Approximation of Fractional-Order Butterworth Filter Using Pole-Placement in<i>W</i>-Plane

Mishra, Shalabh Kumar; Upadhyay, Dharmendra Kumar; Gupta, Maneesha

doi:10.1109/tcsii.2021.3074076

Cited by 10 publications

(16 citation statements)

References 32 publications

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“…The absolute relative magnitude error (ARME) metric, as defined below, is used to evaluate the modeling accuracy. [18,25]. The reported model in [18] exhibits peaking near the cut-off frequency, whereas the rolloff behavior of the FOBF in [25] deviates from the theoretical one.…”

Section: Performance Analysis Using Matlab Simulationsmentioning

confidence: 70%

“…The first technique involves mod-eling in the complex s-plane using the FO [3,10,25] or the integer-order transfer functions (see [16] and the references cited therein). Alternatively, FOBFs were also designed in the complex W -plane (W = s 1/q , where α = r /q; r , q ∈ Z + ) using the pole-placement algorithms [1,18].…”

Section: Introductionmentioning

confidence: 99%

“…A constrained optimization strategy is formulated to guarantee design stability. Relative to the existing W -plane based techniques [1,18], the proposed method provides the following contributions:…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, the proposed approach can directly generate the optimal FOBF model for any value of M, 3. Unlike [18], the all-pole structure of the Mth-order proposed model always requires N+2 terms, which is the same as that of the (N+1)th order Butterworth filter, and 4. Although the W -plane-based techniques [1,18] generate a stable design, these methods do not provide optimal pole placement in the W -plane.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike [18], the all-pole structure of the Mth-order proposed model always requires N+2 terms, which is the same as that of the (N+1)th order Butterworth filter, and 4. Although the W -plane-based techniques [1,18] generate a stable design, these methods do not provide optimal pole placement in the W -plane. Consequently, the retro-fitted model in the s-plane is also not an optimal one.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Optimized fractional-order Butterworth filter design in complex F-plane

Mahata¹,

Herencsár

Kubánek

et al. 2022

Fract Calc Appl Anal

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This paper introduces a new technique to optimally design the fractional-order Butterworth low-pass filter in the complex F-plane. Design stability is assured by incorporating the critical phase angle as an inequality constraint. The poles of the proposed approximants reside on the unit circle in the stable region of the F-plane. The improved accuracy of the suggested scheme as compared to the recently published literature is demonstrated. A mixed-integer genetic algorithm which considers the parallel combinations of resistors and capacitors for the Valsa network is used to optimize the frequency responses of the fractional-order capacitor emulators as part of the experimental verification using the Sallen–Key filter topology. The total harmonic distortion and spurious-free dynamic range of the practical 1.5th-order Butterwoth filter are measured as 0.13% and 62.18 dBc, respectively; the maximum and mean absolute relative magnitude errors are 0.03929 and 0.02051, respectively.

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Section: Performance Analysis Using Matlab Simulationsmentioning

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimized fractional-order Butterworth filter design in complex F-plane

Mahata¹,

Herencsár

Kubánek

et al. 2022

Fract Calc Appl Anal

View full text Add to dashboard Cite

show abstract

Design of fractional-order transitional filters of the Butterworth-Sync-Tuned, Butterworth-Chebyshev, and Chebyshev-Sync-Tuned types: optimization, simulation, and experimental verification

Mahata,

Kubanek,

Herencsar

2024

Computers and Electrical Engineering

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On the Design Flow of the Fractional-Order Analog Filters Between FPAA Implementation and Circuit Realization

et al. 2023

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This work explicitly states the design flows of the fractional-order analog filters that researchers throughout the literature have used. Two main flows are studied: the FPAA implementation and the circuit realization. Partial-fraction expansion representation is used to prepare the approximated fractional-order response for implementation on FPAA. The generalization of the second-order active RC analog filters based on opamp from the integer-order domain to the fractional-order domain is presented. The generalization is studied from both mathematical and circuit realization points of view. It is found that the great benefit of the fractional-order domain is that it adds more degrees of freedom to the filter design process. Simulation and experimental results match the expected theoretical analysis.

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Approximation of Fractional-Order Butterworth Filter Using Pole-Placement inW-Plane

Cited by 10 publications

References 32 publications

Optimized fractional-order Butterworth filter design in complex F-plane

Optimized fractional-order Butterworth filter design in complex F-plane

Design of fractional-order transitional filters of the Butterworth-Sync-Tuned, Butterworth-Chebyshev, and Chebyshev-Sync-Tuned types: optimization, simulation, and experimental verification

On the Design Flow of the Fractional-Order Analog Filters Between FPAA Implementation and Circuit Realization

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