Equivalent diagrams of fractional order elements

Abstract

This paper presents equivalent impedance and operator admittance systems for fractional order elements. Presented models of fractional order elements of the type: s α L α and 1/s α C α, (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.

Keywords

• fractional order derivative
• laplace transformfor fractional order systems
• cfe method
• circuit synthesis
• numerical experiments