用修正特征法模型求解高速VLSI中有耗互连线的瞬态响应

本文提出了用于高速集成电路系统中有耗互连线瞬态响应求解的一个计算模型及其相应的算法。传统的特征法在用于求解无耗传输线或满足ＬＧ＝ＲＣ的有耗传输线时具有简单的递归形式和较高的计算效率,但不能用于一般的有耗传输线。本文在特征法的基础上,通过适当的参数修正,建立了一般有耗传输线瞬态响应的近似特征模型,导出了其对时间变量递归形式的计算公式。     

Nouvelle expression temporelle de ľimpédance interne des conducteurs à section rectangulaire

In this paper, a new time domain internal impedance formula for characterizing the skin effect in interconnects of rectangular cross section is proposed. The comparison with the simulation results of a method involving frequency domain exact formula validates the present model and illustrates its accuracy. We have also shown the lack of precision of the formulations based on conductor losses varying as √ f In order to predict the responses of lossy planar transmission lines, the used methods are the time domain — frequency domain transformation (tdfd) and the finite difference time domain algorithm (fdtd). Theses techniques of analysis are applied to the mtl equations under quasi — tem approximation.     

Crosstalk and transient analyses of high-speed interconnects andpackages

A multiconductor interconnect is modeled using resistors and linear-dependent current and voltage sources. The analysis of a high-speed circuit including lossy interconnection buses is then reduced to simulation of the circuit together with the equivalent circuits of the interconnects. The authors present a new method for the crosstalk and transient analysis of lossy interconnects with arbitrary termination circuits. In order to analyze an interconnect containing N signal conductors, they derive closed-form formulas to determine its transfer functions, and they apply the inverse Fourier transform to obtain its time-domain pulse response functions. Two types of equivalent circuit models can be formulated once the pulse response functions of the interconnect are found. The circuit schematics of the models depend on the number of the signal conductors, irrespective of the physical parameters of the interconnect. These models are compatible with standard circuit simulation tools since they consist of linear resistive networks and linear-dependent sources only. Two example circuits are studied to examine the accuracy and efficiency of the method     

Efficient computation of frequency-dependent parameters for on-chipinterconnects via two-dimensional FDTD and time signal predictiontechnique

An efficient two-dimensional finite difference time domain (2-D-FDTD) method combined with time signal prediction technique has been proposed for the frequency-dependent parameters computation of on-chip interconnects in high-speed integrated circuits (ICs). A graded mesh algorithm and lossy absorbing boundary condition are proposed and adopted in the 2-D FDTD analysis to reduce the number of spatial grid points in the simulation region. The introduction of time signal prediction technique to predict the future signal in the time domain or extract the parameters in the frequency domain of uniform transmission lines reduces the computation time drastically. With these, the substrate and conductor losses are both included in one analysis. This algorithm leads to a significant reduction in CPU time and storage requirements as compared with the conventional FDTD. The simulation results are in good agreement with the results obtained by other methods and measurements     

Application of asymptotic waveform evaluation for analysis of skineffect in lossy interconnects

Asymptotic waveform evaluation (AWE) is a technique for time-domain analysis of electrical interconnects. AWE is a computationally efficient method that asymptotically approximates the response of a large system with a lower-order transfer function. Asymptotic waveform evaluation is used to analyze lossy interconnects including the skin effect. The internal impedance of the interconnect conductors varies as a function of the square root of the frequency. First, an overview of AWE is presented. The AWE formulation for modeling frequency dependent loss in the conductors is derived using two different series expansions of the system response at both s=0 and s≠0 in the Laplace domain. The expansions for s≠0 are determined using a transfer function formulated for inclusion of the frequency-dependent internal impedance. The network response is computed by extracting the dominant poles and residues using the Pade approximation. The proposed method is evaluated using time-domain examples of lossy multiconductor transmission lines     

网孔状地参考面上高速互连的信号完整性分析

本文主要基于实验研究,并结合三维全波电磁和电路系统仿真在频域和时域对高速多层PCB板中网孔状接地层或电源层上高速互连的信号完整性性能进行了测试和仿真分析,并对网孔状地参考面的周期性结构所呈现的频率带通(带阻)特性进行了理论分析.指出,参考面中的网孔会对跨越网孔的信号线传输特性产生较大扰动,甚至在信号频谱范围内产生局部的阻带,影响高速信号传播.最后,给出了网孔状地参考面高速互连的设计规则.     

Accurate modeling of lossy nonuniform transmission lines by using differential quadrature methods

This paper discusses an efficient numerical approximation technique, called the differential quadrature method (DQM), which has been adapted to model lossy uniform and nonuniform transmission lines. The DQM can quickly compute the derivative of a function at any point within its bounded domain by estimating a weighted linear sum of values of the function at a small set of points belonging to the domain. Using the DQM, the frequency-domain Telegrapher's partial differential equations for transmission lines can be discretized into a set of easily solvable algebraic equations. DQM reduces interconnects into multiport models whose port voltages and currents are related by rational formulas in the frequency domain. Although the rationalization process in DQM is comparable with the Pade approximation of asymptotic waveform evaluation (AWE) applied to transmission lines, the derivation mechanisms in these two disparate methods are significantly different. Unlike AWE, which employs a complex moment-matching process to obtain rational approximation, the DQM requires no approximation of transcendental functions, thereby avoiding the process of moment generation and moment matching. Due to global sampling of points in the DQM approximation, it requires far fewer grid points in order to build accurate discrete models than other numerical methods do. The DQM-based time-domain model can be readily integrated in a circuit simulator like SPICE.     

Condition of modal analysis in time domain of lossy coupled lines

Modal decomposition in the time domain is shown to be applicable to lossy coupled transmission lines of equal width. It is rigorous for two lines and is a good approximation for more than two lines. This allows a direct time-domain simulation of buses made of microstrip lossy lines on chip or on board in digital circuits     

Transient Simulation of Lossy Interconnects Based on a Dispersive Hybrid Phase-Pole Macromodel

A transient simulator for interconnect structures that are modeled by lossy transmission lines is outlined in this paper. Since frequency-dependent RLGC parameters must be employed to correctly model skin effects and dielectric losses for high-performance interconnects, we first study the behaviors of various lossy interconnects that are characterized by frequency-dependent line parameters (FDLPs). We then developed a frequency-domain dispersive hybrid phase-pole macromodel (DHPPM) for such lines, which consists of a constant RLGC propagation function multiplied by a residue series. The basic idea is to first extract the dominant physical phenomenology by using a propagation function in the frequency domain that is modeled by frequency-independent line parameters (FILPs). A rational function approximation is then used to account for the remaining effects of FDLP lines. By using a partial fraction expansion and analytically evaluating the required inverse Fourier transform integrals, the time-domain DHPPM can be decomposed as a sum of canonical transient responses for lines with FILP for various excitations (e.g., trapezoidal and unit step). These canonical transient responses are then expressed analytically as closed-form expressions involving incomplete Lipshitz-Hankel integrals of the first kind and Bessel functions. The closed-form expressions for these canonical responses are validated by comparing with simulation results from commercial tools like HSPICE. The DHPPM simulator can simulate transient results for various input waveforms on both single and coupled interconnect structures. Comparisons between the DHPPM results and the results produced by commercial simulation tools like HSPICE and a numerical inverse fast Fourier transform show that the DHPPM results are very accurate.     

Comparison of FDTD and SPICE simulations for lossy and dispersivenonlinear transmission lines

For the first time, a simulation has been carried out of lossy and dispersive nonlinear transmission lines (NLTLs) used for pulse compression, by two different time-domain approaches: SPICE and a full wave 3D finite difference time domain method. Results show good agreement between the two approaches. The output pulse risetime is strongly affected by DC and skin-effect losses     

An efficient implementation of surface impedance boundaryconditions for the finite-difference time-domain method

An efficient way to implement the surface impedance boundary conditions (SIBC) for the finite-difference time-domain (FDTD) method is presented in this paper. Surface impedance boundary conditions are first formulated for a lossy dielectric half-space in the frequency domain. The impedance function of a lossy medium is approximated with a series of first-order rational functions. Then, the resulting time-domain convolution integrals are computed using recursive formulas which are obtained by assuming that the fields are piecewise linear in time. Thus, the recursive formulas derived here are second-order accurate. Unlike a previously published method [7] which requires preprocessing to compute the exponential approximation prior to the FDTD simulation, the preprocessing time is eliminated by performing a rational approximation on the normalized frequency-domain impedance. This approximation is independent of material properties, and the results are tabulated for reference. The implementation of the SIBC for a PEC-backed lossy dielectric shell is also introduced     

Time-domain analysis of lossy coupled transmission lines

A novel method based on numerical inversion of the Laplace transform is presented for the analysis of lossy coupled transmission lines with arbitrary linear terminal and interconnecting networks. The formulation of the network equations is based on a Laplace-domain admittance stamp for the transmission line. The transmission line stamp can be used to formulate equations representing arbitrarily complex networks of transmission lines and interconnects. These equations can be solved to get the frequency-domain response of the network. Numerical inversion of the Laplace transform allows the time-domain response to be calculated directly from Laplace-domain equations. This method is an alternative to calculating the frequency-domain response and using the fast Fourier transform to obtain the time-domain response. The inversion technique is equivalent to high-order, numerically stable integration methods. Numerical examples showing the general application of the method are presented. It is shown that the inverse Laplace technique is able to calculate the step response of a network. The time-domain independence of the solution is exploited by an efficient calculation of the propagation delay of the network     

不等长非均匀有损耗传输线FDTD瞬态分析

以分析等长均匀无损耗多导体传输线的时域有限差分(FDTD)法为基础,在考虑传输线损耗的情况下,对不等长非均匀多导体传输线进行分析。首先,在考虑传输线损耗的情况下给出传输线上各点电压和电流的迭代计算公式;其次,利用该公式对不等长非均匀有损耗传输线模型进行数值计算和理论分析;最后,通过仿真实验,其结果表明所提计算方法是正确和有效的。该方法对不等长非均匀有损耗传输线的研究提供理论计算参考。     

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     

Investigation of tapered multiple microstrip lines for VLSIcircuits

The analysis of tapered, coupled microstrip transmission lines is presented. These lines, used as interconnects between integrated circuit devices, are modeled using an iteration-perturbation approach applied in the spatial domain. From this model, a frequency-dependent scattering parameter characterization is determined. A time-domain simulation of pulse propagation through the tapered, coupled microstrip lines is performed. The frequency-domain scattering parameters are inverse Fourier transformed to obtain the time-domain Green's function. The input pulse is convolved with the Green's function, and a Newton-Raphson algorithm is applied to account for nonlinear loads. Some experimental results are shown, and a simulation approximation is proposed     

有损土壤上的多导体传输线的时域分析

将多导体传输线（ＭＴＬ）的土壤复数阻抗拓展为土壤运算阻抗,采用Ｐａｄｅ展开法,提出了计及土壤影响的多导体传输线的时域模型,建立了该模型的时域有限差分（ＦＤＴＤ）算法。通过对计及土壤影响的架空单导体和双导体传输线的波过程计算,表明本文方法的正确性,并可以应用于超高压变电站高压母线和超高压输电线路的瞬态电磁干扰计算。     

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.     

A novel systematic approach for equivalent model extraction of embedded high-speed interconnects in time domain

Based on time-domain scattered data, an efficient systematic approach in the time domain has been proposed to extract the SPICE-compatible models of embedded high-speed interconnects. The approach combines the layer-peeling technique and the generalized pencil-of-matrix method to obtain a pole-residue representation of the step response of the interconnects. An order-reduction procedure is implemented based on the bandwidth criterion to find the optimum pole-residue representation of the interconnects with minimum pole numbers. The SPICE-compatible lumped circuits are then systematically extracted from the pole-residue rational functions. The discontinuous microstrip lines and bonding wire structure are used to demonstrate the validity of the proposed approach. Good agreement is seen between the modeled and measured transient response. The advantages of this approach are the de-embedding ability for arbitrary nonuniform interconnects, systematically obtaining lower order and more accurate SPICE-compatible circuits, and broad-band performance of the extracted circuits.