Showing papers on "Model order reduction published in 1999"

Passive multipoint moment matching model order reduction algorithm on multiport distributed interconnect networks

Abstract: In this paper, we introduce a general method of interconnect simulation based on distributed circuits. The algorithm is very efficient and consists of two main steps. In the first step, each distributed line is modeled by a finite order system with passivity preservation and multipoint moment matching of its input admittance/impedance matrix. In the second step, an Arnoldi-based congruence transform is applied to the network to form its reduced order model. The main feature of the algorithm is in its first step, where a passive multipoint moment matching model of a distributed line can be generated without any discretization of the line. We provide an integrated-congruence transform which can be directly applied to the partial differential equations of a distributed line and generate a passive finite order system as its model. We also provide an algorithm based on the L/sup 2/ Hilbert space theory so that exact moment matching at multiple points can be obtained, We demonstrate the accuracy of our method with examples and show the advantage of ours over conventional ones based on lumped circuit models.

Model order-reduction of RC(L) interconnect including variational analysis

Abstract: As interconnect feature sizes continue to scale to smaller dimensions, long interconnect can dominate the IC timing performance, but the interconnect parameter variations make it difficult to predict these dominant delay extremes. This paper presents a model order-reduction technique for RLC interconnect circuits that includes variational analysis to capture manufacturing variations. Matrix perturbation theory is combined with dominant-pole-analysis and Krylov-subspace-analysis methods to produce reduced-order models with direct inclusion of statistically independent manufacturing variations. The accuracy of the resulting variational reduced-order models is demonstrated on several industrial examples.

ENOR: model order reduction of RLC circuits using nodal equations for efficient factorization

Abstract: ENOR is an innovative way to produce provably-passive, reciprocal, and compact representations of RLC circuits. Beginning with the nodal equations, ENOR formulates recurrence relations for the moments that involve factorizing a symmetric, positive definite matrix; this contrasts with other RLC order reduction algorithms that require expensive LU factorization. It handles floating capacitors, inductor loops, and resistor links in a uniform way. It distinguishes between active and passive ports, does Gram-Schmidt orthogonalization on the fly, controls error in the time-domain. ENOR is a superbly simple, flexible, and well-conditioned algorithm for lightning reduction of mega-sized RLC trees, meshes, and coupled interconnects-all with excellent accuracy.

Electromagnetic model order reduction for system-level modeling

Abstract: Reduced-order modeling of an electromagnetic system is understood as the approximation of a continuous or discrete model of the system by one of substantially lower order, yet capable of capturing the electromagnetic behavior of the original one with sufficient engineering accuracy. Specific methodologies for model order reduction of distributed electromagnetic systems are discussed in this paper. It is shown that electromagnetic model order reduction enhances computational efficiency and, thus, facilitates system-level modeling and computer simulation of multifunctional systems. The proposed methodologies are demonstrated through applications to the reduced-order modeling of high-speed interconnects, electromagnetic waveguides, and microstrip antennas.

Passive closed-form transmission-line model for general-purpose circuit simulators

Abstract: A passive closed-form model for multiconductor lossy transmission line analysis is presented in this paper. The proposed model is suitable for inclusion in general-purpose circuit simulators and overcomes the mixed frequency/time simulation difficulties encountered during the transient analysis. In addition, the model can handle frequency-dependent line parameters. This method offers an efficient means to discretize transmission lines compared to the conventional lumped discretization, while preserving the passivity of the discrete model. Coefficients describing the discrete model are computed a priori and analytically, using closed-form Pade approximants of exponential matrices. Numerical examples are presented to demonstrate the validity of the proposed model and to illustrate its application to a variety of interconnect structures.

Practical considerations for passive reduction of RLC circuits

Abstract: Krylov space methods initiated a new era for RLC circuit model order reduction. Although theoretically well-founded, these algorithms can fail to produce useful results for some types of circuits. In particular, controlling accuracy and ensuring passivity are required to fully utilize these algorithms in practice. In this paper we propose a methodology for passive reduction of RLC circuits based on extensions of PRIMA, that is both broad and practical. This work is made possible by uncovering the algebraic connections between this passive model order reduction algorithm and other Krylov space methods. In addition, a convergence criteria based on an error measure for PRIMA is presented as a first step towards intelligent order selection schemes. With these extensions and error criterion, examples demonstrate that accurate approximations are possible well into the RF frequency range even with expansions about s=0.

A new discrete transmission line model for passive model order reduction and macromodeling of high-speed interconnections

Abstract: A new, computationally efficient, discrete model is presented for passive model order reduction of high-speed interconnections. The proposed discrete model is based on the use of the theory of compact finite differences for the development of the discrete approximation to the transmission line equations that govern wave propagation on the interconnections. Thus result in a discrete model that utilizes only a few unknowns per wavelength and yet provides highly accurate waveform resolution. In addition to improved computational efficiency, the generated discrete model is passive, and compatible with the passive reduced-order interconnect modeling algorithm (PRIMA), Thus, it is suitable for the development of passive reduced-order models of interconnection networks of high complexity. Numerical experiments from the simulation and model order reduction of coupled interconnections are used to illustrate the validity and efficiency of the proposed model.

Model order reduction of large circuits using balanced truncation

Abstract: A method is introduced for model order reduction of large circuits extracted from layout. The algorithm, which is based on balanced realization, can be used for reducing the order of circuits before circuit-level simulation. In contrast to Pade-based algorithms which match the reduced order system with original system in some given frequencies, balanced realization based model algorithms provide a nearly optimal matching over all frequencies. Hence the balanced realization method produces stable and more accurate results compared to the Pade-based algorithms for model reduction. In addition given an upper bound for error, it is possible to compute the minimum degree for the reduced order model a priori. A numerically efficient method for balanced truncation of large circuits using the Arnoldi algorithm is presented and experimental results are reported.

A new discrete transmission line model for passive model order reduction and macromodeling of high-speed interconnections

Abstract: A new, computationally efficient, discrete model is presented for passive model order reduction of high-speed interconnections. The proposed discrete model is based on the use of the theory of compact finite differences for the development of the discrete approximation to the transmission line equations that govern wave propagation on the interconnections. Thus result in a discrete model that utilizes only a few unknowns per wavelength and yet provides highly accurate waveform resolution. In addition to improved computational efficiency, the generated discrete model is passive, and compatible with the passive reduced-order interconnect modeling algorithm (PRIMA). Thus, it is suitable for the development of passive reduced-order models of interconnection networks of high complexity. Numerical experiments from the simulation and model order reduction of coupled interconnections are used to illustrate the validity and efficiency of the proposed model.

Passive SPICE-compatible models of dispersive interconnects

Abstract: In this paper, the modal network theory of the skin effect is used for the development of discrete models for dispersive, multiconductor interconnects compatible with passive model order reduction algorithms. With the introduction of properly defined auxiliary variables, a passive discrete form of Telegrapher's equations is obtained. The resulting discrete model is then used in conjunction with the passive reduced-order interconnect modeling algorithm (PRIMA) for the generation of low-order, multi-port macromodels for interconnection networks. Numerical examples are used to demonstrate the proposed methodology and the associated computer implementation.

Projective convolution: RLC model-order reduction using the impulse response

Abstract: Projective convolution (PC) is a provably passive and numerically well-conditioned model-order reduction technique for large RLC circuits including those with floating capacitors or inductor loops. Unlike moment-matching which operates in the frequency domain, PC is positioned squarely in the time domain: it matches the impulse response of a circuit by projecting with the Krylov space formed by solving the discretized differential equations of the circuit. PC gives excellent results for coupled lines, large RLC meshes, and clock trees.

Coupled noise estimation for distributed RC interconnect model

Abstract: With the increase in signal speed and the development of process technology, distributed RC line model is found to be more suitable for on-chip interconnects than lumped RC model, especially for interconnects around and below 0.25 /spl mu/m. In this paper, we first describe a new explicit form for crosstalk approximation for coupled RC lines. Then we introduce a novel passive model order reduction technique for distributed RC lines. These two parts serve as two steps in static noise analysis of full on-chip interconnect networks called pruning process and static analysis process.

Improving the efficiency of parasitic extraction and simulation of 3D interconnect models

Abstract: As VLSI circuit speeds and density continue to increase, the need for accurately modeling the effects of three-dimensional interconnects has become essential to accurate chip and system design. Since such models are commonly used inside standard circuit simulators for time or frequency domain computations, efficiency requirements imply that those models must be kept very compact without compromising accuracy. In this paper we describe a technique based on the combination of two model order reduction algorithms applied to an integral equation approach to efficiently generate accurate, yet low order models of the impedance of 3D interconnect structures. The models thus generated are amenable to direction inclusion in standard circuit simulators.

Passivity validation for numerically-generated electromagnetic macromodels

Abstract: The issue of passivity in the macromodeling of electromagnetic components and subsystems is examined. In particular, the way loss of passivity may occur during the numerical characterization of the component/subsystem is investigated in the context of discrete modeling methods. In addition, the way various types of model order reduction techniques impact the passivity of the generated macromodel is considered. Finally, ways to ensure passivity during the numerical modeling and macromodel generation of an electromagnetic subsystem are identified.

Singularly Perturbed Systems

Abstract: The sections in this article are 1 Time-Scale Properties of the Standard Model 2 Examples 3 Stability Analysis 4 Composite Feedback Control 5 Applications to Large Power Systems 6 Further Reading Keywords: two-time-scale systems; model order reduction; slow manifold; boundary layer; relaxation oscillation; multiple time scales; singular perturbation; stability properties under perturbations