Single active element implementation of fractional-order differentiators and integrators

A novel topology for implementing fractional-order differentiator and integrator transfer functions is presented in this paper. This topology is based on the employment of a second generation Current Conveyor with EXtra inputs (EX-CCII), passive resistors, and fractional-order capacitors. The main benefit offered by this implementation is that both fractional-order differentiator and integrator transfer functions are simultaneously available at different output terminals, and that their frequency characteristics can be orthogonally adjusted without disturbing each other. With only one EX-CCII device needed, the proposed design is attractive from the active component count point of view. As an application example, a fractional-order controller is designed in order to control the velocity of a small scale submersible equipped with one propeller. Evaluation of the performance of the presented topology is performed using Cadence and the Design Kit provided by the Austria Mikro Systeme (AMS) 0.35 μ m CMOS process, as well as through experimental results.