M. Kamon, M.J. Tsuk, and J. White. Fasthenry: a multipole-accelerated 3d inductance extraction program. IEEE Trans. on MIT, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....This extraction must be accurate as a correlation with final verification engines, and is needed for design convergence. The extraction must also be e#cient, because it may be performed dozens of times on the full chip level and thousands of times on critical nets. Clearly, numerical extraction [16, 10, 17] is hard to support during iterative procedures of simulation and optimization. In [7] an e#cient table based inductance model was proposed using the partial element equivalent circuit (PEEC) model for coplanar parallel bus structures. The method is able to consider the impact of frequency, and ....

....between inductance for filaments and that for wires. A similar scheme can be used to illustrate the rational behind Equation (3) in this paper. In the next subsection, we will compare the inductance values given by equation (3) with those obtained by the numerical field solver FastHenry [10]. 2.4 Experimental results We have implemented the above table based model for frequencydependent inductance, and proceed to compare the inductance given our model with the numerical solution by FastHenry. We consider first the mutual inductance between two random wires, and then the loop ....

M. Kamon, M. Tsuk, and J. White. Fasthenry: a multipole-accelerated 3d inductance extraction program. IEEE Trans. on MIT, 1994.

....and verification of VLSI circuits. There are three types of inductance extraction algorithms: loop inductance, partial inductance and shape based. The loop inductance algorithms are the most accurate but slowest, while the shape based algorithms are the least accurate but the fastest. FastHenry [8] computes the loop inductance. Due to its high accuracy, FastHenry is often used as a reference for all other extraction algorithms. But FastHenry is very slow, and to improve its speed is one of the most challenging problems. Partial inductance was first proposed by Rosa and introduced to circuit ....

....The numerical value of the potential difference between the two ends of conductor k gives values of the matrix element tcl. The above procedure is repeated s times to compute all columns of . The current density J at a point r is related to the potential by the following integral equation [8] oj(r) jco v J(r )dW: Vqb(r) 1) IIr 11 where u is the magnetic permeability, O is the resistivity, r is a three dimensional position vector, to is the frequency, I I r ll is the Euclidean distance between r and r t, and j = x . The volume of conductors is denoted by V and incremental volume ....

M. Kamon, M. J. Tsuk, and J. White. FASTHENRY: A multipole-accelerated 3D inductance extraction program. IEEE Trans. MTT, Vol. 42:1750-1758, 1994.

....makes calculation of the loop inductances difficult, if not impossible; hence PEEC models are necessary for on chip interconnect. B. Proximity Effect Even without considering capacitive couplings, increasing signal frequencies change the way currents flow within a given interconnect system [11]. Current will tend to flow the path of least impedance. For low frequencies the impedance is dominated by the resistance of the conductors. Since the conductors have a finite cross section, the current will spread out over the given cross section to minimize the overall resistance (see Fig. ....

M. Kamon, M. Tsuk, J. White, FASTHENRY: A Multipole --Accelerated 3--D Inductance Extraction Program, IEEE Trans. Microwave Theory and Techniques, 42, No. 9, pg. 1750--1758 (Sept. 1994).

....focused primarily on the modeling and extraction of on chip interconnect inductance. In [15] loop inductance was calculated in terms of partial inductances defined for wire segments. The Partial Element Equivalent Circuit (PEEC) model was widely used to analyze on chip inductance [7; 14; 4] In [9], frequency dependent inductance and resistance were computed based on the magnetoquasistatic assumption, and in [10] a simple layout rulebased method was used to speed up the computation. This research is supported in part by SRC (99 TJ 689) NSF (CAREER Award CCR 9984553) and a grant from ....

....If parallel termination is adopted at the receiving ends of signal lines, there are no or minimal reflections at the receiving ends. Consequently, noises gathered at the victim nets cancel each other when they reach the receiving ends. Hence, the mutual inductance is still zero. We use FastHenry [9] to verify the effectiveness of the proposed twisted pair layout structure in minimizing coupling inductance. The wire width, height, length, and spacing are 1m, 2m, 200m, and 1m, respectively. We extract the inductance matrix under two frequencies: a high frequency of f H = 10 16 Hz and a low ....

M. Kamon, M. J. Tsuk, and J. K. White. FASTHENRY: A multipole-accelerated 3-D inductance extraction program. IEEE Journal on Microwave Theory and Techniques, 42(9):1750--1758, September 1994.

....This modeling approach is the circuit equivalent to the accumulation and distribution processes seen in the fast potential evaluation methods employed in parasitic extractors. The sparse RLC circuit models are generated directly from the hierarchical extraction results (such as in [2] or [3]) rather than creating, then reducing a large, flattened RLC circuit. This work was supported by the MARCO DARPA Gigascale Silicon Research Center (GSRC) and a grant from Intel Corporation. Michael Beattie was partially supported by a fellowship from the Semiconductor Research Corporation. ....

....three directions which preserves the magnetic flux induced from A into each of its victim groups with a high level of accuracy: 15) The first factor in (14) is the composite inductive coupling from A to G. This composite coupling is regularly generated within hierarchical extractors in use today [3], so there is no extra effort necessary to get these values. b) Distribution of Branch Magnetic Flux (Voltage) The higher level magnetic flux for the victim groups must be redistributed onto the child segments using controlled sources in the hierarchical equivalent circuit model. We will, for ....

M. Kamon, M. Tsuk, J. White, FastHenry: A Multipole Accelerated 3--D Inductance Extraction Program, IEEE Trans. Microwave Theory and Techniques, 42, No. 9, pp. 1750--1758 (Sept. 1994).

....metal layers and the use of copper to replace aluminum) Therefore, modeling and layout optimization for on chip inductance have been drawing increasingly more attentions. The inductance models can be classified into the following categories: i) numerical based inductance extraction such as [1][6][2] that are accurate, but are too expensive to be used for the full chip level, and (ii) formula or table based inductance extraction such as [7] 4] that are reasonably accurate and efficient enough to be used for full chip level timing analysis and simulation. However, all aforementioned methods ....

....3. Formula based k eff models are developed for the two interconnect structures in the two sections. We then apply the k eff models to synthesize 64 bit wide bus structures in Section 4, and verify the synthesized interconnect structures via the numerical inductance extraction tool FastHenry[6]. We conclude the paper in Section 5. 2 Coplanar Structures 2.1 Characteristics of Inductance In this section, we consider parallel wires of the same length in the same layer. In addition to the signal wire (in short, s wires) there are other two types of coplanar wires. One type is ....

Mattan Kamon, M. J. Tsuk, and Jacob White. FastHenry: a multipole-accelerated 3d inductance extraction program. IEEE Trans. on MIT, 1994. REFERENCES 16

....multiplication by A can be accomplished in time proportional to the size of the representation. Because integral equations usually give a relatively well conditioned matrix A, Krylov subspace iterative methods [41] can be used to quickly solve the linear system. FastCap [33] and FastHenry [20] were the first electrostatic extraction tools based on this methodology. Multiplication by the matrix A in these tools is accomplished using the Fast Multipole Method [17] The main weakness of these tools is that the interaction between discretization elements must have a 1=jr , r 0 j ....

M. Kamon, M. J. Tsuk, and J. White. FASTHENRY: A multipole-accelerated 3-d inductance extraction program. IEEE Trans. on Microwave Theory and Techniques, 42(9):1750--1758, September 1994.

....problem is intractable for large chips. The complexity is in computing the return impedance of p g mesh structures. We have studied the feasibility of using an empirical model for fast determination of inductance. With a fixed p g mesh design, we do a few extractions with the tool fasthenry [3] with different combinations of signal line width and signal position with respect to p g mesh. Then, we fit mathematical equations for inductance as a function of line width and position within the p g mesh. The accuracy of the curve fit can be controlled using suitable number of terms. P G P G ....

....of these parameters in terms of empirical formulae. These empirical formulae then can be used to extract R and L from the layout. To demonstrate this idea, we considered the global power and ground meshes in the top four layers. A program was written to generate the p g mesh in the fasthenry [3] format. If W denotes the minimum width on a given layer, then, we used the following width values: W, 2W, 3W, 5W, 10W, 15W, and 20W for the width variable. We determined the formulae for R and L in two steps: in the first step, we determined equations as functions of position, for each value of ....

Kamon, M., Tsuk, T. J. , White, J. K.: FASTHENRY: A Multipole Accelerated 3-D Inductance Extraction Program, IEEE Transactions on Microwave Theory and Techniques, 42, No. 9, Sept. 1994.

....since it requires less spatial subdivision layers and uses the more efficient refinement method for near field modeling rather than direct potential evaluation. Table 3 contains a comparison of the partial inductance results for the same crossing bus structure which were calculated by FastHenry [3] and with our new hierarchical approach which also yields inductance between orthogonal lines due to eddy currents. The error in Table 3 is for inductances between parallel wires only. B. Signal Bus Example To compare the performance of our new potential evaluation approach with the multipole ....

M. Kamon, M. Tsuk, J. White, FastHenry: A Multipole Accelerated 3--D Inductance Extraction Program, IEEE Trans. Microwave Theory and Techniques, 42, No. 9, pp. 1750--1758 (Sept. 1994).

....of these dense matrices. Instead of having to represent the matrix with O(N 2 ) elements with a sparse representation using only O(N) or O(N logN) numbers. This is achieved by exploiting the structure arising from the physical properties of the problem. FastCap [11] and FastHenry [7] employ an algorithm called the Fast Multipole Method [4] The fast multipole method (FMM) 4] while originally developed for particle simulation problems, can be combined with iterative techniques to solve the dense matrices arising from integral equations. This method is based on the ....

M. Kamon, M. J. Tsuk, and J.White. FASTHENRY: A multipole-accelerated 3-D inductance extraction program. IEEE Transactions on Microwave Theory and Techniques, 42(9):1750--1758, Sept. 1994.

....The fast multipole method (FMM) 3] while originally developed for particle simulation problems, can be combined with iterative techniques to solve the dense integral equation matrices that arise from the Laplace equation. Parameter extraction programs such as FastCap [7] and FastHenry [5] use the FMM for accelerating the dense matrix vector products required by an iterative solver. Because the FMM is tailored to the 1=jjx Gamma x 0 jj kernel, dealing with common situations such as layered dielectrics is difficult. For example, in FastCap this requires discretizing the ....

M. Kamon, M. J. Tsuk, and J.White. FASTHENRY: A multipole-accelerated 3-d inductance extraction program. IEEE Transactions on Microwave Theory and Techniques, 42(9):1750--1758, September 1994.

....(MCM) has become increasingly important in determining final circuit performance and reliability. The rigorous characterization of passive components is critical for the first pass of IC and MCM design. A standard approach for parameter extraction is to use a Method of Moments formulation [3] [4]. Integral equation formulations have several advantages (good conditioning, reduction in dimensionality of the problem and the ability to treat arbitrary regions) but have one overriding disadvantage: the high cost of working with large dense matrices. In the last decade, a number of algorithms ....

....One drawback of this algorithm is the fact that the preprocessing step requires O(N 2 ) operations. Fortunately, we have developed an improved algorithm that reduces the initialization time to O(N logN ) this algorithm can be faster and require less memory than the fast multipole algorithms of [4] and [6] These results will be presented at a later date. 6 Acknowledgement The authors thank Professor Vladimir Rokhlin of Yale and David Long, King Tai, and R.C. Frye at Bell Labs. Finally, we thank Professor Wayne Dai at UC Santa Cruz for his advice into MCM passive modelling. ....

M. Kamon, M.J. Tsuk, J. White. Fasthenry: A Multipole Accelerated 3-D Inductance Extraction Program. IEEE Transactions on Microwave theory and techniques., Vol 42(9):1750-1758, 1994.

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M. Kamon, M. J. Tsuk, and J. White. Fasthenry: A multipole-accelerated 3-d inductance extraction program. IEEE Transactions on Microwave Theory and Techniques, 42(9):1750--1758, September 1994.

....more reliant on accurate computer simulation tools. Signal integrity problems, like ground plane noise, are particular hard to simulate because so much of the problem geometry must be included to achieve accurate results. Multipole and precorrected FFT accelerated Method of Moments techniques [1, 3, 2, 4, 8] are one of the few techniques that are fast enough to analyze signal integrity problems, so optimizing these techniques seem worthwhile even if the resulting optimizations are somewhat incremental. In this paper we describe two optimizations to accelerated method of moments simulation, the first ....

....to analyze signal integrity problems, so optimizing these techniques seem worthwhile even if the resulting optimizations are somewhat incremental. In this paper we describe two optimizations to accelerated method of moments simulation, the first is an even better preconditioner than presented in [4] and the second is several optimizations of the FFT based convolution used in precorrected FFT methods [8] 2 A New Preconditioner for Efficient Inductance Extraction Iterative algorithms used to solve the dense systems of equations resulting from the integral equations of magnetoquasistatic ....

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M. Kamon, M. J. Tsuk, and J. White. Fasthenry: A multipole-accelerated 3-d inductance extraction program. IEEE Transactions on Microwave Theory and Techniques, 42(9):1750--1758, September 1994.

....Effect, Parasitic extraction, Interconnect analysis. 1. INTRODUCTION The new generation of fast electromagnetic analysis programs, based on accelerated integral equation methods, has reduced from days to minutes the time required to analyze thousands of simultaneously interacting conductors [1, 2, 3, 4, 5]. As good as these fast solvers are, they are either inappropriate for, or are very inefficient at, analyzing interconnect exhibiting high frequency effects. With processor clock speeds now exceeding two gigahertz and harmonics exceeding twenty gigahertz, it is no longer possible to ignore these ....

....effects are troublesome for present fast solver because they generate an exponentially varying current distribution inside each conductor. Trying to represent that current variation using the piece wise constant [6, 7] or piece wise linear basis functions commonly available in fast solvers [2] requires a large number of unknowns. Since the computation time for fast solvers is supposed to increase only linearly with the total number of basis functions used in the problem, it may seem that the increase in unknowns to represent current variation is not that problematic. However, when many ....

[Article contains additional citation context not shown here]

M. Kamon, M. J. Tsuk, and J. K. White. Fasthenry: A multipole-accelerated 3-d inductance extraction program. IEEE Trans. on Microwave Theory and Techniques, 42(9):1750--8, September 1994.

....resistance matrix, and P the panel potential coefficient matrix. To generate a system of equations, the circuit solution technique known as Mesh nalysis can be used whose solution gives the terminal admittance, Yt. The mesh approach has been used in the context of interconnect analysis in [7] and [8] Kirchoff s voltage law, which implies that the sum of branch voltages around each mesh in the network must be zero, is represented by [vl ] v, 2) MV: M. where V, is the mostly zero vector of source voltages, M involves branches with only filaments, and Mp branches with only ....

....scheme [3, 9] however for any finite expansion point, matrix solution with (7 s0 ) is required at each iteration, which is computationally expensive since 2 has dense blocks. To reduce the computational cost of this solution, fast techniques used for the mesh formulated inductance problem [7] could be directly employed. ....

M. Kamon, M. J. Tsuk, and J. White. Fasthenry: A multipole-acCelerated 3-d inductance extraction program. IEEE Transactions on Microwave Theory and Techniques, 42(9):1750-1758, September 1994.

....to analyze signal integrity problems, so optimizing these techniques seem worthwhile even if the resulting optimizations are somewhat incrementaI. In this paper we describe two optimizations to accelerated method of moments simulation, the first is an even better precondifioner than presented in [4] and the second is several optimizations of the FFT based convolution used in precorrected FFT methods 8] 2 A New Preconditioner for Efficient Inductance Extraction Iterative algorithms used to solve the dense systems of equations resulting from the integral equations of magnetoquasistatic ....

....magnetoquasistatic asalysis rely on preconditioning to insure fast convergence. The preconditioning matrix must be a good approximation to the inverse of the original system and be inexpensive to compute. Various approaches to preconditioning for magnetoquasistatic analysis have been explored in [4, 5] which show that since the original system is positive definite, so must the preconditioner. The dominant technique presented involves deriving a positive definite sparsification of the partial inductance matrix. Recently, a method has been proposed for stably approximating the partial inductance ....

M. Kamon, M. J. Tsuk, and J. White. Fasthenry: A multipole-accelerated 3-d inductance extraction program. IEEE Transactions on Microwave Theory and Techniques, 42(9):1750-1758, September 1994.

....pressing task: the verification problem. The past decade s intense development of accelerated integral equation solvers has made it possible to perform static and quasistatic electromagnetic analysis of packages or circuit boards with hundreds of conductors in just a few minutes on a workstation [1, 2, 3, 4]. The computational performance provided by these fast algorithms makes it now feasible to consider developing tools which can readily perform full board analysis, for use in applications such as SI and EMI diagnosis and resolution. This work was supported by the MARCO Interconnect Focus Center, ....

M. Kamon, M. J. Tsuk, and J. White. Fasthenry: A Multipole-Accelerated 3-D Inductance Extraction Program. IEEE Trans. on Microwave Theory and Techniques, September 1994.

....be used to directly construct reduced order models [2] In this paper, we present a numerically robust and accurate approach for computing reduced order models of magnetoquasistatic coupling in complicated 3 D structures. The approach is based on using the multipole accelerated program FastHenry [3], combined with the block Krylov subspace algorithm Arnoldi [4] We begin, in section 2, by describing the mesh formulation approach of FastHenry. In section 3, the standard Pad e approximation approach as well as an Arnoldi based approach are derived. In section 4 results are presented comparing ....

....present conclusions and acknowledgments. 2 The Mesh Formulation Approach The frequency dependent resistance and inductance matrices describing the terminal behavior of a set of conductors can be rapidly computed with the multipole accelerated mesh formulation approach as implemented in FastHenry [3]. To describe the approach, consider that each conductor is approximated as piecewise straight sections. The volume of each straight section is then discretized into a collection of parallel thin filaments through which current is assumed to flow uniformly. To derive a system of equations for the ....

M. Kamon, M. J. Tsuk, and J. White. Fasthenry: A multipole-accelerated 3-d inductance extraction program. IEEE Transactions on Microwave Theory and Techniques, 42(9):1750-- 1758, September 1994.

....resistance matrix, and P the panel potential coefficient matrix. To generate a system of equations, the circuit solution technique known as Mesh Analysis can be used whose solution gives the terminal admittance, Y t . The mesh approach has been used in the context of interconnect analysis in [7] and [8] Kirchoff s voltage law, which implies that the sum of branch voltages around each mesh in the network must be zero, is represented by MV b = Theta M f M p V f b V p b = V s (2) where V s is the mostly zero vector of source voltages, M f involves branches with only filaments, ....

....scheme [3, 9] however for any finite expansion point, matrix solution with (R s 0 L) is required at each iteration, which is computationally expensive since L has dense blocks. To reduce the computational cost of this solution, fast techniques used for the mesh formulated inductance problem [7] could be directly employed. ....

M. Kamon, M. J. Tsuk, and J. White. Fasthenry: A multipole-accelerated 3-d inductance extraction program. IEEE Transactions on Microwave Theory and Techniques, 42(9):1750--1758, September 1994.

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M. Kamon, M.J. Tsuk, and J. White. Fasthenry: a multipole-accelerated 3d inductance extraction program. IEEE Trans. on MIT, 1994.

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M. Kamon, M.J. Tsuk, and J.K. White. Fasthenry: A multipole-accelerated 3-d inductance extraction program. In DAC, June 1993.

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M. Kamon, M.J. Tsuk, and J.K. White. Fasthenry: A multipole-accelerated 3-d inductance extraction program. In DAC, June 1993.

No context found.

M. Kamon, M. J. Tsuk, and J. K. White. Fasthenry: A multipole-accelerated 3-d inductance extraction program. DAC, June 1993.

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