Two implementations of fractional-order relaxation oscillators


This work proposes general formulas for designing two different topologies of fractional-order relaxation oscillators. One topology contains an Operational Amplifier and the other one relies on an Operational Trans-Resistance Amplifier. The design procedure hinges on the general fractional-order natural and step responses of RC, which is proved in this work depending on Mittag Leffler function. The proposed topologies can be controlled to generate symmetrical and non-symmetrical square wave signals. They also benefit from the employment of fractional-order capacitors (FOCs), which makes it possible to obtain higher frequencies using simple components. Furthermore, these topologies are verified through numerical solutions, circuit simulations, and experimental implementations. This encourages the authors to build circuit emulators for the FOC, which is achieved by applying the Foster-I synthesizing technique to the Matsuda’s approximation of s?. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.


Elwy O., AbdelAty A.M., Said L.A., Madian A.H., Radwan A.G.


Approximation; Fractional-order capacitor; Fractional-order circuits; Matsuda; Relaxation oscillator

Document Type



Analog Integrated Circuits and Signal Processing, Vol. 106, PP. 421 to 432, Doi: 10.1007/s10470-020-01640-x

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