Index characterization of differential–algebraic equations in hybrid analysis for circuit simulation

Modern modeling approaches in circuit simulation naturally lead to differential–algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index, the more difficult it is to solve the DAE. The modified nodal analysis (MNA) is known to yield a DAE with index at most two in a wide class of nonlinear time‐varying electric circuits. In this paper, we consider a broader class of analysis method called the hybrid analysis. For linear time‐invariant RLC circuits, we prove that the index of the DAE arising from the hybrid analysis is at most one, and give a structural characterization for the index of a DAE in the hybrid analysis. This yields an efficient algorithm for finding an optimal hybrid analysis in which the index of the DAE to be solved attains zero. Finally, for linear time‐invariant electric circuits that may contain dependent sources, we prove that the optimal hybrid analysis by no means results in a higher index DAE than MNA. Copyright © 2008 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.     

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.     

MOS‐integrable circuitry for multi‐scroll chaotic grid realization: A SPICE‐assisted proof

A MOS‐integrable circuit realization of the class of Multi‐Scroll Grid attractor using an implementation of nonlinear transconductor is presented. The design can be seen as the MOS‐integrable circuit implementation of modified jerk equations presented in the literature (Int. J. Bifurcat. Chaos 2002; 12 (1):23–41). The proposed design of Multi‐Scroll Grid attractor is adequately supported by SPICE simulation results. Copyright © 2008 John Wiley & Sons, Ltd.     

On stochastic modelling of linear circuits

In this paper, the deterministic modelling of linear circuits is replaced by stochastic modelling by including variance in the parameters (resistance, inductance and capacitance). Our method is based on results from the theory of stochastic differential equations. This method is general in the following sense. Any electrical circuit that consists of resistances, inductances and capacitances can be modelled by ordinary differential equations, in which the parameters of the differential operators are the functions of circuit elements. The deterministic ordinary differential equation can be converted into a stochastic differential equation by adding noise to the input potential source and to the circuit elements. The noise added in the potential source is assumed to be a white noise and that added in the parameters is assumed to be a correlated process because these parameters change very slowly with time and hence must be modelled as a correlated process. In this paper, we model a series RLC circuit by using the proposed method. The stochastic differential equation that describes the concentration of charge in the capacitor of a series RLC circuit is solved. Numerical simulations in MATLAB are obtained using the Euler–Maruyama method. Copyright © 2008 John Wiley & Sons, Ltd.     

基于多元线性回归的阻性和容性电流分解

为了研究交流电压作用下非线性半导体器件和非线性绝缘电介质的绝缘状态和介电性能,提出一种阻性和容性电流分解算法。以非线性电阻和非线性电容构成的并联等效电路为研究对象,推导响应电流关于激励电压的非线性方程。通过坐标变换,将其转化成多元线性方程。利用多元线性回归方法,获得等效电路参数且实现了阻性和容性电流的分解。定性分析该算法的抗干扰能力和对非标准正弦波电压的适应能力。仿真结果表明:该算法可以准确地实现阻性和容性电流的分解;当响应电流含有55 d B的噪声时,电路参数的求解误差较小;激励电压谐波分量对电路参数的求解几乎没有影响。实验结果表明:该算法可以实现MOA阀片在交流电压作用下全泄露电流的分解。     

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 practical guide to multidimensional wave digital algorithms using an example of fluid dynamics

The wave digital concept for numerical integration of partial differential equations leads to algorithms with highly advantageous features as robustness, full localness and massive parallelism. However, the required synthesis of an internally multidimensionally passive reference circuit, from which the algorithm is derived, usually demands an in‐depth knowledge of circuit theory and a high level of intuition. In this practical guide, a step‐by‐step approach for the synthesis of such reference circuits is introduced to relax these requirements, using the nonlinear fluid dynamic equations as a nontrivial example. General implementation issues for the wave digital algorithm are discussed as well as applying arbitrary passive linear multistep methods in place of the commonly used trapezoidal rule. As an example, we take the well‐known numerically critical shock tube problem, the solution of which is problematic when the trapezoidal rule is used as unwanted oscillations occur. These oscillations are suppressed when using the second‐order accurate Gear method instead. Copyright © 2010 John Wiley & Sons, Ltd.     

A tabular source approach to modelling and simulating device and circuit noise in the time domain

Simulation of device and circuit noise at low frequencies is often carried out as part of a small‐signal ac analysis. Moreover, circuit simulators with rf analysis capabilities usually specify circuit performance in terms of S parameters and model high‐frequency noise in terms of noise waves and correlation matrices. It is also unusual to find circuit simulators that extend noise simulation to the time domain. This is particularly true for software packages developed from SPICE 2g6 or 3f5. This paper introduces a simple tabular noise source technique, which adds time‐domain noise to semiconductor device models and integrated circuit macromodels. The proposed technique is suitable for use with any general purpose circuit simulator. To demonstrate the power of the suggested approach the text describes time‐domain noise extensions to the SPICE diode, BJT, JFET, MOSFET and MESFET models. These noise extensions have been implemented and tested with the ‘Quite universal circuit simulator’ (Qucs). Copyright © 2011 John Wiley & Sons, Ltd.     

Model order reduction of nonlinear circuit equations

In this paper, we present a model order reduction approach for nonlinear circuit equations with a small number of nonlinear elements. This approach is based on the decoupling of linear and nonlinear subcircuits and reducing the linear part using balancing‐related model reduction techniques. The efficiency and applicability of the proposed model reduction approach is demonstrated on numerical examples. Copyright © 2012 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.     

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.     

Time domain solutions to partial differential equations using SPICE

In this paper a method for using a time domain circuit code to solve partial differential equations is described. Rather than following the usual approach of developing a lumped-element circuit model, the partial differential equation is finite differenced in space and written in state variable form. The resulting system of coupled ordinary differential equations is then modeled by an array of coupled voltage dependent current sources connected to a string of capacitors. A preprocessor is used to write the network list in a form usable by the SPICE circuit analysis code. Examples for advection, diffusion, and electromagnetic propagation in one spatial dimension are given     

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.     

Finite element power diode model optimized through experiment‐based parameter extraction

This paper presents a finite element physics‐based power diode model with parameters established through an extraction procedure validated experimentally. The model core is a numerical module that solves the ambipolar diffusion equation through a variational formulation followed by an approximate solution with the finite element method. Other zones of the device are modeled with classical methods in an analytical module. This hybrid approach enables accurate modeling and simulation of power bipolar semiconductor devices, using standard SPICE circuit simulators, with low execution times. As physics‐based models need a significant number of parameters, an automatic parameter extraction method has been developed. The procedure, based on an optimization algorithm (simulated annealing), enables an efficient extraction of parameters using some simple device waveform measurements. Implementation details of power diode model, in IsSpice simulator, are presented. Experimental validation is performed. Results prove the usefulness of the proposed methodology for efficient design of power circuits through simulation. Copyright © 2008 John Wiley & Sons, Ltd.     

An efficient algorithm for finding all DC solutions of piecewise‐linear circuits

An efficient algorithm is proposed for finding all DC solutions of transistor circuits where characteristics of transistors are represented by piecewise‐linear (PWL) convex monotone functions. This algorithm is based on a simple test (termed the linear programming, 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 by surrounding component PWL functions by rectangles. Then the dual simplex method is applied, by which the number of pivotings per region becomes very small. In this letter, we propose a new LP test using the dual simplex method and triangles. The proposed test is not only efficient but also more powerful than the conventional test using the simplex method or rectangles. Copyright © 2008 John Wiley & Sons, Ltd.     

SPICE modeling of nonlinear memristive behavior

The recent discovery of the ‘modern’ memristor has drawn great attention of both academia and industry. Given their favorable performance merits, memristors are expected to play a fundamental role in electronic industry. Modeling of memristive devices is essential for circuit design, and a number of Simulation Program with Integrated Circuit Emphasis (SPICE) models have already been introduced. The common problem in most models is that there is no threshold consideration; hence, only a few address the nonlinear nature of the device. This paper aims to present a SPICE implementation of a threshold‐type switching model of a voltage‐controlled memristive device that attributes the switching effect to a tunneling distance modulation. Threshold‐type switching is closer to the actual behavior of most experimentally realizable memristive systems, and our modeling approach addresses the issue of programming thresholds. Both the netlist and the simple schematic are provided, thus making it easy to comprehend and ready to be used. Compared with other modeling solutions, it involves significantly low‐complexity operation under an unlimited set of frequencies, and its simulation results are in good qualitative and quantitative agreement with the theoretical formulation. The proposed model is used to simulate an antiserial memristive switch, proving that it can be efficiently introduced in complex memristive circuits. Copyright © 2013 John Wiley & Sons, Ltd.     

Second order mem‐circuits

This paper presents a comprehensive taxonomy of so‐called second‐order memory devices, which include charge‐controlled memcapacitors and flux‐controlled meminductors, among other novel circuit elements. These devices, which are classified according to their differential and state orders, are necessary to get a complete extension of the family of classical nonlinear circuit elements (resistors, capacitors, and inductors) for all possible controlling variables. Using a fully nonlinear formalism, we obtain nondegeneracy conditions for a broad class of second‐order mem‐circuits. This class of circuits is expected to yield a rich dynamic behavior; in this regard, we explore certain bifurcation phenomena exhibited by a family of circuits including a charge‐controlled memcapacitor and a flux‐controlled meminductor, providing some directions for future research. Copyright © 2014 John Wiley & Sons, Ltd.