Non‐linear circuit modelling via nodal methods

We discuss in this paper several interrelated nodal methods for setting up the equations of non‐linear, lumped electrical circuits. A rather exhaustive framework is presented, aimed at surveying different approaches and terminologies in a comprehensive manner. This framework includes charge‐oriented, conventional, and hybrid systems. Special attention is paid to so‐called augmented node analysis (ANA) models, which somehow articulate the tableau and modified node analysis (MNA) approaches to non‐linear circuit modelling. We use a differential–algebraic formalism and, extending previous results proved in the MNA context, we provide index‐1 conditions for augmented systems, which are shown to be transferred to tableau models. This approach gives, in particular, precise conditions for the feasibility of certain state‐space reductions. We work with very general assumptions on device characteristics; in particular, our approach comprises a wide range of resistive devices, going beyond voltage‐controlled ones. Copyright © 2005 John Wiley & Sons, Ltd.     

Structural analysis of electric circuits and consequences for MNA

The development of integrated circuits requires powerful numerical simulation programs. Naturally, there is no method that treats all the different kinds of circuits successfully. The numerical simulation tools provide reliable results only if the circuit model meets the assumptions that guarantee a successful application of the integration software. Owing to the large dimension of many circuits (about 10⁷ circuit elements) it is often difficult to find the circuit configurations that lead to numerical difficulties. In this paper, we analyse electric circuits with respect to their structural properties in order to give circuit designers some help for fixing modelling problems if the numerical simulation fails. We consider one of the most frequently used modelling techniques, the modified nodal analysis (MNA), and discuss the index of the differential algebraic equations (DAEs) obtained by this kind of modelling. Copyright © 2000 John Wiley & Sons, Ltd.     

Formulating hybrid equations and state equations for nonlinear circuits using SPICE

Hybrid equations are often used in the theoretical study of nonlinear resistive circuits because they have an easy‐to‐analyze structure. They are also advantageous in the numerical analysis of nonlinear resistive circuits because they are separable and consist of a relatively small number of variables. However, the hybrid equations are seldom used in practical applications because their formulation is complicated. In this letter, we propose a simple method for formulating the hybrid equations using SPICE. In the proposed method, we only perform the transient analysis of SPICE on a linear circuit that is obtained through a small modification to the original circuit. It is also shown that state equations for nonlinear dynamic circuits can also be formulated by using the proposed method. Copyright © 2011 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.     

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.     

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.     

An Investigation of Size‐Reduction Effects in High Power Density Boost Converters with a Magnetic Coupling

The dc–dc converter using integrated magnetic components that may achieve high power density has gained attention in environmentally friendly cars such as electric vehicles and hybrid electric vehicles. This paper focused on interleaved boost converters using close‐coupled inductors (CCIs) and loose‐coupled inductors (LCIs) that are the integrated magnetic components. Following, detailed electromagnetically analysis for these circuit types were conducted in order to calculate volume of inductors and capacitors that are occupied the large part of space in the converters. The total volume of inductors and capacitors in these circuits were demonstrated clearly through comparison with conventional circuits such as an interleaved boost converter and a single‐phase boost converter. As a result, it became clear that interleaved boost converter using LCIs was effective for miniaturization of total volume. Furthermore, duty ratio of the minimum volume of CCI method is different from the duty ratio of the minimum volume of LCI method.     

Circuit models for symmetric systems of linear equations

Electric circuit models are constructed for general symmetric systems of linear algebraic equations. The modelling procedure is based on the node‐voltage analysis of linear circuits under steady‐state conditions. These electric circuit models can, in principle, be physically realized and used for the solution of the systems of equations by simply measuring the electric voltage at the circuit nodes. Copyright © 2000 John Wiley & Sons, Ltd.     

Finite difference schemes for heat conduction analysis in integrated circuit design and manufacturing

The importance of thermal effects on the reliability and performance of VLSI circuits has grown in recent years. The heat conduction problem is commonly described as a second‐order partial differential equation (PDE), and several numerical methods, including simple explicit, simple implicit and Crank–Nicolson methods, all having at most second‐order spatial accuracy, have been applied to solve the problem. This paper reviews these methods and further proposes a fourth‐order spatial‐accurate finite difference scheme to better approximate the PDE solution. Moreover, we devise a fourth‐order accurate approximation of the convection boundary condition, and apply it to the proposed finite difference scheme. We use a block cyclic reduction and a recently developed numerically stable algorithm for inversion of block‐tridiagonal and banded matrices to solve the PDE‐based system efficiently. Despite their higher computation complexity than direct computation in a sequential processor, we make it possible for the very first time to employ a divide‐and‐conquer algorithm, viable for parallel computation, in heat conduction analysis. Experimental results prove such possibility, suggesting that applying divide‐and‐conquer algorithms, higher‐order finite difference schemes can achieve better simulation accuracy with even faster speed and less memory requirement than conventional methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Differential equation description and Chebyshev approximation of linear time‐invariant circuits

The approximation technology of analogue circuit functions is crucial to the computer‐aided simulation, analysis, and design automation of electronic circuits. Chebyshev polynomials and various differential equations are proposed in this paper to approximate the functions of linear time‐invariant circuits. The coefficient calculation methods of the Chebyshev expansion and the differential equation matrices are thoroughly deduced, and the construction methods employed in the functions and the actual time mapping of the linear time‐invariant circuits are presented in this paper. An example of an analogue filter verifies the effectiveness and accuracy of the proposed approximation algorithm and elaborates on the selection process of the order number and the time step length of the Chebyshev expansion according to the demanded truncation error.     

A step‐by‐step approach to compute a consistent initialization for the MNA

One of the difficulties of the numerical integration methods for differential–algebraic equations (DAEs) is the computation of consistent initial values before starting the integration, i.e. calculating values that satisfy the given algebraic constraints as well as the hidden constraints if higher index problems are considered. This paper presents an approach to calculate consistent initial values for index‐2 DAEs starting up from possibly inconsistent ones for systems arising from modified nodal analysis (MNA) in circuit simulation. This article is based on the results from Estévez Schwarz and Tischendorf, International Journal of Circuit Theory and Applications 2000; 28 : 131–162. Several of the denotations and results that we use were introduced there in more detail. Copyright © 2001 John Wiley & Sons, Ltd.     

一种混合电动汽车用无刷直流电机转子位置检测方法

提出了一种检测混合电动汽车用无刷直流电机转子位置的新方法,该方法通过检测电机的三相平均线电压获得转子位置信号,与传统的反电势过零检测法相比,提出的方法无需构建电机中性点,无需复杂的延迟电路,电路结构简单,成本低廉。理论分析和实验结果表明提出的方法在较宽的工作范围内对混合电动汽车用无刷直流电机具有良好的控制性能。     

Envelope simulation by SPICE-compatible models of linear electriccircuits driven by modulated signals

SPICE-compatible equivalent circuits were developed to facilitate the analysis and envelope simulation of electric circuits driven by modulated signals. The circuits are based on a novel complex phasor-domain transformation. The proposed method facilitates simulation of any general linear circuit driven by a modulated signal such as amplitude modulation, frequency modulation, or phase modulation. Simulation time by the proposed envelope simulation is much faster than the full cycle-by-cycle simulation of the original circuit and excitation     

Piecewise linear second moment statistical simulation of ICs affected by non‐linear statistical effects

This paper presents a methodology for statistical simulation of non‐linear integrated circuits affected by device mismatch. This simulation technique is aimed at helping designers maximize yield, since it can be orders of magnitude faster than other readily available methods, e.g. Monte Carlo. Statistical analysis is performed by modeling the electrical effects of tolerances by means of stochastic current or voltage sources, which depend on both device geometry and position across the die. They alter the behavior of both linear and non‐linear components according to stochastic device models, which reflect the statistical properties of circuit devices up to the second order (i.e. covariance functions). DC, AC, and transient analyses are performed by means of the stochastic modified nodal analysis, using a piecewise linear stochastic technique with respect to the stochastic sources, around a few automatically selected points. Several experimental results on significant circuits, encompassing both the analog and the digital domains, prove the effectiveness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Transient Magnetic Fields and Current Distributions in an Electric Vehicle Caused by a Lightning Stroke

An electric vehicle has more electronic parts than a gasoline‐powered vehicle. Not only the control circuits but also the driving circuits of electric vehicles are electrical, in contrast to those of gasoline‐powered vehicles. This means that there is a higher possibility of malfunctions in an electric vehicle due to electromagnetic disturbances caused by a lightning stroke. Therefore, it is important to establish lightning protection methodologies for electric vehicles. To clear up with the mechanisms whereby the lightning current following through the vehicle body and some other parts causes the malfunctions, it is important to clarify the transient magnetic fields and current distributions in electric vehicles. In this paper, the transient magnetic fields and the current distributions in an electric vehicle are simulated by the FDTD method, and the probability of lightning damage is discussed.     

故障电力传输线的复频域节点导纳电压方程

基于传输线分布参数理论和传输线节点导纳方程,提出了故障电力传输线终端频域电压响应的一种理论分析方法。当传输线发生故障时,在故障点处将故障电力传输线分为两个子传输线,根据两个子传输线的连接条件及节点导纳方程,利用分块矩阵理论推导了电力传输线发生单相接地、两相短路和两相接地故障情况下的节点导纳方程。     

Some invariant sums of higher‐order sensitivities

In this paper, a new class of invariant sensitivity sums of higher‐order sensitivities is given. Sensitivity sums considered are relevant to a network function of general lumped time‐invariant circuits containing passive and active elements. It is assumed that the circuit is linear and consists of one‐port elements and two‐port elements only. A part of the one‐port elements is described by admittance parameters and the other part by impedance parameters. The rest of the one‐port elements are independent sources. Two‐port elements are only controlled sources. Hybrid matrix should describe functional relationships of the elements. Formulas for invariant sums of sensitivities of first, second, third, and fourth order are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Charging Load Aggregation Potential of Multiple Electric Vehicles Based on Road Traffic Census Data

High penetration of renewable generation systems will lead to supply–demand imbalances, and will also require output curtailment of renewable power plants. We focused on management of electric vehicle fleet charging which can promote charging during specific time zone for reducing this curtailment. In this study, we evaluated the Charging Promoting Potential (CPP) of passenger electric vehicles (EVs) using optimization model based on the mixed‐integer linear programming. In addition, we also evaluated the CPP of other EVs, such as electric buses and electric trucks. We found that wider zone of the charging promoting time led effective concentration of charging load. Furthermore, we found that the CPP of the electric buses is higher than those of the passenger EVs and electric trucks.     

First harmonic analysis: a circuit theory point of view

The first harmonic method is usually applied to nonlinear system analysis, being particularly adequate for the study of oscillations. As shown in this paper, oscillators analysis can be performed by using only basic concepts of circuit theory. The nonlinearities present in the oscillator electric circuits are approximated, via the first harmonic method, by resistance or source-controlled equivalent circuit elements, and the resulting linear circuits are entirely analyzed via conventional circuit theory. As a result, the analysis of electric oscillators and the first harmonic method are introduced in a comprehensible electric circuit context