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.     

Tree‐based characterization of low index circuit configurations without passivity restrictions

The present paper addresses index characterizations in differential‐algebraic models of electrical circuits without the need for passivity assumptions. Positive definiteness conditions on the conductance, capacitance and inductance matrices are replaced by certain algebraic assumptions on the so‐called proper trees for augmented node analysis and normal trees for modified node analysis. The current discussion is restricted to index‐0 and index‐1 systems; for the latter, the analysis is based upon certain matrix factorizations which split the topological information from the electrical features of the devices. Several examples illustrate the scope of our framework. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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.     

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 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.     

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.     

Graph‐theoretical approach to 2‐switch DC–DC converters

This paper presents a graph‐theoretic approach to analyse and synthesize switch mode DC–DC converters. The result is based on the state‐space averaging equation and the fundamental graph theory. Hence our proposed method is applied to various kinds of DC–DC converters with two switches and topological conditions for two‐switch DC–DC converters are obtained systematically. Copyright © 2005 John Wiley & Sons, Ltd.     

Non‐linear adaptive control of a heat exchanger

In this contribution, two methods for adaptation of non‐linear adaptive controllers are presented and compared, namely the data‐driven and the knowledge‐based adaptation. A dynamic Takagi–Sugeno fuzzy model is utilized to model the non‐linear process behaviour. Based on this model, a non‐linear predictive controller is designed to control the process. In the presence of time‐variant process behaviour and changing unmodelled disturbances, high control performance can be achieved by performing an on‐line adaptation of the fuzzy model. First, a local weighted recursive least‐squares algorithm is used for adaptation. It exploits the local linearity of the Takagi–Sugeno fuzzy model. In the second approach, process knowledge that is obtained from theoretical insights is utilized to design a knowledge‐based adaptation strategy. Both approaches are compared and their effectiveness and real‐world applicability are demonstrated by application to temperature control of a heat exchanger. Copyright © 2001 John Wiley & Sons, Ltd.     

Electromagnetic analysis coupled with motion for high‐speed circuit breakers of eddy current repulsion using the tableau approach

Electromagnetic field analysis coupled with motion using the tableau approach has been applied to high‐speed circuit breakers of eddy current repulsion mechanisms. This breaker has an opening time of 1 ms and break time less than 1 cycle (20 ms). The driving part of the breaker is composed of electromagnetic repulsion mechanisms and disk springs with nonlinear characteristics. The mechanisms are composed of two fixed coils and one repulsion plate. A numeric experiment has been applied to investigate the dynamic behavior of the electromagnetic repulsion mechanism using the equivalent circuit method. Calculation results were in good agreement with both measurement results and calculation results by FEM on an experimental model. In addition, repulsive forces depending on material conductivities have been researched. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 152(4): 8–16, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20149     

Higher‐order CN‐FETD method for analysis of microwave circuit structures

In this paper, the hierarchical high‐order basis functions on tetrahedrons are introduced to the Crank–Nicolson (CN) finite‐element time‐domain (FETD) with the 3D Maxwell equations for analysis of the microwave circuit structures. Whitney 1‐form high‐order hierarchical basis functions are used to expand the electric field and Whitney 2‐form high‐order hierarchical basis functions for the magnetic field. The CN scheme is employed in the FETD method to lead to an unconditionally stable algorithm. Numerical results were presented to demonstrate the accuracy and efficiency of the proposed high‐order CN‐FETD method. Copyright © 2012 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.     

Global unique solvability for memristive circuit DAEs of Index 1

Known solvability results for nonlinear index‐1 differential‐algebraic equations (DAEs) are in general local and rely on the Implicit Function Theorem. In this paper, we derive a global result which guarantees unique solvability on a given time interval for a certain class of index‐1 DAEs with certain monotonicity conditions. Based on this result, we show that memristive circuit DAEs arising from the modified nodal analysis are uniquely solvable if they fulfill certain passivity and network topological conditions. Furthermore we present an error estimation for the solution with respect to perturbations on the right‐hand side and in the initial value. Copyright © 2013 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.     

Kronig–Penney model simulation with equivalent circuit method

The Kronig–Penney model is quite useful for illustrating many important features of the quantum behaviour of electrons in periodic lattice. Although the Kronig–Penney model is well‐known and has been discussed in solid state textbooks, we try to use a simple and accessible way without the extremely laborious and tedious algebra evaluation to solve Kronig–Penney model. This paper presents a simple method without solving the difficult eigen‐problem to solve the Kronig–Penney model, and the important energy band characteristics can be easily obtained with circuit concepts. The simulation results are presented to demonstrate the accuracy and superiority of the model. Copyright © 2006 John Wiley & Sons, Ltd.     

Semistate models of electrical circuits including memristors

In this paper we present several semistate or differential‐algebraic models arising in nodal analysis of nonlinear circuits including memristors. The goal is to characterize the tractability index of these models under strict passivity assumptions, a key issue for the numerical simulation of circuit dynamics. We show that the main model, which combines memristors' fluxes and charges, is index two. From a technical point of view, this result is based on the use of a projector along the image of the leading matrix, in contrast to previous index analyses. For charge‐controlled memristors, the elimination of fluxes yields an index one system in topologically nondegenerate circuits, and an index two model otherwise. Analogous results are also proved to hold for flux‐controlled memristors. Our framework accommodates coupling effects among resistors, memristors, capacitors and inductors. Copyright © 2010 John Wiley & Sons, Ltd.     

A simple and accurate dynamical modeling of quantum‐dot semiconductor optical amplifiers

In this article, quantum‐dot semiconductor optical amplifiers (QD‐SOAs) have been modelled using state space method. To derive this model, we have manipulated the rate equation model of the QD‐SOA, where the average values of the occupation probabilities along the QD‐SOA cavity are considered as the state variables of the system. Using these variables, the distance dependence of the rate equations is eliminated. The derived state space model gives the optical gain and output signal of the amplifier with a high accuracy. Simulation results show that the derived model is not only much simpler and faster than conventional rate equation models, but also the optical gain and output signal of the investigated QD‐SOA are calculated with a higher precision compared to the rate equation model. Copyright © 2013 John Wiley & Sons, Ltd.     

Design and analysis of power‐CMOS‐gate‐based switched‐capacitor DC–DC converter with step‐down and step‐up modes

A unified multi‐stage power‐CMOS‐transmission‐gate‐based quasi‐switched‐capacitor (QSC) DC–DC converter is proposed to integrate both step‐down and step‐up modes all in one circuit configuration for low‐power applications. In this paper, by using power‐CMOS‐transmission‐gate as a bi‐directional switch, the various topologies for step‐down and step‐up modes can be integrated in the same circuit configuration, and the configuration does not require any inductive elements, so the IC fabrication is promising for realization. In addition, both large‐signal state‐space equation and small‐signal transfer function are derived by state‐space averaging technique, and expressed all in one unified formulation for both modes. Based on the unified model, it is all presented for control design and theoretical analysis, including steady‐state output and power, power efficiency, maximum voltage conversion ratio, maximum power efficiency, maximum output power, output voltage ripple percentage, capacitance selection, closed‐loop control and stability, etc. Finally, a multi‐stage QSC DC–DC converter with step‐down and step‐up modes is made in circuit layout by PSPICE tool, and some topics are discussed, including (1) voltage conversion, output ripple percentage, and power efficiency, (2) output robustness against source noises and (3) regulation capability of converter with loading variation. The simulated results are illustrated to show the efficacy of the unified configuration proposed. Copyright © 2003 John Wiley & Sons, Ltd.     

Enhancement of steady‐state visual evoked potential‐based brain–computer interface systems via a steady‐state motion visual stimulus modality

Steady‐state visual evoked potential (SSVEP)‐based brain–computer interface (BCI) systems are among the most accurate assistive devices for patients with severe disabilities. However, existing visual stimulation patterns lead to eye fatigue, which affects the system performance. Therefore, in this study, we propose two improvements to SSVEP‐based BCI systems. First, we propose a novel visual stimulator that incorporates a visual motion stimulus for the steady‐state visual stimulus to reduce eye fatigue while maintaining the advantages associated with SSVEPs. We also propose two corresponding feature extraction algorithms, i.e. SSVEP detection and visual attention detection, to capture the phenomena of steady‐state motion visual stimulus responses. The accuracy of the test was ∼83.6%. Second, we propose a novel hybrid BCI‐SSVEP system and a motion visual stimulus hybrid BCI system to enhance the SSVEP‐based BCI system during a state of eye fatigue. Participants used the SSVEP system until reaching a fatigued state and then began using a hybrid motion visual stimulus. The accuracy of the proposed system was ∼85.6%. The proposed improvements can be incorporated into practical BCI systems for wheelchair control. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.