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Stability analysis of fractional-order Colpitts oscillators

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A Correction to this article was published on 07 September 2019

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Abstract

The mathematical formulae of six topologies of fractional-order Colpitts oscillator are introduced in this paper. Half of these topologies are based on MOS transistor, and the other half is based on BJT transistor. The design procedure for all of these topologies is proposed and summarized for each one. Stability analysis is very crucial in oscillators’ design, as oscillators should have its poles on the imaginary axis to obtain a sustained oscillation. Hence, determining the factors that control the oscillator’s stability is very important. An intensive study of the stability of Colpitts oscillator is introduced, including different cases for all topologies. Additionally, circuit simulation is conducted using Valsa’s emulator of the fractional-order capacitor for validating the mathematical formulae and the stability criteria. Experimental work is also included to verify the mathematical findings and circuit simulations.

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  • 07 September 2019

    Unfortunately, in the original version of the article some typos occurred.

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Acknowledgements

Authors would like to thank Science and Technology Development Fund (STDF) for funding the project # 25977 and 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

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

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

    Ahmed H. Madian

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

    Ahmed G. Radwan

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

    Ahmed G. Radwan

  5. Electronics and Communication Engineering Department, Cairo University, Giza, Egypt

    Ahmed M. Soliman

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

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Said, L.A., Elwy, O., Madian, A.H. et al. Stability analysis of fractional-order Colpitts oscillators. Analog Integr Circ Sig Process 101, 267–279 (2019). https://doi.org/10.1007/s10470-019-01501-2

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