integrator using single component fractional order elements. IET Circuits Devices Syst. 5, 334–342 (2011)

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. I. Podlubny, I. Petráš, B.M. Vinagre, P. O’Leary, L’. Dorčák, Analogue realizations of fractional-order controllers. Nonlinear Dyn. 29(1–4), 281–296 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. A.A. Potapov, P.A. Ushakov, A.K. Gil’mutdinov, Elements, devices, and methods for fractal communication technology, electronics, and nanotechnology. Phys. Wave Phenom. 18, 119–142 (2010)

    Article  Google Scholar 

  16. A.G. Radwan, A.S. Elwakil, A.M. Soliman, Fractional-order sinusoidal oscillator: design procedure and practical examples. IEEE Trans. Circuits Syst. I(55), 2051–2063 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. A.G. Radwan, A.S. Elwakil, A.M. Soliman, On the generalization of second order filters to the fractional order domain. J. Circuits Syst. Comput. 18, 361–386 (2009)

    Article  Google Scholar 

  18. A.G. Radwan, A.M. Soliman, A.S. Elwakil, Design equations for fractional-order sinusoidal oscillators: four practical circuits examples. Int. J. Circuit Theory Appl. 36, 473–492 (2007)

    Article  MATH  Google Scholar 

  19. A.G. Radwan, A.M. Soliman, A.S. Elwakil, First-order filters generalized to the fractional domain. J. Circuits Syst. Comput. 17, 55–66 (2008)

    Article  Google Scholar 

  20. S. Roy, On the realization of a constant-argument immittance or fractional operator. IEEE Trans. Circuits Syst. 14, 264–274 (1967)

    Google Scholar 

  21. A.M. Soliman, Generation of oscillators based on grounded capacitor current conveyors with minimum passive components. J. Circuits Syst. Comput. 18(05), 857–873 (2009)

    Article  Google Scholar 

  22. A. Soltan, A.G. Radwan, A.M. Soliman, CCII based fractional filters of different orders. J. Adv. Res. 5, 157–164 (2014)

    Article  Google Scholar 

  23. K. Steiglitz, An RC impedance approximation to \(\text{ s }^{\wedge }(\text{-1/2 })\). IEEE Trans. Circuits Syst. 11, 160–161 (1964)

    Google Scholar 

  24. M. Sugi, Y. Hirano, Y.F. Miura, K. Saito, Simulation of fractal immittance by analog circuits: an approach to the optimized circuits. IEICE Trans. on Fundam. Electron. Commun. Comput. Sci. E82, 1627–1634 (1999)

    Google Scholar 

  25. M.C. Tripathy, K. Biswas, S. Sen, A design example of a fractional-order Kerwin–Huelsman–Newcomb biquad filter with two fractional capacitors of different order. Circuits Syst. Signal Process. 32, 1523–1536 (2013)

    Article  MathSciNet  Google Scholar 

  26. 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, 1183–1196 (2015)

    Article  Google Scholar 

  27. G. Tsirimokou, C. Laoudias, C. Psychalinos, 0.5V fractional-order companding filters. Int. J. Circuit Theory Appl. 43, 1105–1126 (2015)

    Article  Google Scholar 

  28. G. Tsirimokou, C. Psychalinos, Ultra-low voltage fractional-order circuits using current-mirrors. Int. J. Circuit Theory Appl. (2015). doi:10.1002/cta.2066

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

    Article  Google Scholar 

  30. S. Westerlund, L. Ekstam, Capacitor theory. IEEE Trans. Dielectr. Electr. Insul. 1(5), 826–839 (1994)

    Article  Google Scholar 

Download references

Acknowledgments

Research described in this paper was financed by the National Sustainability Program under Grant LO1401 and by the Czech Science Foundation under Grant No. P102-15-21942S. For the research, infrastructure of the SIX Center was used. Also it was supported by Grant E.029 from the Research Committee of the University of Patras (Programme K. Karatheodori).

Author information

Authors and Affiliations

  1. Department of Telecommunications, Brno University of Technology, Technická 12, Brno, Czech Republic

    David Kubánek

  2. Department of Microelectronics, Brno University of Technology, Technicka 10, Brno, Czech Republic

    Fabian Khateb

  3. Faculty of Biomedical Engineering, Czech Technical University in Prague, nám. Sítná 3105, Kladno, Czech Republic

    Fabian Khateb

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

    Georgia Tsirimokou & Costas Psychalinos

Authors
  1. David Kubánek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fabian Khateb
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Georgia Tsirimokou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Costas Psychalinos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fabian Khateb.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kubánek, D., Khateb, F., Tsirimokou, G. et al. Practical Design and Evaluation of Fractional-Order Oscillator Using Differential Voltage Current Conveyors. Circuits Syst Signal Process 35, 2003–2016 (2016). https://doi.org/10.1007/s00034-016-0243-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-016-0243-5

Keywords

Search

Navigation