Electronically Tunable Fractional Order Filter

Fractional-order low-pass filter with electronic tunability of its order and pole frequency

“…The filter consists of OTAs and ACAs. Thanks to the electronically controllable active elements which were used in the proposal, it is possible to electronically control the order and pole frequency of the filter which brings a big advantage in comparison to the most of the previously reported circuits [2,4,8,9,11,21,30,33] which do not offer the electronic control of the filter parameters. Regarding the features of the proposed filter, its structure can be understood as simple, it can be eas-ily implemented and its properties can be verified not only by simulation but also by laboratory measurements with equivalent circuits of active elements as described in Section 2.…”

“…The first method is based on creation of a special fractional-order capacitor with impedance Z C = 1/s α C [3,13,23,33] or inductor with impedance Z L = s α L [29,31], which are then replacing respective passive components in the structure of a conventional fil-ter. These fractional-order passive elements are generally referred to as FOEs (fractional order elements) [14,24].…”

Reconnection–less reconfigurable low–pass filtering topology suitable for higher–order fractional–order design

“…In recent years, the matter of the fractional–order (FO) calculus received an increased attention of many scientists due to its possible utilization in various spectrums of industry branches including medicine [1] , [2] , [3] , agriculture [1] , [4] and, of course, electrical engineering [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] giving many new potential applications a chance to arise. In comparison to the integer–order circuits, FO circuits provide an increased degree of freedom, due to the presence of the non–integer–order parameter ( α ).…”

“…There have been some reports of a fabrication of fractional–order capacitors [34] , [35] , [36] nonetheless, these elements are expensive and difficult to implement and they are not commercially available. Therefore, they are usually substituted by passive elements (RC ladder networks) [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] or electronic emulators [29] , [30] , [31] approximating the FO capacitor (or inductor). The other approach involves the approximation of Laplacian operator of fractional–order s α by an integer–order function [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] .…”

“…Other quite common FO function is a high–pass (HP) 1 + α filter [7] , [16] , [18] , [21] , [22] , [23] . There are also reports of FO band–pass (BP) [5] , [7] , [10] , [17] , [20] , [21] , [22] , [23] , band–stop (BS) [7] , [21] , [22] , [23] and all–pass (AP) [8] , [19] filtering structures. Some structures suppose the replacement of both capacitors (considering the second–order structure having 2 integer–order capacitors turned into a FO filter) by FO capacitors providing an additional degree of freedom of the order control.…”