All Possible Topologies of the Fractional-Order Wien Oscillator Family Using Different Approximation Techniques

Elwy, Omar; Said, Lobna A.; Madian, Ahmed H.; Radwan, Ahmed G.

doi:10.1007/s00034-019-01057-6

Cited by 47 publications

(12 citation statements)

References 28 publications

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“…Moreover, the constitutive equations ( 1) and ( 7), as the equivalent form of (3), can be topologically viewed as the parallel connections of the classical and generalized capacitor, while the constitutive equations (3) and ( 5), as the equivalent form of (1), can be topologically viewed as the series connections of the classical and generalized capacitor and similarly the series connections of the classical and generalized inductor are described by the relations (2) and (8), as the equivalent form of (4), while the parallel connections of the classical and generalized inductor are described by the relations (4) and (6), as the equivalent form of (2). Therefore, dierent topological generalizations of electric elements can still describe the same phenomenology of physical processes by choosing appropriate memory kernels.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Haška

Cvetićanin

Zorica

2021

Preprint

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Generalized capacitor (inductor) is constitutively modeled by expressing charge (magnetic flux) in terms of voltage (current) memory as a sum of instantaneous and power type hereditary contributions and it is proved to be a dissipative electric element by thermodynamic analysis. On the contrary, generalized capacitor (inductor) as a generative electric element is modeled using the same form of the constitutive equation, but by expressing voltage (current) in terms of charge (magnetic flux) memory. These constitutive models are used in transient and steady state regime analysis of the series RC and RL circuits subject to electromotive force, as well as in the study of circuits' frequency characteristics including asymptotic behavior.

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Section: Introductionmentioning

confidence: 99%

“…Frequency characteristics of the fractional RC, RL, and LC circuits including parameter optimization of RL β C α circuit are investigated in [31,32] and in [30]. Wien bridge oscillators and resonance phenomena in fractional order circuits are considered in [8,33] and in [29,42].…”

Section: Introductionmentioning

confidence: 99%

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Haška

Cvetićanin

Zorica

2021

Preprint

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“…This advantage is a direct result of the additional tunability attained by introducing fractional orders as new model parameters. Engineering application of FOS includes: bioengineering [4]- [6], control [7]- [10], filters [11], [12], oscillators [13], [14], energy [15], [16], encryption [17], and chaos [18]- [20].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulations and FPGA Implementations of Fractional-Order Systems Based on Product Integration Rules

et al. 2020

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Product integration (PI) rules are well known numerical techniques that are used to solve differential equations of integer and, recently, fractional orders. Due to the high memory dependency of the PI rules used in solving fractional-order systems (FOS), their hardware implementation is very difficult and resources-demanding. In this paper, modified versions of the PI rules are introduced to facilitate their digital implementations. The studied rules are PI rectangular, PI trapezoidal, and predict-evaluate-correctevaluate (PECE) rules. The three modified versions of the PI rules are validated using a benchmark system of differential equations for different sizes of the memory window to show the effect of the window size on the solution accuracy. Additionally, the three modified versions of the PI rules are used to simulate a novel fractional-order chaotic system (FOCS) where its bifurcation diagrams are discussed with the window length parameter. The chaotic system is then implemented on a Field Programmable Gate Array (FPGA). There are only a few trials in literature to implement the fractional PECE algorithm on FPGA, nevertheless, the proposed FPGA realization is compared with the most recent of these trials. The FPGA implementations of the three PI rules are made using Xilinx ISE 14.7 on Artix 7 kit. The achieved throughput are 1280 Mbits/sec for PI rectangular, 128.8 Mbits/sec for PI trapezoidal, and 129.12 Mbits/sec for fractional-order PECE.

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“…A fractional‐order voltage‐controlled oscillator (VCO) has been presented in [24]. The effects of different approximation techniques on the performance of the fractional oscillators are studied in [26, 28]. Multi‐phase oscillators that use three or more fractional‐order capacitors have been proposed in [8, 14, 15, 19, 21, 25].…”

Section: Introductionmentioning

confidence: 99%

“…It can be seen this table that even though some of the presented works have low counts of active and passive components [17,18,27], they are verified by only the simulations not experimentations. On the other hand, some designs have only two phase-shifted outputs [10,13,17,18,20,24,[26][27][28]. Most of the introduced fractional oscillators have employed only one approximation technique for the emulation of the fractional-order capacitors [7,8,10,11,13,14,17,18,20,27].…”

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confidence: 99%

Design and realisation of a fractional‐order sinusoidal oscillator

Saçu

Alçı²

2020

IET Circuits, Devices & Systems

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In this work, a new fractional-order sinusoidal oscillator is proposed. The proposed oscillator consists of one fractional-order all-pass filter and one fractional-order lossless integrator blocks. In order to emulate fractional-order capacitors, three different approximation methods the R-C pair, Matsuda and Oustaloup are employed and the results are compared. Three sinusoidal voltage signals with different phases that are controlled by fractional orders are provided by the proposed oscillator topology that is not possible for the classical integer-order case. Grounded passive components are used in the introduced oscillator circuit. Additionally, the output voltage signals are available at the low impedance terminal W of AD844ANs. Moreover, the time constant of the fractional-order all-pass filter can be adjusted accurately by means of second resistor R x in the all-pass filter section. In addition to the simulation results, the proposed fractional oscillator is also implemented to verify the oscillator circuit experimentally. For the case of fractional orders α = 1 and β = 0.5, the measurement results are 10.3 kHz, 43.22° and 67.99°, respectively, while the desired values are 10 kHz, 45° and 67.36°, respectively.

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All Possible Topologies of the Fractional-Order Wien Oscillator Family Using Different Approximation Techniques

Cited by 47 publications

References 28 publications

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Numerical Simulations and FPGA Implementations of Fractional-Order Systems Based on Product Integration Rules

Design and realisation of a fractional‐order sinusoidal oscillator

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All Possible Topologies of the Fractional-Order Wien Oscillator Family Using Different Approximation Techniques

Cited by 47 publications

References 28 publications

Dissipative and Generative Fractional Electric Elements in Modeling RC&nbsp;and RL&nbsp;Circuits

Dissipative and Generative Fractional Electric Elements in Modeling RC&nbsp;and RL&nbsp;Circuits

Numerical Simulations and FPGA Implementations of Fractional-Order Systems Based on Product Integration Rules

Design and realisation of a fractional‐order sinusoidal oscillator

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Product

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Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits