Analog Integrated Circuits and Signal Processing

, Volume 101, Issue 2, pp 267–279 | Cite as

Stability analysis of fractional-order Colpitts oscillators

  • Lobna A. Said
  • Omar Elwy
  • Ahmed H. MadianEmail author
  • Ahmed G. Radwan
  • Ahmed M. Soliman


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.


Fractional-order circuits Colpitts Oscillators Stability Valsa’s network Fractional-order capacitor 



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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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityGizaEgypt
  2. 2.Radiation Engineering Department, NCRRTEgyptian Atomic Energy AuthorityCairoEgypt
  3. 3.Engineering Mathematics and Physics Department, Faculty of EngineeringCairo UniversityGizaEgypt
  4. 4.School of Engineering and Applied SciencesNile UniversityGizaEgypt
  5. 5.Electronics and Communication Engineering DepartmentCairo UniversityGizaEgypt

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