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All Possible Topologies of the Fractional-Order Wien Oscillator Family Using Different Approximation Techniques

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Abstract

This paper introduces all the possible topologies of the Wien bridge oscillator family. This family has 72 topologies, 24 of them contain only RC or RL pairs, and the rest contain mixed pairs. The complete mathematical analysis of all twelve possible capacitive-based topologies is proposed in the fractional-order domain. The investigated circuits can be categorized into two groups, each with a similar characteristic equation. Three integer-order approximation techniques for the Laplacian operator \(s^\alpha \) are employed to solve and simulate the Wien bridge system. The studied approximations are those of Matsuda, Oustaloup, and Valsa’s network. Fractional-order capacitor (FOC) emulators are built using these approximations and applied in the circuit simulation. Comparisons are made on different levels, starting with the mathematical solution of the characteristic equation, followed by PSpice simulation, which compares topologies of the Wien bridge oscillator family. Hardware implementation of the FOC emulators is presented applying passive discrete components using the Foster-I technique. Additionally, sensitivity tests of the discrete components of the FOC emulators are performed using Monte Carlo analysis. Experimental results are introduced to validate the theoretical findings.

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Acknowledgements

The authors would like to thank the Science and Technology Development Fund (STDF) for funding the project \(\#\) 25977 and the Nile University for facilitating all procedures required to complete this study.

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Authors and Affiliations

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

    Omar Elwy, Lobna A. Said & Ahmed H. Madian

  2. Radiation Engineering Department, NCRRT, Egyptian Atomic Energy Authority, Cairo, Egypt

    Ahmed H. Madian

  3. Engineering Mathematics Department, Faculty of Engineering, Cairo University, Giza, 12613, Egypt

    Ahmed G. Radwan

  4. School of Engineering and Applied Sciences, Nile University, Giza, 12588, Egypt

    Ahmed G. Radwan

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  1. Omar Elwy
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  2. Lobna A. Said
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  3. Ahmed H. Madian
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  4. Ahmed G. Radwan
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Correspondence to Lobna A. Said.

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Elwy, O., Said, L.A., Madian, A.H. et al. All Possible Topologies of the Fractional-Order Wien Oscillator Family Using Different Approximation Techniques. Circuits Syst Signal Process 38, 3931–3951 (2019). https://doi.org/10.1007/s00034-019-01057-6

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