Equivalent diagrams of fractional order elements

This paper presents equivalent impedance and operator admittance systems for fractional order elements. Presented models of fractional order elements of the type: sαLα and 1/sαCα, (0 α 1) were obtained using the Laplace transform based on the expansion of the factor sign to an infinite fraction with varying degrees of accuracy - the continued fraction expansion method (CFE). Then circuit synthesis methods were applied. As a result, equivalent circuit diagrams of fractional order elements were obtained. The obtained equivalent schemes consist both of classical RLC elements, as well as active elements built based on operational amplifiers. Numerical experiments were conducted for the constructed models, presenting responses to selected input signals.

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The article was realized within the framework of the internship of Sebastian Różowicz, Ph.D., realized at the Rzeszow University of Technology from 1 March 2021, to 30 June 2021, Internship topic: Application of mathematical methods to systems analysis in electrical engineering.