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A Novel High-Capacity Electromagnetic Compression Technique Based on a Direct Matrix Solution 一种基于直接矩阵解的新型大容量电磁压缩技术
Pub Date : 2010-12-17 DOI: 10.1109/TADVP.2010.2089788
Youngae Han, Jinsong Zhao
Electromagnetic solvers based on integral equations in conjunction with the method of moments or the partial element equivalent circuit method (PEEC) proved to be popular because of their efficiency and accuracy. There is one serious drawback of the integral equation approach: it often leads to a linear system involving a full matrix. Many efficient approaches have been proposed to overcome this, largely based on compressing the matrix-vector product operation and using an iterative solver. Iterative EM solvers, however, suffer from slow convergence, which does not have a totally reliable method to address; further, large multiple right-hand sides significantly increase the solving time. In this paper, we present a novel method to compress low rank sub-block matrixes into sparse matrix to be used with a direct sparse matrix solver to obtain an efficient high-capacity electromagnetic solver based on an integral equation formulation. The full-rank system matrix is represented in a hierarchical matrix format that has its sub-matrixes compressed with numerically controllable accuracy; it is then analytically converted to a sparse matrix which is further solved by a direct sparse matrix solver. Analytically this method results in O(N (log N)2) complexity for computing the inverse of a hierarchical matrix presented in Fig. 2 where N is the number of unknowns.
基于积分方程的电磁求解器与矩量法或部分单元等效电路法(PEEC)相结合,以其效率高、精度好而广受欢迎。积分方程方法有一个严重的缺点:它经常导致一个包含满矩阵的线性系统。已经提出了许多有效的方法来克服这个问题,主要是基于压缩矩阵向量乘积运算和使用迭代求解器。然而,迭代EM求解器收敛速度慢,没有完全可靠的方法来解决;此外,大的多个右手边显著地增加了求解时间。本文提出了一种将低秩子块矩阵压缩成稀疏矩阵的新方法,并将其与直接稀疏矩阵求解器结合使用,得到了一种基于积分方程公式的高效高容量电磁求解器。该全秩系统矩阵用层次矩阵格式表示,其子矩阵被压缩,精度可控制;然后将其解析转换为稀疏矩阵,再用直接稀疏矩阵求解器求解。解析地说,这种方法的结果是O(N (log N)2)复杂度,用于计算如图2所示的层次矩阵的逆,其中N是未知数的数量。
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引用次数: 0
Random Rough Surface Effects on Wave Propagation in Interconnects 随机粗糙表面对互连中波传播的影响
Pub Date : 2010-12-17 DOI: 10.1109/TADVP.2010.2089789
L. Tsang, H. Braunisch, R. Ding, X. Gu
To address the rough surface effects in high-speed interconnects on printed circuit boards (PCBs) and microelectronic packages, we study the electromagnetic wave propagation in a rough surface environment. In our model, the rough surface is characterized by a stochastic random process with correlation function or spectral density. This paper reviews the analytical theory, numerical simulations and experimental results based on such a model. We describe the rough surface characterization and the extraction of roughness parameters from 3D profile measurements. Initially we study the 2D case with the rough surface height function varying in only one horizontal direction and consider the case of plane wave incidence. Analytic second-order small perturbation method (SPM2) was used to obtain simple closed-form expressions for the absorption enhancement factor. The numerical transfer matrix (T-matrix) method and the method of moments (MoM) were also used. We next consider the case of the 3D problem with the rough surface height varying in both horizontal directions. We also used SPM2 to obtain a simple closed form expression for the enhancement factor. In interconnect problems, electromagnetic (EM) waves propagate in a guided wave environment. Thus, we next considered a waveguide model to study the effects of random roughness on wave propagation and compare with results from the plane wave formulation. Analytic SPM2 and numerical finite element method (FEM) with mode matching were used to obtain the enhancement factor. We also describe experimental results and correlation with the theoretical models. Finally, we explain how the enhancement factor concept used throughout lends itself to direct inclusion of rough surface effects in a wide variety of modeling problems.
为了解决印刷电路板(pcb)和微电子封装高速互连中的粗糙表面效应,我们研究了电磁波在粗糙表面环境中的传播。在我们的模型中,粗糙表面是一个具有相关函数或谱密度的随机过程。本文综述了基于该模型的解析理论、数值模拟和实验结果。我们描述了粗糙表面表征和从三维轮廓测量中提取粗糙度参数。我们首先研究了粗糙表面高度函数仅在一个水平方向上变化的二维情况,并考虑了平面波入射的情况。利用解析二阶小摄动法(SPM2)得到了吸收增强因子的简单封闭表达式。采用了数值传递矩阵法和矩量法。接下来,我们考虑粗糙表面高度在两个水平方向上变化的三维问题。我们还使用SPM2得到了增强因子的简单封闭形式表达式。在互连问题中,电磁波在导波环境中传播。因此,我们接下来考虑一个波导模型来研究随机粗糙度对波传播的影响,并与平面波公式的结果进行比较。采用解析SPM2法和模态匹配的数值有限元法(FEM)计算增强因子。本文还描述了实验结果及其与理论模型的相关性。最后,我们解释了增强因子概念如何在各种建模问题中直接包含粗糙表面效应。
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引用次数: 52
Foreword Special Section on Recent Progress in Electrical Modeling and Simulation of High-Speed ICs and Packages 引言:关于高速集成电路和封装的电气建模和仿真的最新进展的专题部分
Pub Date : 2010-12-17 DOI: 10.1109/TADVP.2010.2099155
D. Jiao
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引用次数: 0
A Markov Chain Based Hierarchical Algorithm for Fabric-Aware Capacitance Extraction 基于马尔可夫链的织物感知电容提取分层算法
Pub Date : 2010-12-17 DOI: 10.1109/TADVP.2010.2091504
T. El-Moselhy, Ibrahim M. Elfadel, Luca Daniel
In this paper, we propose a hierarchical algorithm to compute the 3-D capacitances of a large number of topologically different layout configurations that are all assembled from the same basic layout motifs. Our algorithm uses the boundary element method in order to compute a Markov transition matrix (MTM) for each motif. The individual motifs are connected together by building a large Markov chain. Such Markov chain can be simulated extremely efficiently using Monte Carlo simulations (e.g., random walks). The main practical advantage of the proposed algorithm is its ability to extract the capacitance of a large number of layout configurations in a complexity that is basically independent of the number of configurations. For instance, in a large 3-D layout example, the capacitance calculation of 1000 different configurations assembled from the same motifs is accomplished in the time required to solve independently two configurations, i.e., a 500 × speedup.
在本文中,我们提出了一种分层算法来计算大量拓扑不同的布局构型的三维电容,这些布局构型都是由相同的基本布局基元组装而成的。我们的算法使用边界元方法来计算每个基序的马尔可夫转移矩阵(MTM)。单个的图案通过建立一个大的马尔可夫链连接在一起。这样的马尔可夫链可以非常有效地模拟使用蒙特卡罗模拟(例如,随机漫步)。该算法的主要实用优点是能够在基本上与配置数量无关的复杂度下提取大量布局配置的电容。例如,在一个大型三维布局示例中,由相同的模块组装而成的1000种不同构型的电容计算,在独立求解两种构型所需的时间内完成,即加速500倍。
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引用次数: 16
A Thermal Simulation Process Based on Electrical Modeling for Complex Interconnect, Packaging, and 3DI Structures 基于复杂互连、封装和3DI结构电建模的热仿真过程
Pub Date : 2010-11-01 DOI: 10.1109/TADVP.2010.2090348
Lijun Jiang, Chuan Xu, B. Rubin, A. Weger, A. Deutsch, H. Smith, A. Caron, K. Banerjee
To reduce the product development time and achieve first-pass silicon success, fast and accurate estimation of very-large-scale integration (VLSI) interconnect, packaging and 3DI (3D integrated circuits) thermal profiles has become important. Present commercial thermal analysis tools are incapable of handling very complex structures and have integration difficulties with existing design flows. Many analytical thermal models, which could provide fast estimates, are either too specific or oversimplified. This paper highlights a methodology, which exploits electrical resistance solvers for thermal simulation, to allow acquisition of thermal profiles of complex structures with good accuracy and reasonable computation cost. Moreover, a novel accurate closed-form thermal model is developed. The model allows an isotropic or anisotropic equivalent medium to replace the noncritical back-end-of-line (BEOL) regions so that the simulation complexity is dramatically reduced. Using these techniques, this paper introduces the thermal modeling of practical complex VLSI structures to facilitate thermal guideline generation. It also demonstrates the benefits of the proposed anisotropic equivalent medium approximation for real VLSI structures in terms of the accuracy and computational cost.
为了缩短产品开发时间并实现首次通过硅的成功,快速准确地估计超大规模集成(VLSI)互连,封装和3DI (3D集成电路)热分布已经变得非常重要。目前的商业热分析工具无法处理非常复杂的结构,并且与现有的设计流程存在集成困难。许多可以提供快速估计的分析性热模型要么过于具体,要么过于简化。本文重点介绍了一种利用电阻求解法进行热模拟的方法,以较高的精度和合理的计算成本获取复杂结构的热分布。此外,还建立了一种新的精确的闭式热模型。该模型允许各向同性或各向异性等效介质取代非关键后端(BEOL)区域,从而大大降低了模拟复杂性。利用这些技术,本文介绍了实际复杂VLSI结构的热建模,以方便热导线的生成。本文还从精度和计算成本两方面证明了所提出的各向异性等效介质近似在实际VLSI结构中的优势。
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引用次数: 13
Accurate Characterization of Broadband Multiconductor Transmission Lines for High-Speed Digital Systems 高速数字系统宽带多导体传输线的精确表征
Pub Date : 2010-11-01 DOI: 10.1109/TADVP.2010.2050204
Joong-Ho Kim, D. Oh, Woopoung Kim
Accurate modeling of transmission lines becomes increasingly important in high-speed interconnect system design. However, it is rather difficult to obtain broadband transmission line models, in particular using frequency-domain measurements. This paper points out two potential accuracy issues. First, inaccurate DC values of the frequency-domain data cause a severe error in the time-domain simulations. Second, it is difficult to characterize the characteristic impedance over a wide frequency range due to the reflection caused by the port discontinuities. This paper proposes the combination of both time and frequency measurement data to mitigate the DC accuracy issue. For the characteristic impedance model, a new de-embedding technique is presented to mitigate the port discontinuity issue. Several numerical examples, such as MCM-L coplanar lines and package microstrip lines, are studied to validate the accuracy of the proposed method.
传输线的精确建模在高速互连系统设计中变得越来越重要。然而,获得宽带传输线模型是相当困难的,特别是使用频域测量。本文指出了两个潜在的准确性问题。首先,频域数据的直流值不准确会导致时域模拟的严重误差。其次,由于端口不连续引起的反射,很难在很宽的频率范围内表征特征阻抗。本文提出了时间和频率测量数据相结合的方法来缓解直流精度问题。对于特征阻抗模型,提出了一种新的去嵌入技术来缓解端口不连续问题。以MCM-L共面线和封装微带线为例,验证了该方法的准确性。
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引用次数: 55
Interfacial Design of Anisotropic Conductive Adhesive Based Interconnects Using Molecular Wires and Understanding of Their Electrical Conduction 基于分子线的各向异性导电胶粘剂互连界面设计及其导电性研究
Pub Date : 2010-10-14 DOI: 10.1109/TADVP.2010.2081987
Rongwei Zhang, K. Moon, Wei Lin, Yiqun Duan, S. Lotz, C. Wong
Anisotropic conductive adhesives (ACAs) have been considered a promising interconnect material for next generation high performance devices. However, high joint resistance and low current carrying capability of ACA interconnects have been the limitations to utilizing ACAs in high power devices. In this study, we have introduced conjugated dithiols into ACA formulations to create molecular wire junctions between conductive fillers and metal pads as a means to facilitate the electron transport through the ACA joints. With the introduction of molecular wires, there is evidence of measured improvements in both the electrical conductivity and current carrying capability. The factors leading to these improvements in electrical properties are also discussed.
各向异性导电胶粘剂(ACAs)被认为是一种很有前途的下一代高性能器件互连材料。然而,高连接电阻和低载流能力一直是限制在大功率器件中使用ACAs的原因。在这项研究中,我们将共轭二硫醇引入到ACA配方中,在导电填料和金属垫之间创建分子线结,作为促进电子通过ACA关节传递的一种手段。随着分子导线的引入,有证据表明在导电性和载流能力方面都有了明显的改善。还讨论了导致电性能改善的因素。
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引用次数: 2
A Wideband Common-Mode Suppression Filter for Bend Discontinuities in Differential Signaling Using Tightly Coupled Microstrips 基于紧密耦合微带的差分信号弯曲不连续宽带共模抑制滤波器
Pub Date : 2010-10-04 DOI: 10.1109/TADVP.2010.2077287
C. Gazda, D. Vande Ginste, H. Rogier, R. Wu, D. De Zutter
A new type of bend is proposed that reduces differential-to-common mode conversion occuring at the bend discontinuity in coupled microstrip lines for high-speed digital circuits. Simultaneously, great care has been taken to minimize the differential reflection coefficient and insertion loss, leading to an overall improved signal integrity. This is achieved by tapering the microstrip lines to tightly or very tightly coupled ones in the area of the bend. Full-wave simulations in the DC to 6 GHz frequency range show that over 9 dB and 14 dB suppression of conversion noise is achieved for tightly coupled and very tightly coupled bends, respectively. Also for these new structures, with a total length of 100 mm, the insertion loss remains below 0.6 dB. Measurements on prototype bends show very good agreement with full-wave simulations. Also time domain measurements demonstrate the significant reduction in conversion noise while keeping return loss low. Moreover, for design purposes, a dedicated circuit model which closely matches the full-wave characteristics of the proposed bends is presented.
针对高速数字电路中耦合微带线在弯曲不连续处产生的差共模转换问题,提出了一种新型弯曲方式。同时,该系统还非常小心地将微分反射系数和插入损耗降至最低,从而提高了信号完整性。这是通过将微带线逐渐变细,使其在弯曲区域紧密或非常紧密地耦合在一起来实现的。在直流至6 GHz频率范围内的全波仿真表明,紧耦合弯管和极紧耦合弯管分别实现了超过9 dB和14 dB的转换噪声抑制。此外,对于这些总长度为100mm的新结构,插入损耗保持在0.6 dB以下。原型弯管的测量结果与全波模拟结果非常吻合。时域测量也表明在保持低回波损耗的同时显著降低了转换噪声。此外,为了设计目的,提出了一个与所提出的弯管的全波特性密切匹配的专用电路模型。
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引用次数: 69
Transient Thermal Network Modeling Applied to Multiscale Systems. Part II: Application to an Electronic Control Unit of an Automobile 瞬态热网络建模在多尺度系统中的应用第二部分:在汽车电子控制单元中的应用
Pub Date : 2010-10-04 DOI: 10.1109/TADVP.2010.2074201
M. Miana, C. Cortés, J. Pelegay, J. R. Valdés, T. Pütz, M. Moczala
This paper applies the methodology of transient thermal network modelling (TTNM) introduced in Part I to the heat transfer analysis of an electronic control unit (ECU) located in the engine enclosure of a motorcar. The complexity of the geometry, the diverse heat transfer mechanisms involved and the duration of the operating cycle prevent the use of both simple, lumped models and detailed numerical simulations. The TTNM methodology relies instead in steady, approximate heat transfer correlations and a division of the system into the largest possible isothermal elements, based on the analysis of characteristic time and length scales. The dynamic heat balance of each element is then written down, conforming the TTNM of the system, which is numerically integrated with an adequate time step. The practical aspects of the TTNM methodology (design stage) are finally demonstrated; in this particular case-study, the model reveals a very high risk of damage of electronic components due to the radiative heat load received from the exhaust pipe of the engine. A design modification consisting of a radiative shield is proposed and model-tested, achieving an appropriate reduction of heat flux and temperatures, and thus an adequate protection of critical components.
本文将第一部分介绍的瞬态热网络建模(TTNM)方法应用于汽车发动机外壳中的电子控制单元(ECU)的传热分析。几何结构的复杂性、涉及的不同传热机制和运行周期的持续时间阻碍了简单、集总模型和详细数值模拟的使用。TTNM方法依赖于稳定的,近似的传热相关性,并根据特征时间和长度尺度的分析,将系统划分为最大可能的等温元素。然后记录各元素的动态热平衡,符合系统的TTNM,并在适当的时间步长下进行数值积分。最后展示了TTNM方法(设计阶段)的实践方面;在这个特殊的案例研究中,该模型显示,由于从发动机排气管接收的辐射热负荷,电子元件损坏的风险非常高。提出了一种由辐射屏蔽组成的设计修改,并对模型进行了测试,从而适当降低了热流密度和温度,从而充分保护了关键部件。
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引用次数: 10
Transient Thermal Network Modeling Applied to Multiscale Systems. Part I: Definition and Validation 瞬态热网络建模在多尺度系统中的应用第一部分:定义和验证
Pub Date : 2010-10-04 DOI: 10.1109/TADVP.2010.2074200
M. Miana, C. Cortés, J. Pelegay, J. R. Valdés, T. Pütz
This paper formulates the methodology of transient thermal network modeling (TTNM) for the study of unsteady heat transfer in systems where the presence of multiple length and time scales prevents the analysis by means of current computational or experimental techniques. The TTNM is based on reduced order models (ROMs) and it is established under the essential premise that a transient heat transfer process can be modeled by its division in a succession of stationary states and the division of the geometry in isothermal elements, according to the characteristic time and length scales obtained by scale analysis. The methodology is subsequently validated with canonical examples and considerations are given for the application to practical problems.
本文阐述了瞬态热网络建模(TTNM)的方法,用于研究系统中的非定常传热,其中多长度和时间尺度的存在使现有的计算或实验技术无法进行分析。TTNM基于降阶模型(ROMs),其建立的基本前提是,瞬态传热过程可以根据尺度分析得到的特征时间和长度尺度,通过连续的定态划分和等温元件的几何划分来建模。随后用典型的例子验证了该方法,并给出了应用于实际问题的考虑。
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引用次数: 8
期刊
IEEE Transactions on Advanced Packaging
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