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300
PRIMA: Passive Reducedorder Interconnect Macromodeling Algorithm
, 1997
"... This paper describes PRIMA, an algorithm for generating provably passive reduced order Nport models for RLC interconnect circuits. It is demonstrated that, in addition to requiring macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and pa ..."
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Cited by 402 (10 self)
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This paper describes PRIMA, an algorithm for generating provably passive reduced order Nport models for RLC interconnect circuits. It is demonstrated that, in addition to requiring macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. PRIMA extends the block Arnoldi technique to include guaranteed passivity. Moreover, it is empirically observed that the accuracy is superior to existing block Arnoldi methods. While the same passivity extension is not possible for MPVL, we observed comparable accuracy in the frequency domain for all examples considered. Additionally, a path tracing algorithm is used to calculate the reduced order macromodel with the utmost efficiency for generalized RLC interconnects.
A trajectory piecewiselinear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices
 in Proc. Int. Conf. ComputerAided Design
"... Abstract—In this paper, we present an approach to nonlinear model reduction based on representing a nonlinear system with a piecewiselinear system and then reducing each of the pieces with a Krylov projection. However, rather than approximating the individual components as piecewise linear and then ..."
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Cited by 128 (9 self)
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Abstract—In this paper, we present an approach to nonlinear model reduction based on representing a nonlinear system with a piecewiselinear system and then reducing each of the pieces with a Krylov projection. However, rather than approximating the individual components as piecewise linear and then composing hundreds of components to make a system with exponentially many different linear regions, we instead generate a small set of linearizations about the state trajectory which is the response to a “training input. ” Computational results and performance data are presented for an example of a micromachined switch and selected nonlinear circuits. These examples demonstrate that the macromodels obtained with the proposed reduction algorithm are significantly more accurate than models obtained with linear or recently developed quadratic reduction techniques. Also, we propose a procedure for a posteriori estimation of the simulation error, which may be used to determine the accuracy of the extracted trajectory piecewiselinear reducedorder models. Finally, it is shown that the proposed model order reduction technique is computationally inexpensive, and that the models can be constructed “on the fly, ” to accelerate simulation of the system response. Index Terms—Microelectromechanical systems (MEMS), model order reduction, nonlinear analog circuits, nonlinear dynamical systems, piecewiselinear models. I.
Reducedorder modeling of large linear subcircuits via a block Lanczos algorithm
 In Proc. 32nd ACM/IEEE Design Automation Conf
, 1995
"... A method for the e�cient computation of accu� rate reduced�order models of large linear circuits is de� scribed. The method � called MPVL � employs a novel block Lanczos algorithm to compute matrix Pad�e ap� proximations of matrix�valued network transfer func� tions. The reduced�order models � compu ..."
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Cited by 86 (21 self)
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A method for the e�cient computation of accu� rate reduced�order models of large linear circuits is de� scribed. The method � called MPVL � employs a novel block Lanczos algorithm to compute matrix Pad�e ap� proximations of matrix�valued network transfer func� tions. The reduced�order models � computed to the re� quired level of accuracy � are used tospeed up the anal� ysis of circuits containing large linear blocks. The lin� ear blocks are replaced by their reduced�order models� and the resulting smaller circuit can be analyzed with general�purpose simulators � with signi�cant savings in simulation time and � practically � no loss of accuracy. 1
A CoordinateTransformed Arnoldi Algorithm for Generating Guaranteed Stable ReducedOrder Models of RLC Circuits
, 1996
"... Since the first papers on asymptotic waveform evaluation (AWE), Padébased reducedorder models have become standard for improving coupled circuitinterconnect simulation efficiency. Such models can be accurately computed using biorthogonalization algorithms like Padé via Lanczos (PVL), but the res ..."
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Cited by 85 (20 self)
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Since the first papers on asymptotic waveform evaluation (AWE), Padébased reducedorder models have become standard for improving coupled circuitinterconnect simulation efficiency. Such models can be accurately computed using biorthogonalization algorithms like Padé via Lanczos (PVL), but the resulting Padé approximates can still be unstable even when generated from stable RLC circuits. For certain classes of RC circuits it has been shown that congruence transforms, like the Arnoldi algorithm, can generate guaranteed stable and passive reducedorder models. In this paper we present a computationally efficient modelorder reduction technique, the coordinatetransformed Arnoldi algorithm, and show that this method generates arbitrarily accurate and guaranteed stable reducedorder models for RLC circuits. Examples are presented which demonstrates the enhanced stability and efficiency of the new method.
A survey of model reduction methods for largescale systems
 Contemporary Mathematics
, 2001
"... An overview of model reduction methods and a comparison of the resulting algorithms is presented. These approaches are divided into two broad categories, namely SVD based and moment matching based methods. It turns out that the approximation error in the former case behaves better globally in freque ..."
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Cited by 84 (10 self)
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An overview of model reduction methods and a comparison of the resulting algorithms is presented. These approaches are divided into two broad categories, namely SVD based and moment matching based methods. It turns out that the approximation error in the former case behaves better globally in frequency while in the latter case the local behavior is better. 1 Introduction and problem statement Direct numerical simulation of dynamical systems has been an extremely successful means for studying complex physical phenomena. However, as more detail is included, the dimensionality of such simulations may increase to unmanageable levels of storage and computational requirements. One approach to overcoming this is through model reduction. The goal is to produce a low dimensional system that has
Interconnect design for deep submicron ICs
 IN PROC. INT. CONF. ON COMPUTER AIDED DESIGN
, 1997
"... Interconnect has become the dominating factor in determining circuit performance and reliability in deep submicron designs. In this embedded tutorial, we first discuss the trends and challenges of interconnect design as the technology feature size rapidly decreases towards below 0.1 micron. Then, we ..."
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Cited by 75 (22 self)
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Interconnect has become the dominating factor in determining circuit performance and reliability in deep submicron designs. In this embedded tutorial, we first discuss the trends and challenges of interconnect design as the technology feature size rapidly decreases towards below 0.1 micron. Then, we present commonly used interconnect models and a set of interconnect design and optimization techniques for improving interconnect performance and reliability. Finally, we present comparisons of different optimization techniques in terms of their efficiency and optimization results, and show the impact of these optimization techniques on interconnect performance in each technology generation from the 0.35µm to 0.07µm projected in the National Technology Roadmap for Semiconductors.
Efficient ReducedOrder Modeling of FrequencyDependent Coupling Inductances associated with 3D Interconnect Structures
, 1994
"... Reducedorder modeling techniques are now commonly used to efficiently simulate circuits combined with interconnect, but generating reducedorder models from realistic 3D structures has received less attention. In this paper we describe a Krylovsubspace based method for deriving reducedorder mode ..."
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Cited by 65 (13 self)
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Reducedorder modeling techniques are now commonly used to efficiently simulate circuits combined with interconnect, but generating reducedorder models from realistic 3D structures has received less attention. In this paper we describe a Krylovsubspace based method for deriving reducedorder models directly from the 3D magnetoquasistatic analysis program FastHenry. This new approach is no more expensive than computing an impedance matrix at a single frequency.
Approximation of largescale dynamical systems: An overview
, 2001
"... In this paper we review the state of affairs in the area of approximation of largescale systems. We distinguish among three basic categories, namely the SVDbased, the Krylovbased and the SVDKrylovbased approximation methods. The first two were developed independently of each other and have dist ..."
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Cited by 65 (3 self)
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In this paper we review the state of affairs in the area of approximation of largescale systems. We distinguish among three basic categories, namely the SVDbased, the Krylovbased and the SVDKrylovbased approximation methods. The first two were developed independently of each other and have distinct sets of attributes and drawbacks. The third approach seeks to combine the best attributes of the first two. Contents 1 Introduction and problem statement 1 2 Motivating Examples 3 3 Approximation methods 4 3.1 SVDbased approximation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.1 The Singular value decomposition: SVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.2 Proper Orthogonal Decomposition (POD) methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.3 Approximation by balanced truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
Reducedorder modeling techniques based on Krylov subspaces and their use in circuit simulation
 in Applied and Computational Control, Signals, and Circuits
, 1999
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Guaranteed Passive Balancing Transformations for Model Order Reduction
, 2002
"... The major concerns in stateoftheart model reduction algorithms are: achieving accurate models of sufficiently small size, numerically stable and efficient generation of the models, and preservation of system properties such as passivity. Algorithms such as PRIMA generate guaranteedpassive models ..."
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Cited by 61 (8 self)
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The major concerns in stateoftheart model reduction algorithms are: achieving accurate models of sufficiently small size, numerically stable and efficient generation of the models, and preservation of system properties such as passivity. Algorithms such as PRIMA generate guaranteedpassive models, for systems with special internal structure, using numerically stable and efficient Krylovsubspace iterations. Truncated Balanced Realization (TBR) algorithms, as used to date in the design automation community, can achieve smaller models with better error control, but do not necessarily preserve passivity. In this paper we show how to construct TBRlike methods that guarantee passive reduced models and in addition are applicable to statespace systems with arbitrary internal structure.