Efficient computation of high-frequency two-dimensional effects inmulticonductor printed interconnects

The spectral domain technique with a Galerkin moment method solution is used to study high-frequency, two-dimensional effects such as dispersion and leakage in multiconductor printed interconnects. A simple asymptotic procedure is used to significantly improve the convergence of oscillatory spectral integrals involving distant expansion and testing functions. Examples are given for leaky waves on two multiconductor printed transmission line geometries     

A simple technique for calculating the propagation dispersion ofmulticonductor transmission lines in multilayer dielectric media

A multiconductor transmission line in a multilayer dielectric medium is complicated and therefore is frequently analyzed by the simple quasi-TEM (transverse electromagnetic) approach. Unlike the full wave eigenvalue approach, the quasi-TEM approach does not give the propagation dispersion characteristics of the line. This work overcomes this problem by first obtaining the solution of each multiconductor mode from the quasi-TEM approach. Then these solutions are used as both basis and testing functions in a variational formulation of the full wave eigenvalue analysis. The result is high accuracy in the dispersive propagation constants of the multiconductor modes. By solving only for high frequency eigenvalues, not for the high frequency eigenvectors, the method is simpler and faster than the conventional full wave dispersion analyses     

Fast EMI Analysis via Transverse Partitioning and Waveform Relaxation

High-speed interconnects are increasingly becoming susceptible to electromagnetic interference (EMI). Hence, there is a growing need for fast simulation of interconnect lines in the presence of incident field coupling using circuit simulators such as SPICE. However, the presence of a large number of coupled lines in modern interconnect structures is a serious limiting factor in these simulations. In order to simultaneously address these difficulties, a new algorithm is presented in this paper for EMI analysis of large number of coupled interconnects. The new method exploits the recently developed waveform relaxation (WR) and transverse partitioning algorithms for fast EMI analysis. The same WR sources that are computed for multiconductor transmission line analysis are also employed for EMI analysis. The computational complexity of the proposed EMI analysis grows only linearly with the number of lines. In addition, the algorithm lends itself to parallel implementation leading to further reduction in CPU time.      

Lightning-induced effects on lossy MTL terminated on arbitraryloads: a wavelet approach

Lightning-induced electromagnetic effects propagating on multiconductor transmission-line (MTL) structures are a severe threat for many electronic devices. The solution of uniform MTL equations with frequency-dependent losses and nonlinear loads is proposed in the wavelet domain. Some remarkable features of the wavelets are presented and applied in order to speed up the solution time of the induced effects and to open possibilities to use them for signal integrity analysis. Validation of the obtained results with others given by well-established numerical techniques is also presented     

Physically consistent transmission line models for high-speed interconnects in lossy dielectrics

The development of a physically consistent multiconductor transmission line model for high-speed interconnects in lossy, dispersive dielectrics is presented. Based on this model, a methodology is presented which constructs SPICE-compatible equivalent circuits that take into account dielectric loss and dispersion. Simulations using wideband measurement data of alumina demonstrate the effect of the Debye based permittivity model.     

多芯片组件带网孔接地板多导体互连线结构的电磁特性分析

本文给出一基于准静态场的直线法,来分析多芯片组件（ＭＣＭ）带有网孔接地板的多层多导体互连线结构的分析方法,以此提取等效传输线的特性参数。最后给出几个实例的计算结果。     

外部电磁场对屏蔽多导体电缆系统耦合影响的分析

本文给出了一个有效的、用以分析外部电磁场对屏蔽多导体电缆系统电耦合影响的方法，适用于电缆的频域或时域电磁兼容分析。     

Efficient quasi-TEM frequency-dependent analysis of lossy multiconductor lines through a fast reduced-order FEM model

An efficient finite-element reduced-order quasi-TEM model for the frequency-dependent characteristics of lossy multiconductor transmission lines is presented. Conductor losses are evaluated as functions of frequency through a magneto-quasi-static model. Numerically generated problem-matched basis functions reduce the problem size and, therefore, the CPU time required by frequency sweeps without appreciable loss of accuracy. The proposed approach is applied to complex coplanar waveguides and to multiconductor interconnects; its results are compared with quasi-analytical techniques and with the full-wave finite-element method.     

On the frequency-dependent line admittance of VLSI interconnect lines on silicon-based semiconductor substrates

In this paper, a method for analysis and modelling of transmission interconnect lines with zero- or non-zero thickness on Si–SiO₂ substrate is presented. The analysis is based on semi-analytical expressions for the frequency-dependent transmission line admittances. The electromagnetic concept of free charge density is applied. It allows us to obtain integral equations between electric scalar potential and charge density distributions. These equations are solved by the Galerkin procedure of the method of moments. This new model represents narrow and thick line interconnect behaviour over a wide range of frequencies up to 20 GHz. The accuracy of the developed method in this work is validated by comparing with the rigorous simulation data obtained by full-wave electromagnetic solver and CAD-oriented equivalent-circuit modelling approach. The response of the proposed model is shown to be in good agreement with the frequency-dependent capacitance and conductance characteristics of general coupled multiconductor on-chip interconnects.     

Analysis of crosstalk and field coupling to lossy MTLs in a SPICEenvironment

This paper proposes a circuit model for lossy multiconductor transmission lines (MTLs) suitable for implementation in modern SPICE simulators, as well as in any simulator supporting differential operators. The model includes the effects of a uniform or nonuniform disturbing field illuminating the line and is especially devised for the transient simulation of electrically long wideband interconnects with frequency dependent per-unit-length parameters. The MTL is characterized by its transient matched scattering responses, which are computed including both dc and skin losses by means of a specific algorithm for the inversion of the Laplace transform. The line characteristics are then represented in terms of differential operators and ideal delays to improve the numerical efficiency and to simplify the coding of the model in existing simulators. The model can be successfully applied to many kinds of interconnects ranging from micrometric high-resistivity metallizations to low-loss PCBs and cables, and can be considered a practical extension of the widely appreciated lossless MTL SPICE model, which maintains the simplicity and efficiency     

A time-domain full-wave extraction method of frequency-dependentequivalent circuit parameters of multiconductor interconnection lines

A time-domain full-wave method for the extraction of frequency-dependent equivalent circuit parameters of multiconductor 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 a 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 circuit model of a system of VLSI interconnects for time responsecomputation

A novel computational model based on the spectral-domain approach for the characterization of a dispersive multiconductor system is developed for time response computation. The model consists of two identical impedance networks and equivalent voltage-controlled voltage sources, and it is particularly suitable for timing analysis. Since the model is constructed based on full-wave analysis, the hybrid nature of the VLSI interconnects is taken care of, and thus the model is valid at high frequencies when the longitudinal field components are no longer negligible. Signal distortions due to the dispersive nature of a multiconductor system are demonstrated by an example     

一种提取多导体互连线等效电路频变分布参数的时域全波方法

本文给出了一种基于时域有限差分（ＦＤＴＤ）法，提取多导体互连线等效电路频变分布参数的时域全波方法．提取出的频率分布参数可用来研究含有多种导体互连线的高速集成电路（ＶＬＳＩ）系统的时域响应．由于在全波分析中电压和电流没有唯一的定义，本文还给出了基于不同电压、电流定义而得到的电路参数之间的转换关系．计算结果表明：这种方法是可靠的．     

Capacitance extraction for electrostatic multiconductor problems byon-surface MEI

In this paper, on-surface measured equation of invariance (OSMEI) method is implemented for capacitance extraction of electrostatic multiconductor interconnect problems. OSMEI uses the same mesh as that in method of moments (MoM), but generates highly sparse matrices rather than a full matrix. In comparison with “standard” MEI which contains a few finite difference (FD) or finite element (FE) mesh layers, the number of unknowns and the computation memory can be saved. For each OSMEI equation in the multiconductor interconnects, a given node on a given conductor is forced into coupling with the few adjacent nodes on conductor itself and the few sampled nodes on other conductors. Thus, the system sparse matrices can be generated. The convergent behavior of the capacitance with the number of the nodes in the OSMEI equations has been widely investigated, Numerical examples of the capacitance extraction for two-dimensional (2-D) and three-dimensional (3-D) multiconductor interconnects show that the computing errors are within 24%. The OSMEI method may become a powerful technique for the more complex interconnect problems     

Analysis of Integrated Circuit System s by An Innovative Wavelet-Based Scattering Matrix Approach

This paper proposes the use of scattering parameters (S-parameters) in the wavelet domain for the analysis of coupled multiconductor transmission lines, high-speed integrated circuits, and interconnects. S-parameters-based computing techniques are widely used in the analysis of networks characterized by a large number of integrated devices and interconnects. The theoretical and practical definition of the wavelet-based S matrix is shown, and then some numerical examples of its use and potential in the analysis of systems with linear and nonlinear terminations is shown and compared with other numerical techniques. The computational costs and the memory requirements of the wavelet representation of scattering matrix are also addressed     

Modeling of magnetic-field coupling with cable bundle harnesses

A field-to-line coupling model is developed for cable bundle harnesses in terms of the scattering currents and total line voltages. The equivalent distributed sources representing the effects of electromagnetic coupling are expressed as a function of the incident magnetic-field components. Such a formulation is particularly suitable to be used for the analysis of multiconductor transmission lines excited by a transient field, when data for the incident electric field are either inaccurate or not available. This model allows the accurate calculation of the induced voltages and currents on complex cable bundles. The effects on the induced voltages and currents due to ground losses and to the presence of the dielectric sheath in shielded and unshielded cables is discussed, considering bundles excited by either slow or fast transient fields. Numerical applications demonstrate the validity of the proposed procedure.     

Dispersion analysis of the shielded Sievenpiper structure using multiconductor transmission-line theory

Dispersion curves for the shielded Sievenpiper "mushroom" structure are obtained by means of multiconductor transmission-line (MTL) theory. This inherently quasitransverse electromagnetic mode (quasi-TEM) analysis is used to quickly and accurately calculate the dispersion of the lowest pass-band and several of the upper pass-bands. The first pass-band reveals dual mode behavior, supporting one forward-wave and one backward-wave mode, with the first stop-band formed as a result of contra-directional coupling between the two modes. The dispersion curves obtained using MTL theory are compared with full-wave simulations, with excellent agreement between the two methods. Moreover, the analysis reveals an interesting modal behavior within the stop-band, corresponding to complex conjugate propagation constants. The overall modal structure within the various bands is examined and related to corresponding applications.     

Analysis of the time response of multiconductor transmission lineswith frequency-dependent losses by the method ofconvolution-characteristics

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 networks. Particularly, it can analyze nonuniform lines with frequency-dependent losses, for which no effective method for analyzing their time response exists. This method starts from the frequency-domain telegrapher's equations. After decoupling and inversely Fourier transforming, then a set of decoupled 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     

Spectral domain analysis of conductor losses in a multiconductorsystem via the incremental inductance rule

Spectral domain analysis is adapted to analyse the conductor losses of a multiconductor system embedded in a multilayered medium using a quasi-TEM approach and assuming a strong skin effect. After adapting the incremental rule to a multiconductor system, the conductor losses are computed in terms of the derivative of the inductance matrix     

TDSE方法用于多导体传输线端接动态元件的分析

利用时域空间扩展方法(TDSE)对多导体传输线端接动态元件的情况进行了分析，为电磁兼容分析提供了一种新的途径。利用该方法分别对由独立激励源和入射电磁波激励的传输线的终端感应电压和电流进行了分析。仿真结果表明：当传输线端接动态元件的时候，终端感应电压和电流的过渡过程时间将会变长。