Fractional Order Sallen-Key and KHN Filters: Stability and Poles Allocation

This paper presents the analysis for allocating the system poles and hence controlling the system stability for KHN and Sallen-Key fractional order filters. The stability analysis and stability contours for two different fractional order transfer functions with two different fractional order elements are presented. The effect of the transfer function parameters on the singularities of the system is demonstrated where the number of poles becomes dependent on the transfer function parameters as well as the fractional orders. Numerical, circuit simulation, and experimental work are used in the design to test the proposed stability contours.