Analysis and realization of fractional step filters of order (1+α)

The modeling of physical-world procedures as an integer representation gives an approximated view of their realization. However, these procedures are commonly fractional in nature. Fractional-order models are characterized by infinite memory over the integer-order systems. Due to the workability and advancement in fractional-order circuits, we endeavor here to introduce the analysis and realization of fractional step filters (FSFs) of order (1+α). In this chapter, two methods with different mathematical formulations and circuit devices are investigated for the realization of FSFs. In the first method, FSFs using a fractional-order capacitor (FOC) of order a are presented by calculating the critical frequencies and conducting stability analysis and sensitivity analysis. In the second method, the FSFs are approximated into higher-order integer filters and are presented by the signal flow graph approach. Corner analysis and AC analysis are performed to evaluate the proposed filters. Magnitude responses of the FSFs are verified using MATLAB® and conjointly with PSpice.