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2 Poznan University of Technology Academic Journals. Electrical Engineering

2 2016

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Electronic realizations of fractional-order elements: II. Simulation studies

Jakubowska A., Szymczak M.

Poznan University of Technology Academic Journals. Electrical Engineering

2016

No. 85

149--159

The paper presents simulation studies on the synthesis of new fractional-order elements, using classic fractional-order components, such as supercapacitors and real coils with ferromagnetic cores. These new fractional-order elements have been realized using a generalized impedance converter GIC. Firstly, a new method for fractional-order elements modeling in PSpice has been described, which involves the use of controlled voltage E or current G sources, defined in Analog Behavioral Modeling (ABM). An equivalence of the classic and proposed description of the fractional-order capacitor have been presented. For the GIC structure, two cases of the have been analyzed in the PSpice: first, with models of ideal operational amplifiers, modeled as controlled voltage sources, and the second with models of the real operational amplifiers, of type OPA549. The obtained frequency characteristics of an exemplary GIC structure with one fractionalorder element show big similarity for both types of models. The impact of different values of the parameter α and the type of the used real amplifier on the solution has been analyzed too.

Electronic realizations of fractional-order elements: I. Synthesis of the arbitrary order elements

Jakubowska A., Walczak J.

Poznan University of Technology Academic Journals. Electrical Engineering

2016

No. 85

137--148

The paper presents a synthesis method of new fractional-order elements, using classic fractional-order components, such as supercapacitors and real coils with ferromagnetic cores. These new fractional-order elements have been realized using a generalized impedance converter GIC. Two cases have been analyzed in the paper: first, with only one fractional-order element being a load impedance of the generalized impedance converter, and second, with two fractional-order elements - one being a part of the structure of the GIC and the second being the load impedance. The derived relations are illustrated by simulation examples for the circuit. The impact of different values of the parameter α on the solution of the considered problem has been analyzed too.