Minimization of Spread of Time-Constants and Scaling Factors in Fractional-Order Differentiator and Integrator Realizations

Abstract

The approximations of fractional-order differentiator/integrator transfer functions are currently performed using integer-order rational functions, which are in general implemented through appropriate multi-feedback topologies. The spreading in the values of time-constants and scaling factors, needed to implement these topologies, increases as the order of the differentiator/integrator and/or the order of the approximation increases. This leads to non-practical values of capacitances and resistances/transconductances in the implementation. A solution to overcome this obstacle is introduced in this paper, based on the employment of a combination of fractional-order and integer-order integrators and differentiators for implementing the desired function. The performance of the proposed scheme is verified through post-layout simulations using Cadence and the Design Kit provided by the Austria Mikro Systeme $$0.35~\upmu \mathrm{m}$$ CMOS technology process.