Performance Analysis of Fractional Order Low-pass Filter

Biswal, Kumar; Tripathy, Madhab Chandra; Kar, Sanjeeb Kumar

doi:10.1007/978-981-15-2774-6_28

Cited by 12 publications

(5 citation statements)

References 13 publications

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“…Compared to integer-order systems, the fractionalorder ones are governed by a fractional-order differential equation, 39 and these systems producing fractional-order output have additional useful properties as a result of the increased number of parameters or boundary conditions. 20,40 As with fractional-order filters, [40][41][42] the additional degrees of freedom that allow precise adjustment of the filter's characteristics can be provided by inserting one or more fractional exponents into the filter function. Presently, fractionalorder filters have thrust the scientific field of filtering into a new era, making it applicable in a wide range of interdisciplinary fields such as, 43 bioimpedance spectroscopy, 44 and control systems.…”

Section: Fractional-order Bandreject Filter Circuitmentioning

confidence: 99%

“…FOEs are increasingly used as elements for the design and construction of circuits and systems with fractional calculus operational functions, that is, fractional‐order circuits and systems. Compared to integer‐order systems, the fractional‐order ones are governed by a fractional‐order differential equation, 39 and these systems producing fractional‐order output have additional useful properties as a result of the increased number of parameters or boundary conditions 20,40 . As with fractional‐order filters, 40–42 the additional degrees of freedom that allow precise adjustment of the filter's characteristics can be provided by inserting one or more fractional exponents into the filter function.…”

Section: Fractional‐order Bandreject Filter Circuitmentioning

confidence: 99%

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Passive realization of the fractional‐order capacitor based on fractional‐order inductor and its application

Hao

Wang

2023

Circuit Theory & Apps

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This paper investigates a new implementation of a passive fractional-order capacitor (FOC) based on a single-component fractional-order inductor (FOI).The significance of this approach lies in providing the fractional-order passive circuit to synthesize an FOC, which avoids the approximation that only depends on the integer-order transfer function and reflects truly the infinitedimensional nature of fractional-order impedance characteristic. For this purpose, the realizable conditions of this passive FOC are obtained and the main ideas of the proposed method are described by examples. The sensitivity of the impedance magnitude and phase angle on required components parameters is also analyzed in order to facilitate the design of the FOC emulator. Furthermore, the bandwidth is extended by modular structures connected in series, and the proposed approach shows an improvement over some previous methods in terms of accuracy. Also, based on the fractional calculus Grünwald-Letnikov definition, a single-component FOI circuit element is packaged to build simulation circuit in Matlab/Simulink, and the effectiveness of the proposed method are validated by simulated and experimental results.In the application of an FOC, the results from in the series-parallel fractionalorder RLC β bandreject filter circuit indicate that the fractional-order counterpart can reduce the ripple and improve the suppression level at a certain frequency, and the peak amplitude and the overshoot decrease initially with decreasing order. Moreover, under the fixed inductance, capacitance, and resistance, the rise time varies almost inversely with order, whereas the setting time is on the decrease as the order is decreasing.

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Section: Fractional-order Bandreject Filter Circuitmentioning

confidence: 99%

Section: Fractional‐order Bandreject Filter Circuitmentioning

confidence: 99%

Passive realization of the fractional‐order capacitor based on fractional‐order inductor and its application

Hao

Wang

2023

Circuit Theory & Apps

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“…Where n is an unsigned integer number, often between 1 and 10, and α is defined as a real number in the range [0 1]. transfer function of FOLPF is given by (10) [24]: (10) where n is an integer and 0 < α < 1. The following are the values of k's as (11):…”

Section: Fractional Order Low-pass Filtermentioning

confidence: 99%

“…The models are built on fractional-order elements, implemented with active components, and may reflect bio-impedance characteristics up to 10 kHz. A fractional-order passive RC low-pass filter is investigated in [24]. The progression of behavior in the temporal realm was revealed through fractional orders.…”

Section: Introductionmentioning

confidence: 99%

Realization of fractional order lowpass filter using different approximation techniques

Krishna,

Janarthanan

2023

Bulletin EEI

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Many research groups are starting to pay serious attention to the problem of fractional-order circuits. In this paper, a new approach to designing fractional order low-pass filter (FOLPF) is presented. Finding a rational approximation of the fractional Laplace operator sα is a crucial step in the design of fractional order filters. A comparative study of the most widely used approximation techniques named continued fraction expansion (CFE) method and Biquadratic Approximation (RE) method is performed. Then the transfer function of the proposed FOLPF is calculated. Using operational amplifier, the proposed filter is synthesized. The proposed circuit is simulated using Texas instruments TINA software. The results obtained outperform the existing methods.

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“…Due to the absence of commercial availability of such elements, they are approximated by RC schemes, such as the Foster and Cauer networks. The price paid for the offered quick design procedure is the absence of on-the-fly tuning of the filter's characteristics, making it suitable only for cases of filters with pre-defined type and frequency characteristics [3][4][5]. (b) Approximation of the fractional-order Laplace operators in (1) using appropriate tools, such as Continued Fraction Expansion, Oustaloup, Matsuda and Carlson [6], and then substitution of the resulting rational function approximations of these operators.…”

Section: Introductionmentioning

confidence: 99%

FPAA-Based Realization of Filters with Fractional Laplace Operators of Different Orders

2021

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A simple and direct procedure for implementing fractional-order filters with transfer functions that contain Laplace operators of different fractional orders is presented in this work. Based on a general fractional-order transfer function that describes fractional-order low-pass, high-pass, band-pass, band-stop and all-pass filters, the introduced concept deals with the consideration of this function as a whole, with its approximation being performed using a curve-fitting-based technique. Compared to the conventional procedure, where each fractional-order Laplace operator of the transfer function is individually approximated, the main offered benefit is the significant reduction in the order of the resulting rational function. Experimental results, obtained using a field-programmable analog array device, verify the validity of this concept.

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Performance Analysis of Fractional Order Low-pass Filter

Cited by 12 publications

References 13 publications

Passive realization of the fractional‐order capacitor based on fractional‐order inductor and its application

Passive realization of the fractional‐order capacitor based on fractional‐order inductor and its application

Realization of fractional order lowpass filter using different approximation techniques

FPAA-Based Realization of Filters with Fractional Laplace Operators of Different Orders

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