Wavelet-Based High-Order Adaptive Modeling of Lossy Interconnects

Abstract—This paper presents a numerical-modeling strategy for simulation of fast transients in lossy electrical interconnects. The proposed algorithm makes use of wavelet representations of voltages and currents along the structure, with the aim of reducing the computational complexity of standard time-domain solvers. A special weak procedure for the implementation of possibly dynamic and nonlinear boundary conditions allows to preserve stability as well as a high approximation order, thus leading to very accurate schemes. On the other hand, the wavelet expansion allows the computation of the solution by using few significant coefficients which are automatically determined at each time step. A dynamically refinable mesh is then used to perform a sparse time-stepping. Several numerical results illustrate the high efficiency of the proposed algorithm, which has been tuned and optimized for best performance in fast digital applications typically found on modern PCB structures. Index Terms—Finite difference methods, time-domain analysis, transmission lines, wavelet transforms. I

Wavelet-Based Adaptive Solution for the Nonuniform Multiconductor Transmission Lines

Abstract—A time-domain technique for the solution of arbi-trary nonuniform multiconductor transmission lines (NMTL’s) is presented. The technique is based on a weak formulation of the NMTL equations obtained through spatial expansion of the voltage and current vectors into biorthogonal wavelet func-tions. Wavelets allow adaptive representations of the solution by using few expansion coefficients, with any fixed approximation order. The set of significant expansion coefficients is determined automatically from the solution, which can be computed very efficiently. A numerical example illustrates the high adaptivity of the method. Index Terms—Distributed parameter circuits, multiconductor transmission lines, time domain analysis, wavelet transforms. I

A fractal model for the lightning induced current on a transmission line

This article presents a model of a tortuous lightning channel, and a study of the consequent electromagnetic coupling to a transmission line. We analyse the fractal dimension of the induced current on the line, compared with the fractal dimension of the lightning channel and the impinging electromagnetic field on the line. This comparison confirms our previous studies pointing out that the channel fractal dimension and the electromagnetic field fractal dimension are related (in particular, for typical lightning parameters they are the same). A comparison of simulated fields and line currents with experimental measurements is also attempte

Susceptibility analysis of complex systems

A study of electromagnetic coupling effects on systems containing distributed elements and lumped linear components is presented. The structure is decomposed into sections containing multiconductor transmission lines and interconnection blocks holding lumped elements. The external field is assumed to interfere with line sections, but mutual influences among different sections are neglected. Both the sections and the blocks are treated as multiport components and characterized by their scattering parameters. The analysis is based on a correspondence matrix that accounts for the topology of connections between sections and blocks. Closed-form solutions are derived in the Laplace domain, and the temporal evolution of voltages and currents at any of the system ports is obtained by a numerical inversion. This method makes it possible to predict the susceptibility of complex systems and to verify the intra-system compatibility (especially crosstalk). The relative influence of circuit components and of line layouts on the severity of interferences is evidenced by simulation result