Realization of Tunable Fractional-order Device based on Ladder Network Approximation

Abstract

This paper describes a design and realization of a fractional-order device or constant phase element (CPE) using the approximation method. The rational function is applied for the fractional-order function. The rational function can be rewritten in the continue fraction expansions (CFE) form. The Cauer network type is realized from the CFE as RC ladder network. The signal flow graph (SFG) method is preferred to realize the active network from the passive RC ladder network. The finalized CPE requires the gains and integrators in voltage-mode. The OTAs are deployed as tunable active devices with grounded capacitors to realize the tunable fractional-order device. From the design procedure, the proposed CPE can be constructed in arbitrarily order and frequency operation. Moreover, the tunable of magnitude and frequency operation can be electronically tuned. The good agreement results of proposed CPE are carried out by PSpice compared to the theoretical expectation.