Realization of fractional order integrator by rational function in the form of continued product

Arbitrary fractional order integrator can be designed by a method of constructing the rational approximation function in the form of continued product. This paper takes half order integrator as an example to exhibit the design process. The circuit is made up of level-N active operational amplifier network in which the size of N is equal to the order of rational function. Since the rational approximation function in the form of continued product consists of several first order damp elements and first derivative elements, it will greatly simplify the design process of fractional integrator. It only needs four different resistors and a series of regular capacitors. Thanks to the properties, the fractional integrator can be easily manufactured for industrial production and commercial purpose. It shows that the designed fractional integrator based on the proposed method is rational through performance simulations comparison with other methods and the test by Multisim 10.