Current feedback operational amplifier (CFOA) based fractional order oscillators

This paper presents a study of fractional order oscillators based on current feedback operational amplifiers (CFOA). Two general cases have been discussed for the oscillation frequency and condition with the use of two fractional order elements of different orders. Design procedure for the two general cases is illustrated with numerical discussions. Circuit simulations for some special cases are presented to validate the theoretical findings. The simulations have been done using Ad844 commercial CFOA model.

[1]  I. Podlubny.  Matrix Approach to Discrete Fractional Calculus , 2000 .

[2]  M. Rich.  Designing phase locked oscillators for synchronization , 1974 .

[3]  M. Nakagawa,et al.  Basic Characteristics of a Fractance Device , 1992 .

[4]  Yoshiaki Hirano,et al.  Simulation of Fractal Immittance by Analog Circuits: An Approach to the Optimized Circuits , 1999 .

[5]  Raoul R. Nigmatullin,et al.  Theory of dielectric relaxation in non-crystalline solids: from a set of micromotions to the averaged collective motion in the mesoscale region , 2005 .

[6]  L. Dorcak.  Numerical Models for the Simulation of the Fractional-Order Control Systems , 2002 .

[7]  José António Tenreiro Machado,et al.  Experimental Signal Analysis of Robot Impacts in a Fractional Calculus Perspective , 2007, J. Adv. Comput. Intell. Intell. Informatics.

[8]  Meng Jian,et al.  A Digitally Controlled Oscillator for wireless communication application , 2011 .

[9]  Ahmed S. Elwakil,et al.  Fractional-order sinusoidal oscillators: Design procedure and practical examples , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  K. Salama,et al.  Theory of Fractional Order Elements Based Impedance Matching Networks , 2011, IEEE Microwave and Wireless Components Letters.

[11]  Ahmed M. Soliman,et al.  Current conveyor based or unity gain cells based two integrator loop oscillators , 2011, Microelectron. J..

[12]  Shlomo Havlin,et al.  Fractals in Science , 1995 .

[13]  Ahmed S. Elwakil,et al.  Design equations for fractional-order sinusoidal oscillators: Practical circuit examples , 2007 .

[14]  Hakan Kuntman,et al.  CFOA-Based Lossless and Lossy Inductance Simulators , 2011 .

[15]  Ahmed M. Soliman.  Current Feedback Operational Amplifier Based Oscillators , 2000 .

[16]  I. Podlubny,et al.  Analogue Realizations of Fractional-Order Controllers , 2002 .

[17]  Frederick E. Riewe,et al.  Mechanics with fractional derivatives , 1997 .

[18]  Kenneth S. Miller,et al.  Derivatives of Noninteger Order , 1995 .

[19]  Raj Senani,et al.  State variable synthesis of single resistance controlled grounded capacitor oscillators using only two CFOAs , 1998 .

[20]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[21]  C. Aldea,et al.  Grounded resistor controlled sinusoidal oscillator using CFOAs , 1997 .