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Efficient linear circuit analysis by Padé approximation via the Lanczos process
, 1994
"... This paper describes a highly efficient and numerically stable algorithm for the iterative computation of dominant poles and zeros of large linear networks. The algorithm is based on a new implementation of the Pad'e approximation via the Lanczos process. This implementation has considerably superio ..."
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Cited by 219 (31 self)
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This paper describes a highly efficient and numerically stable algorithm for the iterative computation of dominant poles and zeros of large linear networks. The algorithm is based on a new implementation of the Pad'e approximation via the Lanczos process. This implementation has considerably superior numerical properties, while maintaining the same computational efficiency as its predecessors. In addition, the algorithm provides a bound on the pole approximation error. 1 Introduction Circuit simulation tasks, such as the accurate prediction of interconnect effects at the board and chip level, or analog circuit analysis with full accounting of parasitic elements, may require the solution of large linear networks. These networks can become extremely large, especially when circuits are automatically extracted from layout, or contain models of distributed elements, such as transmission lines, ground planes, antennas, and other threedimensional 2 Peter Feldmann and Roland W. Freund stru...
Coping with RC(L) Interconnect Design Headaches
 in Proc. of the International Conference on ComputerAided Design
, 1995
"... Physical interconnect effects have a dominant impact on today’s deep submicron IC designs. In this tutorial paper we will describe the technology trends which have brought about this interconnect dominance, then consider some of the modeling and analysis approximations available for both pre and po ..."
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Cited by 20 (0 self)
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Physical interconnect effects have a dominant impact on today’s deep submicron IC designs. In this tutorial paper we will describe the technology trends which have brought about this interconnect dominance, then consider some of the modeling and analysis approximations available for both pre and postlayout interconnect design.This coverage will not be an exhaustive summary, but one that is primarily focused on momentbased analysis techniques, from the Elmore delay, to the more recent advances in momentmatching approximations, and the corresponding nonlinear driver/load interfaces. Future modeling, analysis, and design challenges will be considered throughout this paper. 1
Padé Approximation Of LargeScale Dynamic Systems With Lanczos Methods
, 1994
"... The utility of Lanczos methods for the approximation of largescale dynamical systems is considered. In particular, it is shown that the Lanczos method is a technique for yielding Pad'e approximants which has several advantages over more traditional explicit moment matching approaches. An extension ..."
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Cited by 18 (1 self)
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The utility of Lanczos methods for the approximation of largescale dynamical systems is considered. In particular, it is shown that the Lanczos method is a technique for yielding Pad'e approximants which has several advantages over more traditional explicit moment matching approaches. An extension of the Lanczos algorithm is developed for computing multipoint Pad'e approximations of descriptor systems. Keywords: Dynamic system, Pad'e approximation, Lanczos algorithm, model reduction. 1. Introduction This paper explores the use of Lanczos techniques for the reducedorder modeling and simulation of largescale, SISO dynamical systems. One can define such a system through the set of state space equations ae E x(t) = Ax(t) + bu(t) y(t) = cx(t) + du(t): (1) The scalar functions u(t) and y(t) are the system's input and output while x(t) is the state vector of dimension n. For simplicity, the directcoupling term, d, will be assumed to be zero. The system matrix, A 2 R n\Thetan ...
Simulation of High Speed Digital Circuit Interconnection Networks
, 1993
"... The purpose of this research and the intent of this dissertation is to describe a comprehensive method for simulating interconnection structures in the realm of high speed digital systems. The method treats the distributed interconnection elements in the frequency domain (as admittance parameters) a ..."
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Cited by 1 (0 self)
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The purpose of this research and the intent of this dissertation is to describe a comprehensive method for simulating interconnection structures in the realm of high speed digital systems. The method treats the distributed interconnection elements in the frequency domain (as admittance parameters) and converts them to the time domain for transient analysis. Packaging parasitics are included in a manner that provides a natural bandlimit on the frequency domain terms, reducing aliasing problems without resorting to artificial filtering as used by other methods. A new matching network is introduced to limit the impulse response length of resulting time domain admittance parameters and the concept of thresholding is also introduced to limit the number of terms in the impulse response and thereby drastically reduce the computation time in the convolution stages of the...