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.     

A delta‐method technique in the wavelet domain to determine statistical quantities of the response of electromagnetic devices with uncertain parameters

In this paper a method to determine the mean value and the variance of the response of a system with uncertain parameters is proposed. With the term ‘response of a system’ we indicate either the value of a single parameter that represents a figure of merit of a device (e.g. the efficiency of a transmission system or the band width of a communication channel) or a characteristic function of the system (e.g. the impulse or the frequency response). In the latter case we estimate the mean value and the variance at every sample of the response. The estimate is performed by using the delta method, a technique for approximating expected values of functions of random variables when the direct evaluation is not feasible. Two examples of the application of the proposed procedure are reported and the results are compared with simulations performed by a Monte Carlo analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Application of Filippov method for the analysis of subharmonic instability in dc–dc converters

We propose a method of estimating the fast‐scale stability margin of dc–dc converters based on Filippov's theory—originally developed for mechanical systems with impacts and stick‐slip motion. In this method one calculates the state transition matrix over a complete clock cycle, and the eigenvalues of this matrix indicate the stability margin. Important components of this matrix are the state transition matrices across the switching events, called saltation matrices. We applied this method to estimate the stability margins of a few commonly used converter and control schemes. Finally, we show that the form of the saltation matrix suggests new control strategies to increase the stability margin, which we experimentally demonstrate using a voltage‐mode‐controlled buck converter. Copyright © 2008 John Wiley & Sons, Ltd.     

On the asymptotic behavior of the Durbin–Watson statistic for ARX processes in adaptive tracking

A wide literature is available on the asymptotic behavior of the Durbin–Watson statistic for autoregressive models. However, it is impossible to find results on the Durbin–Watson statistic for autoregressive models with adaptive control. Our purpose is to fill the gap by establishing the asymptotic behavior of the Durbin–Watson statistic for ARX models in adaptive tracking. On the one hand, we show the almost sure convergence as well as the asymptotic normality of the least squares estimators of the unknown parameters of the ARX models. On the other hand, we establish the almost sure convergence of the Durbin–Watson statistic and its asymptotic normality. Finally, we propose a bilateral statistical test for residual autocorrelation in adaptive tracking. Copyright © 2013 John Wiley & Sons, Ltd.     

An improvement in the calculation of the magnetic field for an arbitrary geometry coil with rectangular cross section

Hong Lei, Lian‐Ze Wang and Zi‐Niu Wu presented new simple and convenient solutions of the magnetic field for an arbitrary geometry coil with rectangular cross section. They treated two types of basic forms: the trapezoidal prism segment and curved prism segment. The curved prism segment has been divided into a series of small trapezoidal prism segments with the same cross section and its magnetic field is a vector sum of the individual fields created by each small trapezoidal prism conductor. For one trapezoidal prism conductor the magnetic field is obtained by 1‐D integrals using Romberg numerical integration. In this paper, we give a completely analytical solution of these 1‐D integrals that considerably saves the computational time especially in the computation of the magnetic field nearby the conductor surface, at the conductor surface and inside the conductor. From obtained analytical expressions the treatment of singularities can be easily done. Also, we tested four types of numerical integration (Gaussian, Romberg, Simpson and Lobatto) to find the most convenient singularity treatment of 1‐D integrals. These obtained results are compared with those obtained analytically so that one can understand the advantage of the proposed approach. The paper points out on the accuracy and the computational cost. Copyright © 2005 John Wiley & Sons, Ltd.