Synthesis of fractional-order elements using the RC-EDP approach

Using the theory of analyzing the properties of RC-EDP (resistive-capacitive elements with distributed parameters) structures we propose the synthesis of elements with fractional impedance (EFI) - fractional capacitors C
_α
(0 <; α <; 1) suitable for analogue function block design. The direct utilization of such fractional elements overcomes the problem of approximating the needed fractional order element by an RC ladder or any other similar structure or approximating the fractional transfer function by an integer-order one. For the EFI synthesis, a genetic algorithm based tool has been developed that based on the required properties of the EFI to be designed determines the parameters of individual R-C-NR sections and their interconnection, whereas the parasitic parameteres relevant for the implementation process can also be assumed. Using the outputs of the software, we show the further usage of the R-C-NR section's parameters resulting in the layout design of the final fractional capacitor.