A class of versatile circuits,made up of standard electrical components,are memristors

In this paper, we propose a whole class of memristor circuits. Each element from the class consists of the cascade connection between a static nonlinear two‐port and a dynamic one‐port. The class may be divided into two subclasses depending on the input variable (voltage or current). Within each of these subclasses, two further sets of memristor circuits may be distinguished according to which output voltage and current of the two‐port represents one of the system states. The simplest memristor circuits make only use of purely passive elementary components from circuit theory, an absolute novelty in this field of research. Thus they are suitable circuit primers for the introduction of the topic of memristors to undergraduate students. A sample circuit is built using discrete devices and its memristive nature is validated experimentally. In case the one‐port is purely passive, the proposed circuits feature volatile memristive behavior. Allowing active devices into the dynamic one‐port, non‐volatile dynamics may also emerge, as proved through concepts from the theory of nonlinear dynamics. Given the generality of the proposed class, the topology of the emulators may be adjusted so as to induce a large variety of dynamical behaviors, which may be exploited to accomplish new signal processing tasks, which conventional circuits are unable to perform. Copyright © 2015 John Wiley & Sons, Ltd.     

Positive‐real property of passive fractional circuits in W‐domain

Fractional circuits have attracted extensive attention of scholars and researchers for their superior performance and potential applications. Fractional circuits constitute a new challenge for the analysis and synthesis methods of traditional circuits theory. Passivity is the fundamental property of traditional circuits (integer order electric circuits). As is known to all, passivity is equivalent to positive realness in traditional linear circuits. However, this equivalence is broken down by introducing fractional elements into electrical networks in s‐domain. To address this issue, on the basis of s‐W transformation, we study the passive criteria of fractional circuits with rational order elements in this paper. Definitions of positive‐real (matrix) function in W‐domain are given, and the equivalence conditions of positive realness are derived. In addition, a conclusion is proposed in which the immittance (matrix) function of passive fractional circuits with rational order elements is positive real in W‐domain. The applications of passive criteria in circuit synthesis are shown.     

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.     

A minimum five‐component five‐term single‐nonlinearity chaotic jerk circuit based on a twin‐jerk single‐op‐amp technique

A minimum 5‐component 5‐term single‐nonlinearity chaotic jerk circuit is presented as the first simplest chaotic jerk circuit in a category that a single op‐amp is employed. Such a simplest circuit displays 5 simultaneous advantages of (1) 5 minimum basic electronic components, (2) 5 minimum algebraic terms in a set of 3 coupled first‐order ordinary differential equations (ODEs), (3) a single minimum term of nonlinearity in the ODEs, (4) a simple passive component for nonlinearity, and (5) a single op‐amp. The proposed 5‐term single‐nonlinearity chaotic jerk circuit and a slightly modified version of an existing 6‐term 2‐nonlinearity chaotic jerk circuit form mirrored images of each other. Although both mirrored circuits yield 2 different sets of the ODEs, both sets however can be recast into a pair of twin jerk equations. Both mirrored circuits are therefore algebraically twin 5‐component chaotic jerk circuits, leading to a twin‐jerk single‐op‐amp approach to the proposed minimum chaotic jerk circuit. Two cross verifications of trajectories of both circuits are illustrated through numerical and experimental results. Dynamical properties are also presented.     

A note on stability of linear time‐variant electrical circuits having constant eigenvalues

The main aspect of this paper is to show that the stability of linear time‐variant systems cannot be estimated from the location of the eigenvalues. For this purpose, two simple time‐variant electrical circuits are presented, which have constant eigenvalues. As will be shown, the time‐variant circuits can be asymptotically stable although there is a positive eigenvalue and this circuit can be unstable despite negative eigenvalues only. The idea behind is a suited time‐variant state transformation of a linear time‐invariant system. An electrical interpretation of both systems and of state transformations allows for an energetic evaluation from an electrical point of view even though the analytical solution is not necessarily known. Copyright © 2012 John Wiley & Sons, Ltd.     

Circuit theoretic approach to the tank-hopfield A/D converter

The ‘neural’ A/D converter of Tank and Hopfield is analysed from the viewpoint of circuit theory. It is shown to be a particular case of the canonical non-linear programming circuit of Chua and Lin. Several qualitative properties concerning the DC solutions are proved. A piecewise-linear analysis of trajectories in the state space is carried out on the basis of the eigenvalues and eigenvectors of the corresponding dynamical matrix. It is shown that the eigenvalues are related to the driving point impedance of an RC one-port network. Asymptotic expressions of the eigenvalues are derived for large N, N being the number of bits. It is shown that the dynamic behaviour represents a sort of successive-approximation A/D conversion. However the conversion time does not increase appreciably as the number of bits increases. the cases of incorrect behaviour and the amount of the maximum conversion error are derived for N > 5. Simulation results are presented for N ≤ 5.     

励磁机时间常数对电力系统动态稳定性的影响

励磁机时间常数对电力系统动稳定有显著影响.在高放大倍数的AVR控制下,快速励磁较慢速励磁更容易恶化系统阻尼;但是在同时附加励磁控制的情况下,快速励磁可使系统的机电模式根轨迹远离虚轴,机电模式阻尼较大;而慢速励磁下,系统机电模式根轨迹接近虚轴,机电模式阻尼较小,快速励磁优于慢速励磁.通过对一个8机系统在AVR、AVR PSS和分散协调励磁调节三种控制规律下的特征分析和动态仿真表明:有附加励磁时,快速励磁比慢速励磁更有利于电力系统动态稳定性.最后借助特征向量理论揭示了所得结论的数学本质.     

Improved static and dynamic performances of a two‐cell DC–DC buck converter using a digital dynamic time‐delayed control

Multi‐cell converters have been developed to overcome shortcomings in usual switching devices. The control system in these circuits is twofold: first, to balance voltages of the switches and second to regulate the load current to a desired value. However, with a purely proportional controller, the system presents a static error. With a PI controller the static error is annihilated, but at the expense of shortening the stability region and increasing settling time. In this work, a zero static error dynamic controller for a two‐cell DC–DC buck converter is designed. To achieve zero current error, we propose a generalized scheme of a dynamic controller. Then, using nonlinear analysis and Lyapunov stability theory and bifurcation prediction tools, we prove that zero static error is achieved. The proposed controller outperforms the PI controller in terms of settling time in the presence of saturating effect during the start‐up transients. Numerical simulations in the form of time domain waveforms and bifurcation diagrams from switched circuit‐based model are presented to confirm our theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.     

On the symmetry features of some electrical circuits

The use of symmetry of some nonlinear circuits, composed of similar resistive (more generally, algebraic) elements, is considered for the analysis of the input resistive function of such a circuit. The focus is on recursively obtained (‘fractal’‐type) 1‐ports, analysed using the concept of α‐circuit introduced by Gluskin. The methods under study should be of interest for the analysis and calculation of complicated nonlinear resistive (algebraic) 1‐port structures, e.g. grid cuts for different symmetry conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

A unified set‐theoretic approach to the analysis of PWL resistive circuits and composite N‐ports

We consider the search for all DC solutions of resistive piecewise‐linear (PWL) circuits and the analysis of the characteristics of resistive PWL composite N‐ports. These problems are unified from a theoretical and operating point of view by introducing the so‐called N‐augmented circuit, obtained from the N‐port by closing its ports with N norators. Set‐theoretic approach is used to describe the properties of the N‐augmented circuits leading to the formulation of a general DC analysis algorithm, based on linear programming techniques. The examples at the end of the paper show some practical and efficient application of the general DC analysis algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

Time‐mode circuits for analog computation

We introduce time‐mode circuits, a set of basic circuit building blocks for analog computation using a temporal step function representation for the inputs and outputs. These novel time‐mode circuits are low power, provide good noise performance and offer improved dynamic range. The design, IC implementation and detailed theoretical signal‐to‐noise ratio (SNR) analysis of a prototype time‐mode circuit—a weighted average computation circuit—are discussed. This new way of computation is studied with respect to existing conventional voltage‐mode and current‐mode circuits. Two possible applications of these time‐mode circuits are presented: an edge detection circuit for 16 pixels and a 3‐tap FIR filter that provides an SNR of 64 dB. Copyright © 2008 John Wiley & Sons, Ltd.     

A matrix pencil approach to the local stability analysis of non‐linear circuits

This paper addresses local stability issues in non‐linear circuits via matrix pencil theory. The limitations of the state–space approach in circuit modelling have led to semistate formulations, currently framed within the context of differential‐algebraic equations (DAEs). Stability results for these DAE models can be stated in terms of matrix pencils, avoiding the need for state–space reductions which are not advisable in actual circuit simulation problems. The stability results here presented are applied to electrical circuits containing non‐linear devices such as Josephson junctions or MOS transistors. Copyright © 2004 John Wiley & Sons, Ltd.     

An approach to modelling DC-DC converter circuits using graph theoretic concepts

An approach to modelling DC-DC converter circuits based on graph theoretic concepts is discussed in this paper. the DC-DC converter circuits are treated as networks containing switches, with the magnitudes of their associated eigenvalues much smaller than the switching frequency. the procedure for modelling this class of networks essentially involves separating the original network into two N-port networks, one containing those branches responsible for all phenomena peculiar to the switching action and the other containing the remaining branches of the network. the two N-port networks thus formed lead to a systematic and convenient way of developing low-frequency circuit models for DC-DC converter circuits.     

A uniform approach to mixed-signal circuit test

Owing to the analogue nature of many industrial processes and the increasing use of microprocessor techniques, many circuits nowadays carry mixed (digital and analogue) signals. As complexities of these circuits increase, the testability of mixed-signal circuits has become an important issue that must be dealt with by both design and test engineers. A systematic approach to study the testability of mixed-signal circuits is urgently needed, because current ad hoc methods cannot efficiently handle increasingly complex and ever-changing circuits. In this paper we develop a uniform and systematic approach to the mixed-signal circuit testability problem. The approach is based on a recently developed theory of discrete event systems. It is suitable for the following tasks: (i) checking the testability of a circuit; (ii) computing the minimum test set; (iii) finding the fault coverage; (iv) dividing a circuit into testable modules. © 1997 by John Wiley & Sons, Ltd.     

Envelope analysis of nonlinear electronic circuits based on harmonic balance method

We propose here a Spice‐oriented envelope analysis based on the HB (harmonic balance) method, where Fourier coefficients are assumed to be slowly varying. The Fourier expansions of nonlinear devices are executed by MATLAB in the symbolic forms. In this time, the nonlinearities need to be approximated by the polynomial functions. The determining equation of the HB method is formulated as Sine–Cosine circuit in the form of schematic diagram using ABMs (analog behavior models) of Spice. Each sub‐circuit corresponding to the higher harmonic component is almost the same circuit topology as the original one and has dynamic elements such as capacitors and inductors. The Sine–Cosine circuit can be solved by the transient analysis of Spice. Thus, our method is rather a symbolic approach in the meaning that the HB determining equation is given by the schematic diagram of Spice. Our method can be easily applied to the analysis of middle order of nonlinear communication circuits such as mixers and amplitude modulators and to the analysis of interesting phenomena in the nonlinear oscillations. After many simulation experiments, the results show that our envelope analysis is about 50 times faster than the direct transient analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

The CCII+ and the ICCII as basic building blocks in low‐pass filter realizations

Three new grounded capacitor current mode low‐pass filters using two inverting second‐generation current conveyor (ICCII) or one double output ICCII are given. The circuits employ the minimum number of passive circuit components, namely two resistors and two capacitors. The circuits are generated from three new voltage mode low‐pass filters realized with the ICCII. A new grounded capacitor CCII+ current mode low‐pass filter is generated from one of the new voltage mode low‐pass filters employing two ICCII?. A new grounded passive component low‐pass filter with independent control on Q and using three ICCII+ is also introduced. Spice simulation results based on using the 0.5 µm CMOS model are included to support the theoretical analysis. Copyright © 2007 John Wiley & Sons, Ltd.     

Complex permeability of polycrystalline Mn-Zn and Ni-Zn ferrites

The complex permeability of ferrites is frequency dependent. The real part of the complex permeability deteriorates in a high frequency range and the imaginary part has a peak after starting the deterioration. This paper examines the possibility that the frequency characteristics for some ferrites can be approximately derived from a first-order linear differential equation for the magnetic field intensity and magnetic flux density. The first-order differential equation is expressed by the reciprocal of the complex permeability and provides first-order magnetic and electric circuits for ferrite cores. In contrast with the commonly used series R_s-L_s, circuit for the cores, obtained from B = (μ′ − jμ′)H, the first-order electric circuit derived consists of an inductance (L) and resistance connected in parallel. In this paper, it is demonstrated that the inductance L remains constant, whereas Ls decrease with the increase in frequency. In other words, the real part of the reciprocal of the complex permeability remains constant for an increase in frequency. In addition, it is found that the imaginary part of the reciprocal of the complex permeability is approximately proportional to the frequency. © 1998 Scripta Technica, Electr Eng Jpn, 123(2): 1–7, 1998