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

Článek WoS

Due to the absence of commercially available fractional-order capacitors and inductors, their implementation can be performed using fractional-order differentiators and integrators, respectively, combined with a voltage-to-current conversion stage. The transfer function of fractional-order differentiators 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 differentiators/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 offered 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 amplifiers, operational transconductance amplifiers, current conveyors, and current feedback operational amplifiers realized in commercially available discrete-component IC form, are compared in terms of the most important performance characteristics. The most suitable of them are further compared using the OrCAD PSpice software.

Due to the absence of commercially available fractional-order capacitors and inductors, their implementation can be performed using fractional-order differentiators and integrators, respectively, combined with a voltage-to-current conversion stage. The transfer function of fractional-order differentiators 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 differentiators/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 offered 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 amplifiers, operational transconductance amplifiers, current conveyors, and current feedback operational amplifiers realized in commercially available discrete-component IC form, are compared in terms of the most important performance characteristics. The most suitable of them are further compared using the OrCAD PSpice software.

Continued Fraction Expansion; current conveyor; current feedback operational amplifier; fractional-order differentiator; fractional-order integrator; op-amp; operational transconductance amplifier; Oustaloup’s approximation

Continued Fraction Expansion; current conveyor; current feedback operational amplifier; fractional-order differentiator; fractional-order integrator; op-amp; operational transconductance amplifier; Oustaloup’s approximation

TSIRIMOKOU, G.; KARTCI, A.; KOTON, J.; HERENCSÁR, N.; PSYCHALINOS, C.

2019

06.02.2018

World Scientific

0218-1266

JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS

27

11

Singapurská republika

1850170-1

1850170-26

26

https://www.worldscientific.com/doi/abs/10.1142/S0218126618501700

http://hdl.handle.net/11012/70925

2018 Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators
s0218126618501700