Comparative study of fractional-order differentiators and integrators

The transfer function of fractional-order differentiators and integrators can be approximated through the utilization of appropriate integer-order transfer functions. Efficient tools towards this goal include the Continued Fraction Expansion as well as the Oustaloup's approximations. In this paper, the accuracy of the expressions derived through the various orders of these approximations, in terms of magnitude and phase response, is studied. In addition, the corresponding implementations 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 presented and compared.