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

Scattering analysis of signal degradation and interferences on long and lossy interconnects

A time domain scattering formulation for low-loss nonlinearly loaded multiconductor transmission lines is presented. It is suitable for an efficient and accurate evaluation of crosstalk and field coupling. A simulation of the effects of interference on a long interconnect is give

Time-domain parametric sensitivity analysis of multiconductor transmission lines

We present a new parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs). This technique can handle design parameters, such as substrate or geometrical layout features, and provide time-domain sensitivity information for voltage and currents at the ports of the lines. It is based on a recently introduced spectral approach for the analysis of lossy and dispersive MTLs [1], [2] and it is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels which provide sensitivity information are well suited for design space exploration, design optimization and crosstalk analysis. A numerical example validates the proposed approach in both frequency and time domain

Parametric macromodeling of lossy and dispersive multiconductor transmission lines

We propose an innovative parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs) that can be used for interconnect modeling. It is based on a recently developed method for the analysis of lossy and dispersive MTLs extended by using the multivariate orthonormal vector fitting (MOVF) technique to build parametric macromodels in a rational form. They take into account design parameters, such as geometrical layout or substrate features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to perform design space exploration, design optimization, and sensitivity analysis efficiently. Numerical examples validate the proposed approach in both frequency and time domain

Time-domain green's function-based parametric sensitivity analysis of multiconductor transmission lines

We present a new parametric macromodeling technique for lossy and dispersive multiconductor transmission lines. This technique can handle multiple design parameters, such as substrate or geometrical layout features, and provide time-domain sensitivity information for voltages and currents at the ports of the lines. It is derived from the dyadic Green's function of the 1-D wave propagation problem. The rational nature of the Green's function permits the generation of a time-domain macromodel for the computation of transient voltage and current sensitivities with respect to both electrical and physical parameters, completely avoiding similarity transformation, and it is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels that provide sensitivity information are well suited for design space exploration, design optimization, and crosstalk analysis. Two numerical examples validate the proposed approach in both frequency and time-domain

Adaptive transient solution of nonuniform multiconductor transmission lines using wavelets

Abstract—This paper presents a highly adaptive algorithm for the transient simulation of nonuniform interconnects loaded with arbitrary nonlinear and dynamic terminations. The discretization of the governing equations is obtained through a weak formula-tion using biorthogonal wavelet bases as trial and test functions. It is shown how the multiresolution properties of wavelets lead to very sparse approximations of the voltages and currents in typical transient analyzes. A simple yet effective time–space adaptive al-gorithm capable of selecting the minimal number of unknowns at each time iteration is described. Numerical results show the high degree of adaptivity of the proposed scheme. Index Terms—Electromagnetic (EM) transient analysis, multi-conductor transmission lines (TLs), wavelet transforms. I

Measuring line parameters of multiconductor cables using a vector impedance meter

In the present paper, a method to measure the parameters of a multiconductor transmission line is given. The method is accurate, straightforward and only needs a single vector impedance meter or equivalent. The method has been applied for frequencies in a range from 20 kHz up to 30 MHz

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