Frequency Response of a Fractional Order Shunt Resonator of the Class R-RLβCα

Mehmet Emir Koksal

Fractional order derivative, frequency response, fractional inductance, fractional capacitance.

Frequency domain analysis of a fractional order parallel shunt resonator of the class R-RL_β C_αis conducted. The voltage and current waveforms are computed in the frequency domain. It is shown that the circuit exhibits all three types of basic filtering characteristics; namely low-pass, band-pass, and high-pass.

10.22161/ijaers.5.12.26

I.Podlubny, Fractional Differential Equations, Academic Press, 1999.
L. Zhang, Y. Yang, F. Wang, “Synchronization analysis of fractional-order neural networks with time-varying delays via discontinuous neuron activations”, Neuroscience,vol. 275, pp. 40-49, 2018.
V. Wesh, A. Vyawahare, G.E. Paredes, “On the stability of linear fractional-space neutron kinetics (F-SNPK) models for nuclear reactor dynamics”, Annuals of Nuclear Energy, vol. 111, pp. 12-21, 2018.
H. Singh, “Approximate solutions of fractional vibration equation using Jacobi polynomials”, Applied Mathematics and Computation, vol. 317, pp. 85-100, 2018.
A. Dabiri, M. Poursina, E. Butcher, M. Nazari, “Optimal Periodic-Gain Fractional Delayed State Feedback Control for Linear Fractional Periodic Time-Delayed Systems”, April 2018, IEEE Transactions on Automatic Control PP(99), DOI: 10.1109/TAC.2017.2731522.
D. Bouagadaa, S. Melchiorb, P.V. Dooren, “Calculating the H∞ norm of a fractional system given in state-space form”, Applied Mathematics Letters, vol. 79, pp. 51-57, 2018.
L. Marinangeli, F. Alijani, S.H. Hosseina, ”Fractional-order positive position feedback compensator for active vibration control of a smart composite plat”, Journal of Sound and Vibration, vol. 412, pp. 1-16, 2017
F. Gomez, J. Rosales, M. Guia, “RLC electrical circuits of non-integer order”, Central European Journal of Physics, vol. 11, pp. 1361-1365, 2013.
J.F. Gomez-Aguilar, A. Atangana, V.F. Morales-Delgado, “Electrical circuits RC, LC, RL described by Atangana-Baleanu fractional derivatives”, Int. J. Circuit Theory and Appl., DOI: 10.1002/cta.2348, 2017.
R. Zhou, D. Chen, “Fractional-Order 2xn RLC circuit network“, Journal of Circuits, Systems, and Computers, vol. 24, pp. 1-25, 2015.
A.G. Radwan, M. E. Fouda, “Optimization of fractional-order RLC filters”, Circuits, Systems, and Signal Processing, vol. 32, pp 2097–2118, 2013.
J. Walczak and A. Jjukobowska, “Resonance in series fractional order RL_β C_α circuit, Electronics Review, vol. 4, pp. 210-213, 2014.
A.J. Ciszek, J. Walczak, “Analysis of the transient state in a parallel circuit of the class RL_β C_α”, Applied Mathematics and Computation, vol. 319, pp. 287-300, 2018.