A Low-Power Compact DDCC Based Fractional-Order Filter

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] .…”

“…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. Let us mention LP α + β filters [6] , [9] , [13] , LP α + α filter assuming two FO capacitors of identical orders [10] and even LP α + β + γ supposing a FO filter originated from a second–order filter consisting of 3 capacitors [12] . Furthermore, Refs.…”

“…The first thing, which is necessary to understand from Table 1 , is the fact that the proposed filter is based on a different premise than other mentioned filters. Some filters [8] , [11] , [19] , [14] , [15] , [16] , [17] , [21] , [22] , [23] work with one fractional–order parameter while filters in [9] , [10] , [13] , [5] , [6] , [7] consider two fractional–order parameters. Based on this fact these filters have either one or two (fractional) orders which can be controlled theoretically.…”

“…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.…”