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Emerging and Selected Topics in Circuits and Systems, IEEE Journal on

Issue 3 • Date Sept. 2013

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Displaying Results 1 - 25 of 26
  • Table of Contents

    Page(s): C1 - C4
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  • IEEE Journal on Emerging and Selected Topics in Circuits and Systems publication information

    Page(s): C2
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  • Guest Editorial Fractional-Order Circuits and Systems

    Page(s): 297 - 300
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  • A Systematic Approach for Implementing Fractional-Order Operators and Systems

    Page(s): 301 - 312
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1577 KB) |  | HTML iconHTML  

    In this paper a generalized class of fractional-order systems is realized in digital hardware using a low-cost field programmable gate array (FPGA) device. First, fractional-order derivatives and integrals are realized in fixed-point hardware, wherein each coefficient and signal is represented with a custom number of bits. Both shift-form and delta-form structures are used for discretization, and are combined in the digital hardware realization to achieve a desired accuracy with low hardware cost. A methodology is then developed to construct general fractional-order transfer functions using the fractional-order derivatives and integrals as building blocks, in the same way that their integer-order counterparts are used in an integer-order system. Three systems are presented to illustrate the methodology using partitioned-form and feedback-form realization structures; the hardware results verify that the high-speed realizations achieve the desired accuracy with a low-cost solution. View full abstract»

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  • Minimal Realizations for Some Classes of Fractional Order Transfer Functions

    Page(s): 313 - 321
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    It has been known that finding a minimal pseudo state space realization for a fractional order transfer function is helpful in circuitry implementation of such a transfer function with the minimum number of fractional capacitors. Considering this importance, the present paper deals with finding minimal realizations for some classes of fractional order transfer functions. To this end, at first some upper bounds are obtained for the minimal inner dimension of a fractional order transfer function. By considering these upper bounds and also the lower bounds, previously presented in literature, the minimal inner dimension is exactly found for some classes of fractional order transfer functions. Moreover, the minimal realizations for these classes are also suggested. View full abstract»

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  • Closed-Form Rational Approximations of Fractional, Analog and Digital Differentiators/Integrators

    Page(s): 322 - 329
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    This paper provides closed-form formulas for coefficients of convergents of some popular continued fraction expansions (CFEs) approximating sν, with , and (2/T)ν((z-1)/(z+1))ν. The expressions of the coefficients are given in terms of ν and of the degree n of the polynomials defining the convergents. The formulas greatly reduce the effort for approximating fractional operators and show the equivalence between two well-known CFEs in a given condition. View full abstract»

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  • Caputo-Based Fractional Derivative in Fractional Fourier Transform Domain

    Page(s): 330 - 337
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    This paper proposes a novel closed-form analytical expression of the fractional derivative of a signal in the Fourier transform (FT) and the fractional Fourier transform (FrFT) domain by utilizing the fundamental principles of the fractional order calculus. The generalization of the differentiation property in the FT and the FrFT domain to the fractional orders has been presented based on the Caputo's definition of the fractional differintegral, thereby achieving the flexibility of different rotation angles in the time-frequency plane with varying fractional order parameter. The closed-form analytical expression is derived in terms of the well-known higher transcendental function known as confluent hypergeometric function. The design examples are demonstrated to show the comparative analysis between the established and the proposed method for causal signals corrupted with high-frequency chirp noise and it is shown that the fractional order differentiating filter based on Caputo's definition is presenting good performance than the established results. An application example of a low-pass finite impulse response fractional order differentiating filter in the FrFT domain based on the definition of Caputo fractional differintegral method has also been investigated taking into account amplitude-modulated signal corrupted with high-frequency chirp noise. View full abstract»

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  • Approximate Realization of Fractional-Order 2-D IIR Frequency-Planar Filters

    Page(s): 338 - 345
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    Starting with the established concepts of multi-dimensional network resonance, practical-bounded-input-bounded-output (BIBO) stability of multi-dimensional discrete systems, and the integer order approximation of fractional order filters, a new method for the realization of integer-order approximations of 2-D fractional-order systems having frequency-planar beam shaped passbands is proposed. The method results in 2-D infinite impulse response (IIR) filters having nonseparable denominators in their transfer-functions while having guaranteed practical-BIBO stability for zero initial conditions in the corresponding discrete system. The resulting integer-order filters are shown to approximate 2-D fractional order frequency-planar beam shapes in both magnitude and phase leading to a new theoretical tool for use in the emerging area of multi-dimensional fractional-order circuits and systems. Although examples are provided for frequency-planar filters in two dimensions, the proposed methods are equally applicable to other types of transfer-functions having prototypes based on resistively-terminated passive networks defined over any integer number of dimensions. View full abstract»

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  • Fractional Order Butterworth Filter: Active and Passive Realizations

    Page(s): 346 - 354
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    This paper presents a general procedure to obtain Butterworth filter specifications in the fractional-order domain where an infinite number of relationships could be obtained due to the extra independent fractional-order parameters which increase the filter degrees-of-freedom. The necessary and sufficient condition for achieving fractional-order Butterworth filter with a specific cutoff frequency is derived as a function of the orders in addition to the transfer function parameters. The effect of equal-orders on the filter bandwidth is discussed showing how the integer-order case is considered as a special case from the proposed procedure. Several passive and active filters are studied to validate the concept such as Kerwin-Huelsman-Newcomb and Sallen-Key filters through numerical and Advanced Design System (ADS) simulations. Moreover, these circuits are tested experimentally using discrete components to model the fractional order capacitor showing great matching with the numerical and circuit simulations. View full abstract»

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  • Design and Analysis of CMOS-Based Terahertz Integrated Circuits by Causal Fractional-Order RLGC Transmission Line Model

    Page(s): 355 - 366
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    A causal and compact fractional-order model is developed for complementary metal-oxide-semiconductor (CMOS) on-chip transmission line (T-line) at Terahertz (THz) frequencies. With consideration of the loss from frequency-dependent dispersion and nonquasi-static effects at THz, good agreement of characteristic impedance is observed between the proposed fractional-order model and the measurement up to 110 GHz, while traditional integer-order model can only match up to 10 GHz. The developed fractional-order model is further deployed in the design and analysis of CMOS-based THz integrated circuits that utilize T-line, such as standing-wave oscillator, which has significantly improved accuracy with causality. View full abstract»

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  • Measurement of Supercapacitor Fractional-Order Model Parameters From Voltage-Excited Step Response

    Page(s): 367 - 376
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    In this paper, we propose using a numerically solved least squares fitting process to estimate the impedance parameters of a fractional order model of supercapacitors from their voltage excited step response, without requiring direct measurement of the impedance or frequency response. Experimentally estimated parameters from low capacity supercapacitors of 0.33, 1, and 1.5 F in the time range 0.2-30 s and high capacity supercapacitors of 1500 and 3000 F in the time range 0.2-90 s verify the proposed time domain method showing less than 3% relative error between the simulated response (using the extracted fractional parameters) and the experimental step response in these time ranges. An application of employing supercapacitors in a multivibrator circuit is presented to highlight their fractional time-domain behavior. View full abstract»

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  • Resonance and Quality Factor of the RL_{\alpha } C_{\alpha } Fractional Circuit

    Page(s): 377 - 385
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    This paper introduces the general fundamentals of the fractional order RLαCα circuit, where α is the order of the elements. The generalized complex impedance of the RLαCα circuit can be purely real, imaginary, or short circuit. The stability analyses where two regions have been classified are introduced with many numerical examples. General maps for transient and frequency responses are investigated showing the damping parameters for each case. The resonance, 3 dB frequencies, bandwidth, and quality factor for all possible cases have been investigated with detailed analytical formulas. Numerical and PSpice simulations are provided using different examples to validate these concepts. View full abstract»

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  • Analog Circuit Implementation of Fractional Order Damped Sine and Cosine Functions

    Page(s): 386 - 393
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    This paper introduces for the first time analog circuit implementations of two fundamental linear fractional order systems whose impulse responses called fractional order damped sine and cosine functions are the inverse Laplace transform of their irrational transfer functions. These analog circuit implementations are derived through rational function approximations of their irrational transfer functions. View full abstract»

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  • Analog Modeling of Fractional Switched Order Derivative Using Different Switching Schemes

    Page(s): 394 - 403
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    The paper presents comparison of two different switching schemes of variable order derivatives. The first one is additive-switching scheme, when change of order is caused by adding a derivative at the beginning of the system. The second one, introduced in this paper, is reductive-switching scheme, when change of order is caused by removing a derivative at the beginning of the system. For both methods numerical schemes are given and analyzed. Based on presented switching schemes results of analog modeling are presented. Results were obtained using analog approximations of integrators of orders 0.5 and 0.25. Finally, results of analog modeling were compared with numerical approach. View full abstract»

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  • On FIR Filter Approximation of Fractional-Order Differentiators and Integrators

    Page(s): 404 - 415
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1860 KB) |  | HTML iconHTML  

    This paper considers finite-length impulse response (FIR) filter approximation of differentiators and integrators, collectively called differintegrators. The paper introduces and compares three different FIR filter structures for this purpose, all of which are optimized in the minimax sense using iterative reweighted l1-norm minimization. One of the structures is the direct-form structure, but featuring equal-valued taps and zero-valued taps, the latter corresponding to sparse filters. The other two structures comprise two subfilters in parallel and cascade, respectively. In their basic forms, nothing is gained by realizing the filters in parallel or in cascade, instead of directly. However, as the paper will show, these forms enable substantial further complexity reductions, because they comprise symmetric and antisymmetric subfilters of different orders, and also features additional equal-valued and zero-valued taps. The cascade structure employs a structurally sparse filter. The additional sparsity, as well as tap equalities, are for all three structures found automatically in the design via the l1-norm minimization. Design examples included reveal feasible multiplication complexity savings of more than 50% in comparison with regular (unconstrained) direct-form structures. In addition, an example shows that the proposed designs can even have lower complexity than existing infinite-length impulse response filter designs. View full abstract»

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  • A Survey of Fractional-Order Circuit Models for Biology and Biomedicine

    Page(s): 416 - 424
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    In this survey, we present many of the fractional- order circuit models used in biomedicine and biology to fit experimentally collected impedance data. An overview of the different methods used to extract the impedance parameters from collected datasets are also presented. Applications of fractional order circuit models for modelling human tissue, plant physiology, respiratory systems, and tissue-electrode interfaces are presented to highlight the significance of these models and their potential for further research. This survey is of a tutorial nature intended as an introduction to fractional-order circuit models and to consolidate the many models reported across literature. View full abstract»

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  • Emerging Tools in Engineering: Fractional Order Ladder Impedance Models for Respiratory and Neural Systems

    Page(s): 425 - 431
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    This paper introduces the emerging tool from mathematics in engineering: fractional calculus. Consequently, it enables a novel concept of modelling biological systems by means of preserving the natural rules governing the system's dynamics, i.e., their intrinsic fractal (recurrent) structure. A generally valid ladder network model allows to preserve the anatomy of the system, thereby merging between engineering and medicine. By aid of two original illustrative examples, the advantage and use of these models is explained. Current insight and prospective use for clinical analysis are discussed. View full abstract»

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  • Fractional Order Generalization of Anomalous Diffusion as a Multidimensional Extension of the Transmission Line Equation

    Page(s): 432 - 441
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    In this paper, a new fractional order generalization of the diffusion equation is developed to describe the anisotropy of anomalous diffusion that is often observed in brain tissues using magnetic resonance imaging (MRI). The new model embeds three different fractional order exponents-corresponding to the principal directions of water diffusion-into the governing Bloch-Torrey equation. The model was used to analyze diffusion weighted MRI data acquired from a normal human brain using a 3T clinical MRI scanner. Analysis of the data revealed normal Gaussian diffusion in the cerebral spinal fluid (isotropic fractional order exponent of (0.90 ±0.1), and anomalous diffusion in both the white (0.67 ±0.1) and the gray (0.77 ±0.1) matter. In addition, we observed anisotropy in the fractional exponent values for white mater (0.59 ±0.1) along the fibers versus 0.68 ±0.1 across the fibers), but not for gray matter. This model introduces new parameters to describe the complexity of the tissue microenvironment that may be sensitive biomarkers of the structural changes arising in neural tissues with the onset of disease. View full abstract»

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  • Observer-Based Approach for Fractional-Order Chaotic Synchronization and Secure Communication

    Page(s): 442 - 450
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    This paper presents a method based on the state observer design for constructing a chaotically synchronized systems. Fractional-order direct Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer-based controller are obtained in terms of linear matrix inequalities (LMIs) formulation. The proposed approach is then applied to secure communications. The method combines chaotic masking and chaotic modulation, where the information signal is injected into the transmitter and simultaneously transmitted to the receiver. Chaotic synchronization and chaotic communication are achieved simultaneously via a state observer design technique. The fractional-order chaotic Lorenz and Lü systems are given to demonstrate the applicability of the proposed approach. View full abstract»

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  • Reduced Order Approximation of MIMO Fractional Order Systems

    Page(s): 451 - 458
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    A new two-stage method for reduced integer order approximation of fractional multiple-input, multiple-output (MIMO) systems is proposed. In the first stage, the transfer function matrix (TFM) Gf(s) of the given fractional order MIMO system is obtained and an integer order approximate TFM R(s) is formed by applying an existing approximation method to each fractional order transfer function (FOTF) of Gf(s). In the second stage, a reduced order state space model is formed. The system matrix of the reduced order system is constructed by selecting the dominant poles from the intermediate high integer order model R(s). The input and output matrices are found by matching approximate time moments and Markov parameters of the final reduced order model and the original system. The proposed method has been illustrated by an example. View full abstract»

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  • Using Self-Synchronization Error Dynamics Formulation Based Controller for Maximum Photovoltaic Power Tracking in Micro-Grid Systems

    Page(s): 459 - 467
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    This paper proposes a self-synchronization error dynamics formulation based controller for maximum photovoltaic power tracking (MPPT) of a photovoltaic (PV) array. The output power conversion of a PV array depends on atmospheric conditions, such as the solar radiation and ambient temperature, and its conversion efficiency is low. Therefore, a MPPT controller is necessary for a PV conversion system, in order to improve the output power. A PV cell is a p-n semiconductor junction. Photon motion, temperature, or electricity conduction cause anomalous diffusion phenomena in inhomogeneous media. In order to describe nonlinear-characteristics, fractional-order calculus can be used to express the dynamic behaviors using fractional-order incremental conductance and to adjust the terminal voltage to the maximum power point. Inspired by the synchronization of Sprott system, a voltage detector is formulated to trace the desired voltage and to control the duty cycle of a boost converter. For a small photovoltaic system, the numerical experiments demonstrate that the proposed method can reduce the tracking time and can improve the conversion efficiency. View full abstract»

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  • Symbolic Fractional Dynamics

    Page(s): 468 - 474
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    Fractional dynamics reveals long range memory properties of systems described by means of signals represented by real numbers. Alternatively, dynamical systems and signals can adopt a representation where states are quantified using a set of symbols. Such signals occur both in nature and in man made processes and have the potential of a aftermath as relevant as the classical counterpart. This paper explores the association of Fractional calculus and symbolic dynamics. The results are visualized by means of the multidimensional technique and reveal the association between the fractal dimension and one definition of fractional derivative. View full abstract»

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  • Study on Control Input Energy Efficiency of Fractional Order Control Systems

    Page(s): 475 - 482
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    Control input energy efficiency is an important issue which should be considered in designing any control system. Due to the importance of this subject, in the present paper fractional order control systems are studied in the viewpoint of control input energy efficiency. In this study, the divergent terms of the control input energy function of fractional order control systems are obtained. It is shown that these terms have a significant role in the amount of the energy injected to the plant by the controller. Finally, two examples are provided to demonstrate the usefulness of the presented results in the paper. View full abstract»

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  • IEEE Journal on Emerging and Selected Topics in Circuits and Systems information for authors

    Page(s): 483
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    Page(s): 484
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Aims & Scope

The IEEE Journal on Emerging and Selected Topics in Circuits and Systems publishes special issues covering the entire Field of Interest of the IEEE Circuits and Systems Society and with particular focus on emerging areas.

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Meet Our Editors

Editor-in-Chief
Manuel Delgado-Restituto
Instituto Nacional de Microelectrónica de Sevilla
IMSE-CNM (CSIC/Universidad de Sevilla)