Design and Examples of Fractional-Order Capacitor Based on C-R-NC Layer Structure

The design method and examples of analog circuit elements with fractional (non-integer) order immittance of capacitive character are presented. The elements are based on distributed layer structures of the C-R-NC type (capacitive, resistive, capacitive with N-times the capacitance) and are therefore suitable for integrated implementation, e.g. using thick-film, thin-film, or metal-oxide-semiconductor (MOS) technology. The design method uses a genetic algorithm that optimizes the interconnections between and parameters of individual C-R-NC structures that form the resulting element. To calculate the fitness function for the algorithm, the admittance matrix of the C-R-N C structure and modified nodal analysis are used. Practical tests confirm the success of this method, especially for fractional orders between 0.5 and 1, where it was possible to design circuits working in a frequency band of around 4 decades with a maximum admittance phase deviation of 2 degrees.