(1+ α ) Fractional-order transfer functions to approximate low-pass magnitude responses with arbitrary quality factor

Multifunctional Electronically Reconfigurable and Tunable Fractional-Order Filter

“…s ss (1) where ω0 = 2πf0 rad/s and coefficients k1, k2 and k3 are used to influence the shape of the obtained transfer function. The values of the coefficients k1, k2 and k3 are adopted from [15]. Thanks to selection of these coefficients, quality factor of the filter can be tuned as is described in [15].…”

“…The values of the coefficients k1, k2 and k3 are adopted from [15]. Thanks to selection of these coefficients, quality factor of the filter can be tuned as is described in [15]. The proposed filter, which is depicted in Fig.…”

“…An integer order is usually given for the analogue circuits (filters, oscillators, generators...). Fractional-order systems can find use in biochemistry [6], [9], agriculture [9], control systems [9] and electronics [8], [10]- [15].…”

“…In point of view of the magnitude and phase responses, the fractional-order filters have magnitude slope of attenuation in stop-band region equal to 20(n + α) dB/decade. The phase shift is given by 90(n + α) degrees [8], [12], [15].…”

“…Table I summarizes some relevant previously reported works. The fractional-order low-pass filters without electronic controllable parameters are most commonly proposed [1], [4], [7], [15]. The electronic reconfiguration between two or more transfer functions, without topology modification and with electronically adjustable filter parameters, is presented only in the papers [8], [14].…”