Complexity Reduced Design Procedure of a Fractional Order All-Pass Filter

In this work, the design of continuous time Fractional Order All-Pass Filter (FOAPF) is proposed. Two different design methods to realize the All-Pass Filter in the fractional domain with mathematical formulations and circuit results are investigated. The first design method is based on Fractional Order Elements (FOEs) where, FOEs of order alpha and beta are utilized to develop a second order All-Pass Filter to the fractional domain. Whereas, in second design method, the fractional filter is approximated into higher order integer filters. The frequency response of the proposed design are validated using MATLAB (2018a) and conjointly with PSPICE (OrCAD 17.2). For first circuit design, FOEs are obtained using a single R-C parallel network. However, for the second circuit design Signal Flow Graph (SFG) approach is utilized. The evaluation of the realized FOAPF is also performed through the Lissajous pattern, AC analysis and Transient Analysis. After the simulations, the achieved results show that the second order FOAPF provides almost 180 degrees phase shift for different values of alpha, beta.