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ReducedOrder modeling of large passive linear circuits by means of the SyPVL algorithm
 in Tech. Dig. 1996 IEEE/ACM International Conference on ComputerAided Design
, 1996
"... This paper discusses the analysis of large linear electrical networks consisting of passive components, such as resistors, capacitors, inductors, and transformers. Such networks admit a symmetric formulation of their circuit equations. We introduce SyPVL, an eficient and numerically stable algorit ..."
Abstract

Cited by 42 (14 self)
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This paper discusses the analysis of large linear electrical networks consisting of passive components, such as resistors, capacitors, inductors, and transformers. Such networks admit a symmetric formulation of their circuit equations. We introduce SyPVL, an eficient and numerically stable algorithm for the computation of reducedorder models of large, linear, passive networks. SyPVL represents the specialization of the more general PVL algorithm, to symmetric problems. Besides the gain in eficiency over PVL, SyPVL also preserves the symmetry of the problem, and, as a consequence, can often guarantee the stability of the resulting reducedorder models. Moreover, these reducedorder models can be synthesized as actual physical circuits, thus facilitating compatibility with existing analysis tools. The application of SyPVL is illustrated with two interconnectanalysis examples. 1
PadÃ© 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 ...
SmallSignal Circuit Analysis and Sensitivity Computations with the PVL Algorithm
 IEEE Trans. Circuits and SystemsII: Analog and Digital Signal Processing
, 1996
"... . We describe the application of the PVL algorithm to the smallsignal analysis of circuits, including sensitivity computations. The PVL algorithm is based on the efficient computation of the Pad'e approximation of the network transfer function via the Lanczos process. The numerical stability of the ..."
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Cited by 16 (6 self)
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. We describe the application of the PVL algorithm to the smallsignal analysis of circuits, including sensitivity computations. The PVL algorithm is based on the efficient computation of the Pad'e approximation of the network transfer function via the Lanczos process. The numerical stability of the algorithm permits the computation of the Pad'e approximation to any accuracy over a certain frequency range. We extend the algorithm to compute sensitivities of network transfer functions, their poles, and their zeros, with respect to arbitrary circuit parameters, with minimal additional computational cost. We demonstrate the implementation of our algorithm on circuit examples. 1 Introduction The process of analyzing analog circuits with full accounting of parasitic elements, interconnect analysis at the board or chip level, and numerous other circuitsimulation tasks often require the analysis of large linear networks. These networks can become extremely large, especially when circuits ar...
On some modifications of the Lanczos algorithm and the relation with PadÃ© approximations
, 1995
"... In this paper we try to show the relations between the Lanczos algorithm and Pad'e approximations as used e.g. in identification and model reduction of dynamical systems. 1 1 Introduction For simplicity we assume here that all systems are SISO, although some results do extend to the MIMO case. Let ..."
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Cited by 5 (0 self)
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In this paper we try to show the relations between the Lanczos algorithm and Pad'e approximations as used e.g. in identification and model reduction of dynamical systems. 1 1 Introduction For simplicity we assume here that all systems are SISO, although some results do extend to the MIMO case. Let a nth order dynamical system be described by x = Ax + bu (1.1) y = cx + du (1.2) where A is a square, b is a column vector, c is a row vector, and d is a scalar. It is wellknown that the transfer function of this system : h(s) = c(sI \Gamma A) \Gamma1 b + d has a Taylor expansion around s = 1 that looks like : h(s) = d + cbs \Gamma1 + cAbs \Gamma2 + cA 2 bs \Gamma3 + cA 3 bs \Gamma4 + : : : The coefficients m \Gammai of the powers of s \Gammai satisfy thus m 0 = d ; m \Gammai = cA i\Gamma1 b ; i 1: For i 1 these are also called moments or Markov parameters of the system fA; b; cg. It follows already from the work of Hankel that the first 2n moments 1 To appea...
Asymptotic Waveform Evaluation via a Restarted Lanczos Method
 Appl. Math. Lett
, 1994
"... this paper, it will be demonstrated that a Pad'e approximation of the original circuit can be obtained without explicitly passing via the moments. Through the nonsymmetric Lanczos method [9, 14], one can realize the reducedorder system f ..."
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Cited by 2 (1 self)
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this paper, it will be demonstrated that a Pad'e approximation of the original circuit can be obtained without explicitly passing via the moments. Through the nonsymmetric Lanczos method [9, 14], one can realize the reducedorder system f