Tunable Fractional-Order Band-pass Filter of order 2α

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 ).…”

“…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] . The approximation is applied on the filtering structure as a whole leading to the change of values of standard elements/parameters within the structure (capacitors, resistors, transconductances g m , voltage or current gains A , B ).…”

“…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.…”

“…Most importantly, with an implementation of a suitable electronically controllable FC emulator, we can choose whether we want the resulting order to be of the integer–order, combination of the integer and fractional order, or a combination of multiple fractional orders (either resulting in integer or fractional order). Based on the above–mentioned fact, the proposed filter can offer nine combinations of functions (and 4 additional functions if considering integer–order functions as well) in comparison to only one function in case of [5] , [6] , [8] , [9] , [11] , [12] , [13] , [14] , [15] , [18] , [19] , [20] . This useful feature is not available in case of other discussed solutions.…”