Results 1  10
of
104
PRIMA: passive and reducedorder interconnect macromodeling algorithm
 IEEE Trans. CAD of Integrated Circuits and Systems
, 1998
"... Abstract—This paper describes an algorithm for generating provably passive reducedorder Nport models for RLC interconnect circuits. It is demonstrated that, in addition to macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive d ..."
Abstract

Cited by 396 (10 self)
 Add to MetaCart
(Show Context)
Abstract—This paper describes an algorithm for generating provably passive reducedorder Nport models for RLC interconnect circuits. It is demonstrated that, in addition to macromodel stability, macromodel passivity is needed to guarantee the overall circuit stability once the active and passive driver/load models are connected. The approach proposed here, PRIMA, is a general method for obtaining passive reducedorder macromodels for linear RLC systems. In this paper, PRIMA is demonstrated in terms of a simple implementation which extends the block Arnoldi technique to include guaranteed passivity while providing superior accuracy. While the same passivity extension is not possible for MPVL, comparable accuracy in the frequency domain for all examples is observed. I.
A note on the stochastic realization problem
 Hemisphere Publishing Corporation
, 1976
"... Abstract. Given a mean square continuous stochastic vector process y with stationary increments and a rational spectral density such that (oo) is finite and nonsingular, consider the problem of finding all minimal (wide sense) Markov representations (stochastic realizations) of y. All such realizati ..."
Abstract

Cited by 121 (24 self)
 Add to MetaCart
(Show Context)
Abstract. Given a mean square continuous stochastic vector process y with stationary increments and a rational spectral density such that (oo) is finite and nonsingular, consider the problem of finding all minimal (wide sense) Markov representations (stochastic realizations) of y. All such realizations are characterized and classified with respect to deterministic as well as probabilistic properties. It is shown that only certain realizations (internal stochastic realizations) can be determined from the given output process y. All others (external stochastic realizations)require that the probability space be extended with an exogeneous random component. A complete characterization of the sets of internal and external stochastic realizations is provided. It is shown that the state process of any internal stochastic realization can be expressed in terms of two steadystate KalmanBucy filters, one evolving forward in time over the infinite past and one backward over the infinite future. An algorithm is presented which generates families Of external realizations defined on the same probability space and totally ordered with respect to state covariances. 1. Introduction. One
Reducedorder modeling techniques based on Krylov subspaces and their use in circuit simulation,” Bell Laboratories
, 1998
"... ..."
(Show Context)
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 ..."
Abstract

Cited by 59 (8 self)
 Add to MetaCart
(Show Context)
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.
Algorithms for Model Reduction of Large Dynamical Systems
, 1999
"... Three algorithms for the model reduction of largescale, continuoustime, timeinvariant, linear, dynamical systems with a sparse or structured transition matrix and a small number of inputs and outputs are described. They rely on low rank approximations to the controllability and observability Gram ..."
Abstract

Cited by 49 (1 self)
 Add to MetaCart
Three algorithms for the model reduction of largescale, continuoustime, timeinvariant, linear, dynamical systems with a sparse or structured transition matrix and a small number of inputs and outputs are described. They rely on low rank approximations to the controllability and observability Gramians, which can eciently be computed by ADI based iterative low rank methods. The rst two model reduction methods are closely related to the wellknown square root method and Schur method, which are balanced truncation techniques. The third method is a heuristic, balancingfree technique. The performance of the model reduction algorithms is studied in numerical experiments.
Decay Bounds for Solutions of Lyapunov Equations: The Symmetric Case
, 1999
"... We present two new bounds for the eigenvalues of the solutions to a class of continuoustime and discretetime Lyapunov equations. These bounds hold for Lyapunov equations with symmetric coefficient matrices and righthand side matrices of low rank. They reflect the fast decay of the nonincreasingly ..."
Abstract

Cited by 43 (2 self)
 Add to MetaCart
We present two new bounds for the eigenvalues of the solutions to a class of continuoustime and discretetime Lyapunov equations. These bounds hold for Lyapunov equations with symmetric coefficient matrices and righthand side matrices of low rank. They reflect the fast decay of the nonincreasingly ordered eigenvalues of the solution matrix.
A convex programming approach for generating guaranteed passive approximations to tabulated frequencydata
 IEEE Trans. on ComputerAided Design of Integrated Circuits and Systems
, 2004
"... Abstract—In this paper,we present a methodology for generating guaranteed passive timedomain models of subsystems described by tabulated frequencydomain data obtained through measurement or through physical simulation. Such descriptions are commonly used to represent on and offchip interconnect ..."
Abstract

Cited by 31 (1 self)
 Add to MetaCart
(Show Context)
Abstract—In this paper,we present a methodology for generating guaranteed passive timedomain models of subsystems described by tabulated frequencydomain data obtained through measurement or through physical simulation. Such descriptions are commonly used to represent on and offchip interconnect effects,package parasitics,and passive devices common in highfrequency integrated circuit applications. The approach,which incorporates passivity constraints via convex optimization algorithms,is guaranteed to produce a passivesystem model that is optimal in the sense of having minimum error in the frequency band of interest over all models with a prescribed set of system poles. We demonstrate that this algorithm is computationally practical for generating accurate highorder models of data sets representing realistic, complicated multiinput,multioutput systems. Index Terms—Behavior modeling,convex optimization,convex programming,interconnect modeling,rational fitting,system identification. I.