Implementation of first and third order fractional order differentiators and integrators using switched capacitors

Abstract

This paper proposes first-order and third-order Switched Capacitor realizations of fractional order differentiators and integrators. First, the s-to-z transformation is expanded for fractional powers using Taylor series expansion (TSE) and continued fraction expansion (CFE). Then, the stabilized models of the fractional order differentiators and integrators are realized using Switched capacitor (SC) circuits and implemented using OrCAD Pspice. The simulation results obtained using Pspice matched with their corresponding MATLAB simulation results and are in close conformity with the theoretical results of the continuous-time (c-t) counter parts. The fractional order of the differentiator or integrator helps in enhancing the system control performance better than the conventional order systems. The major purpose of this paper is to emphasize that the mixed mode realizations of fractional order differentiators and integrators using SC technique allow integration of both digital and analog functions on a single chip, and can be used in various control applications.