Fractional order filter with two fractional elements of dependant orders

This work is aimed at generalizing the design of continuous-time filters in the non-integer-order (fractional-order) domain. In particular, we consider here the case where a filter is constructed using two fractional-order elements of different orders α and β. The design equations for the filter are generalized taking into consideration stability constraints. Also, the relations for the critical frequency points like maximum and minimum frequency points, the half power frequency and the right phase frequency are derived. The design technique presented here is related to a fractional order filter with dependent orders α and β related by a ratio k. Frequency transformations from the fractional low-pass filter to both fractional high-pass and band-pass filters are discussed. Finally, case studies of KHN active filter design examples are illustrated and supported with numerical and ADS simulations.

Graphical AbstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► General fundamentals of the fractional-dependent-order filters are introduced. ► The stability analysis of the fractional-order filters is presented. ► The critical frequencies (max., half-power, and right-phase) are calculated generally. ► A general transformation between the types of these filters is introduced. ► The fractional-order KHN filter is chosen to validate the presented concepts.