Fractional-Order Phase Shifters with Constant Magnitude Frequency Responses

Abstract

This contribution presents and experimentally analyzes the idea how to reach the constant magnitude as well as the phase response in the fractional-order (FO) phase when shifting two-ports. The straightforward method employing the automatic gain control circuit (AGC) in a cascade after so-called constant phase block approximating FO integrator or differentiator is studied. The variable gain amplifier utilized in AGC and simple RC-based FO constant phase elements (approximating capacitors with order alpha = 1/4 and alpha = 1/2 as an example) connected in the feedback of operational amplifier-based integrator are established in the experimental setup. The operation indicated in three decades (between 100 Hz and 100 kHz) is evaluated. The known solutions of the standard FO phase shifting circuits are discussed and generally compared with the features obtained in this paper, together with the supposed effects of AGC on their performances.

Reconnection–less Reconfigurable Fractional–Order Current–Mode Integrator Design With Simple Control

“…Fractional-order systems have found their application in diverse industry branches such as medicine [1,2], modeling and measurement of various signals [3][4][5], agriculture [6], car industry [7], etc. In case of the electrical engineering, the utilization of FO calculus covers circuits filtering the spectrum [8][9][10][11][12][13][14][15][16][17], FO oscillators [18][19][20][21][22][23] and other circuits with fractional-order characteristics [24][25][26][27][28][29], which then can be implemented and find their purpose in applications of above-mentioned industry areas.…”

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 ).…”