A fully integrated implementation of a parallel fractional-order resonator that employs together a fractional-order capacitor and a fractional-order inductor is proposed in this brief. The design utilizes current-controlled operational transconductance amplifiers as building blocks, designed, and fabricated in AMS 0.35-μm CMOS process and based on a second-order approximation of a fractional-order differentiator/integrator magnitude optimized in the range 10 Hz-700 Hz. An attractive benefit of the proposed scheme is its electronic tuning capability.

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.