Microelectronic Implementations of Fractional-Order Integrodifferential Operators

For practical applications, the fractional-order integral and differential operators require to be approximated as stable, causal, minimum-phase integer-order systems, which usually leads, in both continuous and discrete domains, to high order transfer functions. Assuming that an approximation of good quality is available for the fractional operator, efficient implementations, in both cost and speed, are required. The fast development of the microelectronics gives us the opportunity of using cheap, accurate, programmable, and fast devices for implementing reconfigurable analog and digital circuits. Among these devices, field programmable gate arrays, switched capacitor circuits, and field programmable analog arrays are used in this paper for the implementation of a fractional-order integrator, previously approximated by recursive Oustaloup’s method. The fundamentals of the devices as well as the design procedures are given, and the implementations are compared considering their simulated frequency responses, the design efforts, and other important issues.