Analog Modeling of Fractional-Order Elements: A Classical Circuit Theory Approach

Abstract

In this paper a comprehensive procedure for the analog modeling of Fractional-Order Elements (FOEs) is presented. Unlike most already proposed techniques, a standard approach from classical circuit theory is applied. It includes the realization of a system function by a mathematical approximation of the desired phase response, and the synthesis procedure for the realization of basic fractional-order (FO) one-port models as passive RC Cauer- and Foster-form canonical circuits. Based on the presented one-ports, simple realizations of two-port differentiator and integrator models are derived. Beside the description of the design procedure, illustrative examples, circuit diagrams, simulation results and practical realizations are presented.

Keywords

• Fractional-order element
• fractional-order differentiator and integrator
• fractional immittance
• constant-phase element
• approximation
• synthesis