Multivariate theory‐based passivity criteria for linear fractional networks

In traditional linear network theory, the positive‐real (PR) criteria are widely used to judge the passivity of elements and networks in the light of the fact that there exists an equivalent relationship between the passivity and the PR property of their immittance functions (matrices). However, the equivalence will no longer hold when the fractional elements are introduced into the network, and the PR criteria are not suitable in complex frequency domain anymore. On the other hand, the rapid development of fractional‐order circuits and systems and the corresponding study in fractional circuit analysis and designs put forward an urgent requirement for the passivity criterion, which can tackle linear fractional networks. Hence, in this paper, we propose new passivity criteria for linear fractional networks by aid of generalized Tellegen's theorem and multivariable PR theory. By using the proposed criteria, the passivity of linear fractional networks can be judged, and the steps of the proposed criterion are illustrated by examples.     

Electrical circuits RC,LC, and RL described by Atangana–Baleanu fractional derivatives

In this paper, the analytical solutions for the electrical series circuits RC, LC, and RL using novel fractional derivatives of type Atangana–Baleanu with non‐singular and nonlocal kernel in Liouville–Caputo and Riemann–Liouville sense were obtained. The fractional equations in the time domain are considered derivatives in the range α ∈(0;1]; analytical solutions are presented considering different source terms introduced in the fractional equation. We solved analytically the fractional equation using the properties of Laplace transform operator together with the convolution theorem. On the basis of the Mittag–Leffler function, new behaviors for the voltage and current were obtained; the classical cases are recovered when α =1. Copyright © 2017 John Wiley & Sons, Ltd.     

Ultra‐low voltage fractional‐order circuits using current mirrors

Fractional‐order blocks, including differentiators, lossy and lossless integrators as well as filters of order 1 + a (0 < a < 1), are presented in this paper. The proposed topologies offer the benefit of ultra low‐voltage operation; in addition, reduced circuit complexity is achieved compared to the corresponding companding schemes, which have been already introduced in the literature. The ultra‐low voltage operation is performed through the employment of metal oxide semiconductor transistors biased in the subthreshold region. The reduction of circuit complexity is achieved through the utilization of current mirrors as active elements for realizing the required building blocks. The performance of the proposed fractional‐order circuits has been evaluated through the Analog Design Environment of the Cadence software and the design kit provided by the Taiwan Semiconductor Manufacturing Company (TSMC) 180 nm complementary metal oxide semiconductor process. Copyright © 2015 John Wiley & Sons, Ltd.     

Modelling the dynamics of log‐domain circuits

Log‐domain filters are an intriguing form of externally linear, internally nonlinear current‐mode circuits, in which a compression stage is first used to convert the input currents to the logarithmic domain, then analogue processing is carried out on the resulting voltages, and finally input–output linearity is restored by mapping the output voltages to current form through an expansion stage. The compressing and expanding operations confer on log‐domain filters a number of desirable features, but they may be responsible for the loss of external linearity. In this paper, sufficient conditions for the external linearity of log‐domain LC‐ladders are established, and the local nature of this external linearity is highlighted. Certain log‐domain LC‐ladders employing floating capacitors may exhibit externally nonlinear behaviour even for zero input and very small initial conditions. We show how transistor parasitic capacitances are central to the emergence of this behaviour, and must be incorporated in the circuit model. Copyright © 2006 John Wiley & Sons, Ltd.     

A quad‐band W‐CDMA transceiver IC–direct conversion architecture with fractional frequency divider

A quad‐band (0.8, 1.7, 2, and 1.4 GHz) wideband code division multiple access (W‐CDMA) transceiver, which uses a divide‐by‐2.5 frequency divider in local parts of a direct‐conversion architecture, has been developed. Using the fractional‐2.5 frequency divider reduces the fractional bandwidth of the voltage‐controlled oscillator and avoids injection locking of the local RF synthesizer perfectly. This transceiver achieved 3% error‐vector magnitude and—46 dB ACLR, which satisfy the margin given in standard specifications. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

An algorithm for direct identification of passive transfer matrices with positive real fractions via convex programming

The paper presents a new algorithm for the identification of a positive real rational transfer matrix of a multi‐input–multi‐output system from frequency domain data samples. It is based on the combination of least‐squares pole identification by the Vector Fitting algorithm and residue identification based on frequency‐independent passivity constraints by convex programming. Such an approach enables the identification of a priori guaranteed passive lumped models, so avoids the passivity check and subsequent (perturbative) passivity enforcement as required by most of the other available algorithms. As a case study, the algorithm is successfully applied to the macro‐modeling of a twisted cable pair, and the results compared with a passive identification performed with an algorithm based on quadratic programming (QPpassive), highlighting the advantages of the proposed formulation. Copyright © 2010 John Wiley & Sons, Ltd.     

Analysis and realization of a switched fractional‐order‐capacitor integrator

Using fractional calculus, we analyze a classical switched‐capacitor integrator when a fractional‐order capacitor is employed in the feed‐forward path. We show that using of a fractional‐order capacitor, significantly large time constants can be realized with capacitances in the feedback path much smaller in value when compared with a conventional switched‐capacitor integrator. Simulations and experimental results using a commercial super‐capacitor with fractional‐order characteristics confirmed via impedance spectroscopy are provided. Copyright © 2016 John Wiley & Sons, Ltd.     

Properties of anisotropic Ba‐Zn‐Cu system W‐type hexagonal ferrite magnets

Experiments were carried out to investigate the magnetic and physical properties of Ba‐Zn‐Cu W‐type hexagonal ferrites sintered without atmosphere control. Compositions were chosen according to the formula BaZn_2–xCu_xFe₁₆O₂₇, where x was varied 0 ˜ 0.5 and 1.0. The effect of BaO addition after semisintering treatment on magnetic properties of Ba‐Zn‐Cu compounds was examined. It was found that BaO addition for Ba‐Zn‐Cu compounds was very useful in stabilizing the W‐type hexagon. The optimum condition of making magnets and some properties of typical specimens are as follows: composition—BaZn_1.7Cu_0.3Fe₁₆O₂₇ with 4 wt% Ba added; semisintering conditions—1275 °C for 1.0 h in air; sintering conditions—1175°C for 0.5 h in air; magnetic properties and lattice constant are J_m = 0.405 T, J_r = 0.370 T, H_cJ = 88.15 kA/m, (BH)_max = 19.12 kJ/m³, T_c = 356 °C, H_A = 994.7 kA/m, K_A = 2.01 × 10⁵ J/m³, c = 32.928 × 10^–10 m, a = 5.927 × 10^–10 m, c/a = 5.556. © 2001 Scripta Technica, Electr Eng Jpn, 134(4): 36–42, 2001     

Square‐root domain linear transformation filters

A new systematic method for designing square‐root domain (SRD) linear transformation (LT) filter is introduced in this paper. For this purpose, a substitution table containing the SRD LT equivalent of each passive element has been introduced. The proposed equivalents have been realized by employing appropriate SRD building blocks with low‐voltage operation capability. As a design example, a 3rd‐order SRD LT filter has been realized and its performance has been evaluated through simulation results. In addition, the most important performance factors of the SRD filter have been compared with those achieved by the SRD filters derived according to the leapfrog, wave, and topological emulation methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Magnetic properties of Pr‐Fe‐Co‐V‐W‐Si‐B system exchange spring magnets

The melt‐spun ribbons of Pr‐Fe‐Co‐V‐W‐Si‐B system alloys were prepared by single roller rapid‐quenching method. The effects of composition, surface velocity, and heat treatment on the magnetic properties were investigated. The P₉sFe₇₁Co₈V_0.5W_0.5Si_0.5B_10.5 alloy ribbons prepared at a surface velocity of 12.5 m/s were crystallized by heat treatment, and the optimum heat‐treatment condition was found to be at 575°C for 3 min, for which the magnetic properties were (BH)_max = 136.1 kJ/m³, J_r = 0.93 T, H_cJ = 652.2 kA/m, and H_cB = 528.3 kA/m. The temperature coefficients of J_r and H_cJ for the ribbons crystallized from melt‐spun ribbons of Pr₉Fe₇₁Co₈V_0.5W_0.5Si_0.5B_10.5 alloy were α(J_r)_ave = ?0.057%/°C and α(H_cJ) = ?0.450%/°C. The value of (B)_max for the compression molding Pr₉Fe₇₁Co₈V_0.5W_0.5Si_0.5B_10.5 isotropic bonded magnet prepared by using the ribbons annealed at 575°C for 3 min is 80.0 kJ/m³, and the density is 6.24 Mg/m³. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 157(3): 10–16, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20211 Copyright © 2006 Wiley Periodicals, Inc.     

An expression for the voltage response of a current‐excited fractance device based on fractional‐order trigonometric identities

We report a closed‐form expression of the voltage response of a current‐excited fractance device. The derived simple expression is made possible following the introduction of the generalized sine and cosine functions (rmsin_α(t) and cos_α(t)), which are valid on any fractional‐order surface and tend to the normal sin(t) and cos(t) at α = 1 or asymptotically as t→∞. Copyright © 2011 John Wiley & Sons, Ltd.     

Design of square‐root domain filters by substituting the passive elements of the prototype filter by their equivalents

A novel technique for designing square‐root domain (SRD) filters is introduced in this paper. The concept of the proposed method is based on the substitution of the passive elements of the corresponding prototype filter by their SRD equivalents. The signal processing performed by the proposed SRD equivalents achieves that the voltage at each terminal of the SRD equivalent is the compressed version of the voltage at the corresponding terminal of the passive element, and that the current that flows through the SRD equivalent is the same as that flows through the passive element. The main attractive characteristic of the proposed method is that a quick procedure for designing SRD filters is offered. The validity of the proposed technique was verified by studying the behaviour of a 5th‐order SRD low‐pass filter. In order to demonstrate the benefits offered by the proposed technique, a SRD leapfrog filter was also designed and its performance is compared with that of the active filter that topologically simulates the same prototype filter. Copyright © 2007 John Wiley & Sons, Ltd.     

Log‐domain linear transformation filters revised: improved building blocks and comparison results

A method for designing high‐order log‐domain filters has already been proposed in the literature based on the concept of the classical linear transformation (LT) filters. For this purpose, a substitution table containing the log‐domain LT equivalent of each passive element has been introduced. Drawbacks of the log‐domain filter topologies derived according to this table are the following: (a) a dc offset current appears at the output of all pole filters and (b) dc instability is observed in the case of the substitution of LC resonators. In addition, an alternative technique already proposed for simulating filters with LC resonators is valid only under small‐signal conditions. In order to overcome the aforementioned problems, new log‐domain LT equivalents of a number of passive elements are introduced in this paper. The correct operation of the novel blocks has been verified through simulation results. Also, a comparison concerning the behaviour of the log‐domain LT filters and that of the filters derived according to the leapfrog and the wave methods has also been performed. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental studies on realization of fractional inductors and fractional‐order bandpass filters

This paper presents the hardware realization and performance study of fractional inductors of order 0 < α < 2. The fractional inductors used in this work have been realized with the help of general impedance converter circuit and fractional capacitors. Impedance characterization of fractional inductors with different exponents has been carried out experimentally. Also a generalized approach to design a fractional‐order bandpass filter is discussed in this work. The fractional‐order bandpass filter consists of a series combination of a resistor, a fractional inductor of order 1 < α < 2, and a fractional capacitor of order 0 < β < 1. The performance of fractional‐order bandpass filters has been studied and compared with corresponding integer‐order filters through both experimentation and simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

A wavelet‐based piecewise approach for steady‐state analysis of power electronics circuits

Simulation of steady‐state waveforms is important to the design of power electronics circuits, as it reveals the maximum voltage and current stresses being imposed upon specific devices and components. This paper proposes an improved approach to finding steady‐state waveforms of power electronics circuits based on wavelet approximation. The proposed method exploits the time‐domain piecewise property of power electronics circuits in order to improve the accuracy and computational efficiency. Instead of applying one wavelet approximation to the whole period, several wavelet approximations are applied in a piecewise manner to fit the entire waveform. This wavelet‐based piecewise approximation approach can provide very accurate and efficient solution, with much less number of wavelet terms, for approximating steady‐state waveforms of power electronics circuits. Copyright © 2006 John Wiley & Sons, Ltd.     

Time‐domain properties of reactive dual circuits

The present work explores some effects of the replacement of capacitors by inductors and vice versa in state and semistate models of lumped circuits. Such a replacement, when performed together with an inversion of the capacitance and inductance matrices, yields a transformation of the form λ→λ^?1 in the system spectra. In the semistate context, this covers in particular extremal cases in which null eigenvalues or infinite ones with higher index appear in the matrix pencil associated with the model; these cases describe certain pathological circuit configurations. This approach leads to a discussion of new properties of strictly passive circuits; specifically, from the known fact that the index of strictly passive circuits does not exceed two, we derive that the index of null eigenvalues in this setting cannot exceed one. This precludes in particular Takens‐Bogdanov degeneracies, defined by an index‐two double‐zero eigenvalue, in strictly passive circuits. Although the results are addressed in a linear context, they can be extended via linearization to non‐linear problems, as it is the case in the transformation of singularity‐induced bifurcation phenomena into steady bifurcations discussed at the end of the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

An interval algorithm for finding all solutions of non‐linear resistive circuits

In this letter, an efficient algorithm is proposed for finding all solutions of non‐linear (not piecewise‐linear) resistive circuits. This algorithm is based on interval analysis, the dual simplex method, and the contraction methods. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 500–700 non‐linear circuit equations in acceptable computation time. Copyright © 2004 John Wiley & Sons, Ltd.     

Multiple operating points in a square‐root domain first‐order filter

In this paper novel corrective circuits to avoid multiple operating points in a square‐root domain first‐order filter are proposed. By employing a DC test it is demonstrated that the filter possesses three operating points (two stable and one unstable) and the corrective circuits enforce the proper operating mode. The corrective circuits and filter are able to operate with very low supply voltages (as low as V_GS+2V_DSsat). Moreover, a detailed analysis concerning the impact that produces the corrective circuits on the filter performance is discussed. Both measurement and simulation results are provided to validate the circuits and analysis employed. Copyright © 2006 John Wiley & Sons, Ltd.     

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

An efficient algorithm is proposed for finding all solutions of piecewise‐linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of large‐scale problems, including those where the number of variables is 300 and the number of linear regions is 10³⁰⁰, in practical computation time. Copyright © 2002 John Wiley & Sons, Ltd.     

A wavelet approach to fast approximation of steady‐state waveforms of power electronics circuits

Waveforms arising from power electronics circuits often contain slowly changing segments with high‐frequency details concentrated near the switching instants. Such a feature is consistent with the localization property of wavelets which are known in the signal processing literature to be highly suitable for describing fast changing edges embedded in slowly varying backgrounds. This paper considers the application of wavelet approximation to the steady‐state analysis of power electronics circuits. The basic procedure of wavelet approximation is reviewed, and an improved approach by mixing wavelets of different levels is described. When applied to power electronics circuits, the method yields efficient solutions because only a relatively small number of wavelets are needed and the proposed algorithm involves only matrix operations, permitting the steady‐state waveforms to be found fast. Copyright 2003 John Wiley & Sons, Ltd.