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.

Measured equation of invariance (MEI) has been successfully used in many applications. It has been illustrated that the MEI is specially suitable for the decrease of computation time and computer memory space. However, for multiconduc-tor interconnects in multilayered dielectric media, the Green's function is complex and the integrals of Sommerfeld type are time consuming. In this paper, equivalent source and mea-sured equation of invariance (ES-MEI), a modification of the MEI, The node number is further decreased and the integrals of metron multiplied Green's function are avoided. It will be verified by several examples that the ES-MEI is very suitable for fast parameter extraction for mlticonductor interconnects in multilayered dielectric media.

A time-domain full-wave method for the extraction of frequency-dependent equivalent cireuit parameters of multi-conductor interconnection lines is presented in this paper. The circuit parameters extracted by this paper. The circuit parameters extracted by this method can be inserted into circuit simulation software to investigate time-domain responses of high-speed IC system with multiconductor interconnects. Be-cause the definitions of the voltage and the current are not unique in full-wave analysis, transformation among circuit parameters according to diffrent definitions of the voltage and current is also presented. The method is based on the finite-difference time-domain (FDTD) method, and the reliability of this method is illustrated by its application to representative problems.

In this paper nonuniform multiconductor trans-mission lines are considered to be equivalent to a cascaded chain of many multiport subnetworks which are made of short sec-tions of uniform lines. The ABCD matrices of the subnetworks can be obtained by the matrix series expansions of their ana-lytic expressions. As long as the number of the subnetworks is large enough to reflect the line nonuniformity fully, the expan-sions will converge so fast that a few of low-order series terms will be good approximations. After the overall ABCD matrix of the cascaded network chain is evaluated from that of each sub-network, the time of response of transmission lines can be ana-lyzed. The lines may have frequency-dependent parameters and arbitrary nonlinear terminals. Furthermore, transmission sys-tems with branches uniform and nonuniform transmission lines can be studied with this method conveniently. The analysis ac-curacy and efficiency are discussed in detail.

A new method for analysis of the time response of multiconductor transmission lines with frequency-dependent losses is presented. This method can solve the time response of various kinds of transmission lines with arbitrary terminal net-works. Particularly it can analyze nonuniform lines with fre-quency-dependent losses, for which there is no existing effective method to analyze their time response so far. This method starts from the frequency-domain telegrapher's equations. After de-coupling and inversely Fourier transforming, then a set of de-coupled time-domain equations including convolutions are given. These equations can be solved with the characteristic method. The results obtained with this method are stable and accurate. Two examples are given to illustrate the application of this method to various multiconductor transmission lines.