Optimal approximation of asymmetric type fractional‐order bandpass Butterworth filter using decomposition technique

Mahata, Shibendu; Kar, Rajib; Mandal, Durbadal

doi:10.1002/cta.2835

Cited by 10 publications

(7 citation statements)

References 13 publications

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“…In [44], the optimal (2 + α) th -order FOBF was designed by avoiding the cascading method. Optimal rational approximations of the band-pass Butterworth filter exhibiting the symmetric [45] and asymmetric [46] FO roll-off behavior were also reported. It may be noted that the definition of the FOBF is based on the magnitude function; their phase characteristic is not mathematically defined.…”

Section: Introductionmentioning

confidence: 99%

Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters

2021

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In this paper, a new two-steps design strategy is introduced for the optimal rational approximation of the fractional-order Butterworth filter. At first, the weighting factors of the summation between the n th -order and the (n + 1) th -order Butterworth filters are optimally determined. Subsequently, this model is employed as an initial point for another optimization routine, which minimizes the magnitudefrequency error relative to the (n + α) th -order, where α ∈ (0, 1), Butterworth filter. The proposed approximant demonstrates improved performance about the magnitude mean squared error compared to the state-of-the-art design for six decades of bandwidth, but the introduced approach does not require a fractional-order transfer function model and the approximant of the s α operator. The proposed strategy also avoids the use of the cascading technique to yield higher-order fractional-order Butterworth filter models. The performance of the proposed 1.5 th -order Butterworth filter in follow-the-leader feedback topology is verified through SPICE simulations and its hardware implementation based on Analog Devices AD844ANtype current feedback operational amplifier.

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Section: Introductionmentioning

confidence: 99%

Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters

2021

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“…The replacement of the Laplacian operator by its fractional-order counterpart (i.e., s → s α , where 0 < α < 1) has been broadly utilized for transposing integer-order transfer functions into the fractional-order domain [1]. Therefore, the rational approximation of the resulted fractional-order filter functions has gained a significant research interest [2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Electronically Controlled Power-Law Filters Realizations

et al. 2022

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A generalized structure that is capable of implementing power-law filters derived from 1st and 2nd-order mother filter functions is presented in this work. This is achieved thanks to the employment of Operational Transconductance Amplifiers (OTAs) as active elements, because of the electronic tuning capability of their transconductance parameter. Appropriate design examples are provided and the performance of the introduced structure is evaluated through simulation results using the Cadence Integrated Circuits (IC) design suite and Metal Oxide Semiconductor (MOS) transistors models available from the Austria Mikro Systeme (AMS) 0.35 μm Complementary Metal Oxide Semiconductor (CMOS) process.

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“…The modeling of FO RLC filter and low-pass filter transfer functions of the form 1/(s + 1) α using classical optimization techniques has been reported [33,34]. Numerical optimization methods were employed for the approximation of low-pass [35,36] and band-pass [37,38] filters exhibiting fractional-step behavior. The Nelder-Mead simplex [39], Cuckoo Search algorithm [40], and MATLAB-based optimization function fmincon [41,42] were employed to model the magnitude-frequency characteristics of the FO low-pass Butterworth filter.…”

Section: Introductionmentioning

confidence: 99%

On the Design of Power Law Filters and Their Inverse Counterparts

2021

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This paper presents the optimal modeling of Power Law Filters (PLFs) with the low-pass (LP), high-pass (HP), band-pass (BP), and band-stop (BS) responses by means of rational approximants. The optimization is performed for three different objective functions and second-order filter mother functions. The formulated design constraints help avoid placement of the zeros and poles on the right-half s-plane, thus, yielding stable PLF and inverse PLF (IPLF) models. The performances of the approximants exhibiting the fractional-step magnitude and phase responses are evaluated using various statistical indices. At the cost of higher computational complexity, the proposed approach achieved improved accuracy with guaranteed stability when compared to the published literature. The four types of optimal PLFs and IPLFs with an exponent α of 0.5 are implemented using the follow-the-leader feedback topology employing AD844AN current feedback operational amplifiers. The experimental results demonstrate that the Total Harmonic Distortion achieved for all the practical PLF and IPLF circuits was equal or lower than 0.21%, whereas the Spurious-Free Dynamic Range also exceeded 57.23 and 54.72 dBc, respectively.

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Optimal approximation of asymmetric type fractional‐order bandpass Butterworth filter using decomposition technique

Cited by 10 publications

References 13 publications

Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters

Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters

Electronically Controlled Power-Law Filters Realizations

On the Design of Power Law Filters and Their Inverse Counterparts

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