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.












Similar content being viewed by others
References
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)
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)
A.S. Elwakil, Fractional-order circuits and systems: an emerging interdisciplinary research area. IEEE Circuits Syst. Mag. 10, 40–50 (2010)
H.O. Elwan, A.M. Soliman, Novel CMOS differential voltage current conveyor and its applications. Circuits Devices Syst. IEE Proc. 144, 3 (1997)
T. Freeborn, B. Maundy, A. Elwakil, Field programmable analogue array implementation of fractional step filters. IET Circuits Devices Syst. 4, 514–524 (2010)
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)
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)
F. Khateb, The experimental results of the bulk-driven quasi-floating-gate MOS transistor. Int. J. Electron. Commun. (AEU) 69, 462–466 (2015)
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)
B. Maundy, A.S. Elwakil, T. Freeborn, On the practical realization of higher-order filters with fractional stepping. Signal Process. 91, 484–491 (2011)
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)
D. Mondal, K. Biswas, Performance study of fractional order integrator using single component fractional order elements. IET Circuits Devices Syst. 5, 334–342 (2011)
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)
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)
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)
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)
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)
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)
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)
S. Roy, On the realization of a constant-argument immittance or fractional operator. IEEE Trans. Circuits Syst. 14, 264–274 (1967)
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)
A. Soltan, A.G. Radwan, A.M. Soliman, CCII based fractional filters of different orders. J. Adv. Res. 5, 157–164 (2014)
K. Steiglitz, An RC impedance approximation to \(\text{ s }^{\wedge }(\text{-1/2 })\). IEEE Trans. Circuits Syst. 11, 160–161 (1964)
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)
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)
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)
G. Tsirimokou, C. Laoudias, C. Psychalinos, 0.5V fractional-order companding filters. Int. J. Circuit Theory Appl. 43, 1105–1126 (2015)
G. Tsirimokou, C. Psychalinos, Ultra-low voltage fractional-order circuits using current-mirrors. Int. J. Circuit Theory Appl. (2015). doi:10.1002/cta.2066
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)
S. Westerlund, L. Ekstam, Capacitor theory. IEEE Trans. Dielectr. Electr. Insul. 1(5), 826–839 (1994)
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
Corresponding author
Rights and permissions
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-016-0243-5