Fractional Resonance-Based Filters

We propose the use of a fractional order capacitor and fractional order inductor with orders <path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105 q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /> ,   , respectively, in a fractional series circuit to realize fractional-step lowpass, highpass, bandpass, and bandreject filters. MATLAB simulations of lowpass and highpass responses having orders of , 1.5, and 1.9 and bandpass and bandreject responses having orders of 1.5 and 1.9 are given as examples. PSPICE simulations of 1.1, 1.5, and 1.9 order lowpass and 1.0 and 1.4 order bandreject filters using approximated fractional order capacitors and fractional order inductors verify the implementations.

[1]  Ahmed S. Elwakil,et al.  On the Generalization of Second-Order Filters to the fractional-Order Domain , 2009, J. Circuits Syst. Comput..

[2]  Thierry Poinot,et al.  Fractional modelling and identification of thermal systems , 2011, Signal Process..

[3]  José António Tenreiro Machado,et al.  Fractional order electromagnetics , 2006, Signal Process..

[4]  B. Goswami,et al.  Fabrication of a Fractional Order Capacitor With Desired Specifications: A Study on Process Identification and Characterization , 2011, IEEE Transactions on Electron Devices.

[5]  T. Freeborn,et al.  Fractional-step Tow-Thomas biquad filters , 2012 .

[6]  J. J. Quintana,et al.  IDENTIFICATION OF THE FRACTIONAL IMPEDANCE OF ULTRACAPACITORS , 2006 .

[7]  Alain Oustaloup,et al.  Fractional system identification for lead acid battery state of charge estimation , 2006, Signal Process..

[8]  Dominik Sierociuk,et al.  Comparison and validation of integer and fractional order ultracapacitor models , 2011 .

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

[10]  Non-members,et al.  Noise analysis of single stage fractional-order low-pass fllter using stochastic and fractional Calculus , 2009 .

[11]  A. G. Radwan,et al.  Butterworth passive filter in the fractional-order , 2011, ICM 2011 Proceeding.

[12]  Leonard T. Bruton,et al.  Network Transfer Functions Using the Concept of Frequency-Dependent Negative Resistance , 1969 .

[13]  B. T. Krishna,et al.  Active and Passive Realization of Fractance Device of Order 1/2 , 2008 .

[14]  Walter Lauriks,et al.  Application of fractional calculus to ultrasonic wave propagation in human cancellous bone , 2006, Signal Process..

[15]  G. Ablart,et al.  Influence of the electrical parameters on the input impedance of a fractal structure realised on silicon , 2005 .

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

[17]  Ahmed S. Elwakil,et al.  High-quality factor asymmetric-slope band-pass filters: A fractional-order capacitor approach , 2012, IET Circuits Devices Syst..

[18]  Ahmed S. Elwakil,et al.  On the practical realization of higher-order filters with fractional stepping , 2011, Signal Process..

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

[20]  Ahmed S. Elwakil,et al.  Field programmable analogue array implementation of fractional step filters , 2010, IET Circuits Devices Syst..

[21]  Ahmed S Elwakil,et al.  Fractional-order circuits and systems: An emerging interdisciplinary research area , 2010, IEEE Circuits and Systems Magazine.