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An approach to improve the performance of fractional-order sinusoidal oscillators

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  • Mishra, Shalabh Kumar
  • Upadhyay, Dharmendra Kumar
  • Gupta, Maneesha

Abstract

This paper presents a simple technique to approximate fractance devices (FDs) capable of improving the performance of any fractional-order oscillator. The proposed technique is based on an elementary mathematical tool of impedance equalization, and requires significantly lesser number of passive components than the existing FD approximation schemes. To compare the merit of approximated FDs with the existing R-C ladder based FDs, a well-known fractional-order Wien-bridge oscillator is realized using both FDs one by one; and the corresponding results are compared exhaustively. It is observed that the fractional-order oscillator realized using the proposed FDs gives better performance in terms of phase-noise, figure of merit (FoM), total harmonic distortion (THD), settling time, peak-to-peak voltage, power dissipation, and hardware compactness. Authenticity and accuracy of the proposed design has been verified using PSpice simulation and practical implementation.

Suggested Citation

  • Mishra, Shalabh Kumar & Upadhyay, Dharmendra Kumar & Gupta, Maneesha, 2018. "An approach to improve the performance of fractional-order sinusoidal oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 126-135.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:126-135
    DOI: 10.1016/j.chaos.2018.09.015
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    1. Dehghan, Mehdi & Shakourifar, Mohammad & Hamidi, Asgar, 2009. "The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2509-2521.
    2. Li, Ping & Zhong, Shou-Ming & Cui, Jin-Zhong, 2009. "Stability analysis of linear switching systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 474-480.
    3. Narahari Achar, B.N. & Hanneken, John W. & Clarke, T., 2002. "Response characteristics of a fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 275-288.
    4. Radwan, A.G. & Soliman, A.M. & Elwakil, A.S. & Sedeek, A., 2009. "On the stability of linear systems with fractional-order elements," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2317-2328.
    5. Achar, B.N.Narahari & Hanneken, J.W. & Enck, T. & Clarke, T., 2001. "Dynamics of the fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(3), pages 361-367.
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