A novel method for analyzing the bounces on structure of parallel power/ground planes by using the even-odd mode partition is presented in this paper. Based on the distributed RLCG circuit model derived from the two dimensional electromagnetic field equations of the power/ground planar structure, this method can speed up the circuit simulation of the bounces on power/ground planes by using even-odd mode partition. Furthermore, the method can be used to evaluate the effects of the terminated decoupling capacitors and the hole structures on power/ground plane. The numerical examples demonstrate that the method has both high efficiency and good precision.

In this paper, we present some numerical techniques for the time-domain characterization of on-chip interconnects near semiconductor substrate in high-speed very large scale integrated circuits. A time-domain full-wave method for the extraction of frequency-dependent equivalent circuit parameters of these lines is described firstly. Then the method, based on numerical inversion of Laplace transform, is used for the transient simulation of interconnection lines with frequency-dependent parameters. The frequency-dependent effects over a very broad range of frequencies are included in the analysis. A numerical example for realistic geometry and material parameters demonstrates the effects of lossy substrate on the signal propagation, including delay, waveform distortion and crosstalk.

In this paper, the modified method of characteristics (MMC) is presented to analyze lossy interconnects. The method applies lower order Taylor approximation to model the characteristic admittance, and further applies lower order Pade approximation to model propagation functions of a transmission line. However, different from the single-point or multipoint moment-matching approaches, this method does not generate reduced-order model of a transmission line prior to constructing the system matrix. Instead, it takes a special expansion and directly incorporates the coefficients of expansion into the modified nodal admittance (MNA) matrix. On the basis of the specific expansion, a set of time-domain recursive formulae is derived, which concerns only the quantities at the ends of transmission lines. The recursive formulae are similar to those of method of characteristics (MC), with some added modifications. Based on the formulae of MMC, an equivalent time-domain macromodel of uniform lossy transmission line is obtained. It can be easily implemented within the framework of an existing circuit simulator such as SPICE. The examples indicate that the method gives accurate time-domain simulation of interconnects in high-speed IC systems.

In this paper, a modified partial-element equivalent-circuit (PEEC) model, i.e., (Lp, A, R, Ef)PEEC, is introduced. In such a model, no equivalent circuit, but a set of state equations for the variables representing the function of circuit, are given to model a three-dimensional structure. Unlike the original (Lp, A, R, Ef)PEEC model, the definition of vector potential with integral form and the Lorentz gauge are used in expanding the basic integral equation instead of the definition of the scalar potential with integral form. This can directly lead to the state equations, and the capacitance extraction can be replaced by the calculation of the divergence of, which is nalytical. For analysis of most interconnect and packaging problems, generally containing complex dielectric structures, the new model can save a large part of computing time. The validity of the new model is verified by the analysis in time and frequency domain with several examples of typical interconnect and packaging structures, and the results with this new method agree well with those of other papers.

The comutation of the equivalent capacitances for three-dimensional (3-D) interconnects features large memory usage and long computing time. In this paper, a matrix sparsifica-tion approach based on multiresolution representation is applied with the method of moments (MoM) to calculate 3-D capacitances of interconects in a layered media. Instead of direct expansion of the charge distribution by the orthogonal wavelet basis functions, the lare full matrix resulting from discretization of the integral equations is taken as a discrete image and sparsified by two-imensional(2-D) multiresolution representations. The inverse of the obtained sparse matrix is efficiently implemented by Schultz's iterative apprach. Several numerical examples are given and the results obtained show that the proposed method significantly sparsify the matrix equation and the capacitance parameters computed by the matrix equation and the capacitance parameters computed by the matrix equation with high sparsity agree well with the results of other reports and those computed by an established capcitance extractor FASTCAP.