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In this paper, the asymptotic waveform evaluation (AWE) technique is first applied to the conventional eigenmode expansion method for characterizing a power/ground (P/G) plane pair and analyzing the simultaneous switching noise on such plane pairs for printed circuit boards or multichip modules. The application of AWE avoids a large number of iterations in computing the impedance frequency response of a P/G plane pair structure and greatly reduces the computation time. Meanwhile, to obtain an accurate solution in an entire frequency range, we employ the complex frequency hopping technique which can help select multiple expansion points. In addition, the proposed approach can also be used to characterize the P/G plane pair structures with irregular shapes. Three examples demonstrate its high efficiency and good accuracy. Index Terms--Asymptotic waveform evaluation, complex frequency hopping, eigenmode expansion method, power/ground plane pair, simultaneous switching noise.

The eigenmode expansion method (EEM) is a convenient technique for characterizing a power/ground (P/G) plane pair structure. The requirements of the plane pair's shape, however, and a double-infinite series in its equation limit its applications. To overcome its disadvantages and extend its applications, this paper proposes some techniques for the EEM and makes some modifications to it. First, by employing the newly presented inverted composition method and the segmentation method, the improved EEM can be used to characterize a holey P/G plane pair with irregular shapes. Second, by employing a trigonometric Fourier series and a particular Pade approximation method--the [eta]/-algorithm, the double-infinite series in EEM can be changed into a single one and its convergence can be accelerated apparently so that the computation efficiency of the EEM is greatly improved. An example is considered to compare the numerical data of the new EEM with corresponding measurement results, thus demonstrating the good accuracy. The computation time of the proposed method is compared with that of the finite-element method (FEM), which shows that the new method has higher efficiency. Index Terms--Convergence acceleration, eigenmode expansion method (EEM), inverted composition method, segmentation method, simultaneous switching noise (SSN).

A time-domain full-wave method for the extraction of frequency-dependent equivalent circuit parameters of multi-conductor interconnection lines is presented in 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. Because the definitions of the voltage and the current are not unique in full-wave analysis, transformation among circuit parameters according to different 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.

A new method for computing the capacitance matrix of multiconductor interconnects with finite metallization thickness is developed. Converting the vertical wall of the rectangular conductors into the equivalent horizontal strips allows the Green's function in the spectral domain and the FFT algorithm to be used, which makes the method more effective for computing capacitance matrix of the interconnects.

In this paper, the modified method of characteristics (MMC) is presented to analyze lossy interconnects. This 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-do-main 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. Index Terms--Lossy interconnects, macromodel, modified method of characteristics, recursive formulae, transient analysis.

In this paper, a new model of lossy transmission lines is presented for the time-domain simulation of high-speed interconnects. This model is based on the modified method of characteristics (MMC). The characteristic functions are first approximated by applying lower order Taylor series in the frequency domain, and then a set of simple recursive formulas are obtained in the time domain. The formulas, which involve tracking performance between two ends of a transmission line, are similar to those derived by the method of characteristics for lossless and undistorted lossy transmission lines. The algorithm, based on the proposed MMC model, can efficiently evaluate transient responses of high-speed interconnects. It only uses the quantities at two ends of the lines, requiring less computation time and less memory space than required by other methods. Examples indicate that the new method is having high accuracy and is very efficient for the time-domain simulation of interconnects in high-speed integrated circuits. Index Terms--Interconnects, modeling, modified method of characteristics, recursive calculation, transient simulation, transmission line.

In this paper, a modified partial-element equivalent-circuit (PEEC) model, i.e., ([L.sub.p], A, R, [[element of].sub.f])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 ([L.sub.p], P, R, [[element of].sub.f]) PEEC model, the definition of vector potential A with integral form and the Lorentz gauge are used in expanding the basic integral equation instead of the definition of the scalar potential [psi] 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 A, which is analytical. 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. Index Terms--Integrated circuit, interconnect and packaging, Lorentz gauge, PEEC, state equations.

An efficient expression of the effective permittivities along x -, y -, z -direction is obtained by analogy with the circuit concept of series–parallel connection of capacitance. Under the condition of numerical stability, the approximate formulae of effective permittivities for various inhomogeneous cell mesh are combined with the Finite Difference Time Domain (FDTD) scheme of arbitrary spatial cell size to calculate resonant frequency of 3-D cavity. The results are in agreement with that of conventional FDTD method, but the proposed method can save computing time and memory. [ABSTRACT FROM AUTHOR]