Abstract
This chapter introduces a family of fractional-order oscillators based on a single operational amplifier (Op-Amp) with two fractional-order capacitors. Twelve different fractional-order oscillator circuits are investigated where the state matrix, oscillation frequency, and oscillation condition for each circuit are presented. The phase difference between the two oscillatory outputs is deduced in terms of the fractional-order parameters. The fractional-order parameter enhances the oscillator performance by providing an extra degree-of-freedom. Also, the resulting circuits provide independent controllability for the phase difference and the oscillation frequency. Numerical simulations using MATLAB® are performed to study the effect of the fractional-order parameters on the circuit response. Moreover, PSpice simulations are performed on different cases using two different fractional-order capacitors. Selected cases are verified experimentally to confirm the theoretical findings. © 2022 Elsevier Inc. All rights reserved.
Authors
Khalil N.A., Mohsen M., Ahmed G.M., Said L.A., Madian A.H., Radwand A.G.
Source
Fractional Order Systems: An Overview of Mathematics, Design, and Applications for Engineers, Doi:10.1016/B978-0-12-824293-3.00015-6
Document Type
Book Chapter