Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

Kubánek, David; Freeborn, Todd J.; Koton, Jaroslav; Dvořák, Jan

doi:10.3390/app8122603

Cited by 20 publications

(8 citation statements)

References 27 publications

(45 reference statements)

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“…The colored scale is as following: dark blue areas represent fixed point solution, green stands for limit cycle solutions, yellow and white denotes weak (LLE lower than 0.1) and strong (LLE greater than 0.1) chaos behavior. Since three-segment odd-symmetrical PWL functions∈ are considered for memory, this plot represents four-dimensional hypercube with edges g 1 inner ∈(−21, −19), g 1 outer ∈(7, 9), g 2 inner ∈(−16, −14), g 2 outer ∈ (17,19) and resolution 201 × 201 × 201 × 201 points. For this calculation, the fourth-order Runge-Kutta method in Matlab.…”

Section: Wideband Cpe As Part Of Chaotic Systemmentioning

confidence: 99%

“…Some research works are focused on the general properties of this class of analog building blocks [13,14]. Other studies are aimed at specific structures such as Sallen-Key and KHN filters [15], passive and active realizations of filters having a Butterworth-type of frequency response [16], low-pass filter with transfer zeroes [17], low-pass with electronically reconfigurable parameters [18], pseudo-differential all-pass filter [19], etc. A FO filter can be constructed by using field programmable analog array as well [20,21].…”

Section: Introductionmentioning

confidence: 99%

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Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Petržela

2020

Entropy

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This paper provides readers with three partial results that are mutually connected. Firstly, the gallery of the so-called constant phase elements (CPE) dedicated for the wideband applications is presented. CPEs are calculated for 9° (decimal orders) and 10° phase steps including ¼, ½, and ¾ orders, which are the most used mathematical orders between zero and one in practice. For each phase shift, all necessary numerical values to design fully passive RC ladder two-terminal circuits are provided. Individual CPEs are easily distinguishable because of a very high accuracy; maximal phase error is less than 1.5° in wide frequency range beginning with 3 Hz and ending with 1 MHz. Secondly, dynamics of ternary memory composed by a series connection of two resonant tunneling diodes is investigated and, consequently, a robust chaotic behavior is discovered and reported. Finally, CPEs are directly used for realization of fractional-order (FO) ternary memory as lumped chaotic oscillator. Existence of structurally stable strange attractors for different orders is proved, both by numerical analyzed and experimental measurement.

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Section: Wideband Cpe As Part Of Chaotic Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Petržela

2020

Entropy

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“…In the paper [4] by D. Kubanek et al, fractional-order transfer functions to approximate the passband and stopband ripple characteristics of a second-order elliptic lowpass filter are designed and validated. The necessary coefficients for these transfer functions are determined through the application of a least squares fitting process.…”

Section: Dear Readersmentioning

confidence: 99%

Special Issue “Selected Papers from the 2018 41st International Conference on Telecommunications and Signal Processing (TSP)”

2019

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“…Recent works have demonstrated the generalization of the Butterworth [23], Chebyshev [24], inverse Chebyshev [25], and elliptic filters [26] to the FO domain. Another design strategy that involves the approximation of FO filter characteristics using the integer order transfer function was also reported in the literature [27].…”

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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Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

Cited by 20 publications

References 27 publications

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

Special Issue “Selected Papers from the 2018 41st International Conference on Telecommunications and Signal Processing (TSP)”

On the Design of Power Law Filters and Their Inverse Counterparts

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