Analog Realization of Electronically Tunable Fractional-Order Differ-Integrators

Integer-and Fractional-Order Integral and Derivative Two-Port Summations: Practical Design Considerations

“…are not studied. D. Goyal et al [3] presents integrators/differentiators implemented by complex active CMOS circuitry with the benefit of simple electronic reconfiguration. A similar approach was used by G. Tsirimokou et al [4] where resulting integrators/differentiators are used for the design of a special type of filter performing also the sum/subtraction of current outputs.…”

“…The synthesis of an active emulator of FOE based on operational transconductance amplifiers and its implementation in an OA-based lossless integrator is shown by G. Tsirimokou et al [5]. Special active building blocks used in works [3][4][5]8] utilize approximation of the fractional-order behavior by higher-integer-order filtering responses allowing the electronic configuration of transfer coefficients (numerator/denominator). Similarly, G. Tsirimokou et al [6], there is a discrete solution of this topology using passive parameters for appropriate configuration of the transfer.…”

“…(a) Many proposed circuitries (except FPAA, FPGA-based) have quite complex topology, with many active and/or passive elements [9,12,[16][17][18][19], especially circuits with fractional-order behavior and approximations by higher-order filters [3,5,6,13] or chain of bilinear segments [8,9,14,15,[18][19][20][21], (b) some concepts require software programming [12,16,17], (c) tested operational bandwidth is quite narrow in many cases [3][4][5]7,8,[11][12][13]18], (d) summing of fractional-order as well as integer-order two ports was not analyzed deeply in the past, (e) single-parameter electronic adjustment of the time constant of the resulting response of two-port summing was not studied in the past, except R. Sotner et al [9], but the overall circuit topology is based upon a chain of bilinear sections, and therefore, it is not one of the simplest solutions…”

“…Frequency responses influenced by the fractional-order behavior of used components are studied more frequently in recent years [1]. Many works in this field focus on novel solutions of integral and derivative two-ports (for example [2][3][4][5][6][7][8][9]), proportional integral and derivative controllers (for example [10][11][12][13][14][15][16][17][18] and so-called bilinear two ports [8,9,[19][20][21] serving for various purposes. Two ports, known as integrators and differentiators, have started to be interesting for designers of fractional-order systems, and especially for proportional, integral and derivative controllers (PIDs).…”

“…Integrators/Differentiators Only [2] integrator No OAs passive Low Yes <1 MHz N/A - [3] both Yes DVCCTA passive Low Yes <100 kHz N/A - [4] both No CMOS current mirrors active Low Yes <100 Hz…”