First-Order Filters Generalized to the Fractional Domain

Radwan, Ahmed G.; Soliman, Ahmed M.; Elwakil, Ahmed S.

doi:10.1142/s0218126608004162

Cited by 233 publications

(116 citation statements)

References 2 publications

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“…Owing to the interdisciplinary nature of the fractional calculus, 1 there is a growing research interest in the development of fractional-order circuits including¯lters, [2][3][4][5][6][7][8][9] oscillators, [10][11][12][13] biological tissues emulators, 14 and energy storage devices. 15 In these applications, the basic building blocks are the fractional-order capacitors and/or fractional-order inductors.…”

Section: Introductionmentioning

confidence: 99%

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

Τσιριμώκου

Kartci

Koton

et al. 2018

J CIRCUIT SYST COMP

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Due to the absence of commercially available fractional-order capacitors and inductors, their implementation can be performed using fractional-order di®erentiators and integrators, respectively, combined with a voltage-to-current conversion stage. The transfer function of fractional-order di®erentiators and integrators can be approximated through the utilization of appropriate integer-order transfer functions. In order to achieve that, the Continued Fraction Expansion as well as the Oustaloup's approximations can be utilized. The accuracy, in terms of magnitude and phase response, of transfer functions of di®erentiators/integrators derived through the employment of the aforementioned approximations, is very important factor for achieving high performance approximation of the fractional-order elements. A comparative study of the accuracy o®ered by the Continued Fraction Expansion and the Oustaloup's approximation is performed in this paper. As a next step, the corresponding implementations of the emulators of the fractional-order elements, derived using fundamental active cells such as operational ampli¯ers, operational transconductance ampli¯ers, current conveyors, and current feedback operational ampli¯ers realized in commercially available discrete-component IC form,

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Section: Introductionmentioning

confidence: 99%

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

Τσιριμώκου

Kartci

Koton

et al. 2018

J CIRCUIT SYST COMP

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“…Generally for each value of x there are two values of y except at the pinched point (x p , y p ) which can be calculated by 14) and the line y = (a + Fig. 3.8a.…”

Section: Continuous Nonsymmetrical Modelmentioning

confidence: 99%

Memristor Mathematical Models and Emulators

Radwan

Fouda

2015

Studies in Systems, Decision and Control

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Recently, different mathematical models describing the generic memristors have been introduced [1][2][3]. But, the first model of the memristor was introduced by HP in [4], where the memristor current voltage relationship was described bywhere i(t) represents the current through the memristor, v(t) is the voltage across the memristor, R on and R off are the minimum and maximum achievable resistances of the memristor, respectively. The memristor resistance depends on state variable x d (t) which is the ratio between the doped region length and the full length D of the memristor and is given byIntegrating (3.2) and substituting in (3.1); assuming zero initial condition for the current, the memristance R m can then be given by (3.3)where η ∈ −1, 1 represents the memristor polarity, k =/C; μ v is the ion mobility, and R in is the initial resistance of the memristor.

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“…While there are no physical analogies to these derivatives, like slope or area under the curve, they are still applicable to physical systems with varying applications including materials theory [3,4], control theory [5,6], electromagnetics [7], robotics [8,9] and many more. The import of these concepts into circuit theory is relatively new [10] with much recent progress regarding filter theory [11,12], analysis [13] and implementation [14][15][16]. This emerging field has introduced fractional calculus into analog filter design to achieve continuous time filtering circuits with fractional step stopband attenuations.…”

Section: Introductionmentioning

confidence: 99%

Fractional-step Tow-Thomas biquad filters

Freeborn

Maundy

Elwakil

2012

NOLTA

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Abstract:In this paper we propose the use of fractional capacitors in the Tow-Thomas biquad to realize both fractional lowpass and asymmetric bandpass filters of order 0 < α 1 + α 2 ≤ 2, where α 1 and α 2 are the orders of the fractional capacitors and 0 < α 1,2 ≤ 1. We show how these filters can be designed using an integer-order transfer function approximation of the fractional capacitors. MATLAB and PSPICE simulations of first order fractional-step low and bandpass filters of order 1.1, 1.5, and 1.9 are given as examples. Experimental results of fractional low pass filters of order 1.5 implemented with silicon-fabricated fractional capacitors verify the operation of the fractional Tow-Thomas biquad.

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First-Order Filters Generalized to the Fractional Domain

Cited by 233 publications

References 2 publications

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

Memristor Mathematical Models and Emulators

Fractional-step Tow-Thomas biquad filters

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