Luis Miguel Silveira

Guaranteed passive balancing transformations for model order reduction

The major concerns in state-of-the-art 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 guaranteed-passive models for systems with special internal structure, using numerically stable and efficient Krylov-subspace 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 TBR-like methods that generate guaranteed passive reduced models and in addition are applicable to state-space systems with arbitrary internal structure.

A convex programming approach for generating guaranteed passive approximations to tabulated frequency-data

In this paper, we present a methodology for generating guaranteed passive time-domain models of subsystems described by tabulated frequency-domain data obtained through measurement or through physical simulation. Such descriptions are commonly used to represent on- and off-chip interconnect effects, package parasitics, and passive devices common in high-frequency integrated circuit applications. The approach, which incorporates passivity constraints via convex optimization algorithms, is guaranteed to produce a passive-system 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 high-order models of data sets representing realistic, complicated multiinput, multioutput systems.

Efficient techniques for accurate modeling and simulation of substrate coupling in mixed-signal IC's

Industry trends aimed at integrating higher levels of circuit functionality have triggered a proliferation of mixed analog-digital systems. Magnified noise coupling through the common chip substrate has made the design and verification of such systems an increasingly difficult task. In this paper we present a fast eigendecomposition technique that accelerates operator application in BEM methods and avoids the dense-matrix storage while taking all of the substrate boundary effects into account explicitly. This technique can be used for accurate and efficient modeling of substrate coupling effects in mixed-signal integrated circuits.

Robust rational function approximation algorithm for model generation

The problem of computing rational function approximations to tabulated frequency data is of paramount importance in the modeling arena. In this paper, we present a method for generating a state space model from tabular data in the frequency domain that solves some of the numerical difficulties associated with the traditional fitting techniques used in linear least squares approximations. An extension to the MIMO case is also derived.

Poor man's TBR: a simple model reduction scheme

This paper presents a model reduction algorithm motivated by a connection between frequency domain projection methods and approximation of truncated balanced realizations. The method produces guaranteed passive models, has near-optimal error properties, is computationally simple to implement, contains error estimators, and can incorporate frequency weighting information in a straightforward manner. Examples are shown to prove that the method can outperform the standard order reduction techniques by providing similar accuracy with lower models or superior accuracy for the same size model.

Efficient frequency-domain modeling and circuit simulation of transmission lines

In this paper we describe an algorithm for efficient SPICE-level simulation of transmission lines with arbitrary scattering parameter descriptions. That is, the line can be represented in the form of a frequency-domain model or a table of measured frequency-domain data. Our approach initially uses a forced stable decade-by-decade l/sub 2/ minimization approach to construct a sum of rational functions approximation, but the approximation has dozens of poles and zeros. This unnecessarily high-order model is then reduced using a guaranteed stable model order reduction scheme based on balanced realizations. Once the reduced-order model is derived, it can be combined with the transmission lines inherent delay to generate an impulse response. Finally, following what is now a standard approach, the impulse response can be efficiently incorporated in a circuit simulator using recursive convolution. An example of a transmission line with skin-effect is examined to both demonstrate the effectiveness of the approach and to show its generality. >

Efficient reduced-order modeling of frequency-dependent coupling inductances associated with 3-D interconnect structures

Reduced-order modeling techniques are now commonly used to efficiently simulate circuits combined with interconnect, but generating reduced-order models from realistic 3-D structures has received less attention. In this paper we describe a Krylov-subspace based method for deriving reduced-order models directly from the 3-D magnetoquasistatic analysis program FASTHENRY. This new approach is no more expensive than computing an impedance matrix at a single frequency.<<ETX>>

Automatic generation of accurate circuit models of 3-D interconnect

In order to optimize high-speed systems, designers need tools that automatically generate reduced order SPICE compatible models from geometric descriptions of interconnect and packaging. In this paper, we consider structures small compared to a wavelength, and use a discretized integral formulation combined with an Arnoldi-based model-order reduction strategy to compute efficiently accurate reduced-order models from three-dimensional (3-D) structures. Several issues are addressed including: (1) formulation to insure passivity in the reduced-order models; (2) efficient reduction using preconditioned inner-loop iterative methods; (3) expansion about multiple s-domain points. Results are presented on several industrial examples to demonstrate the capabilities and speed of these new methods.

A convex programming approach to positive real rational approximation

As system integration evolves and tighter design constraints must be met, it becomes necessary to account for the non-ideal behavior of all the elements in a system. Certain devices common in high-frequency integrated circuit applications, such as spiral inductors, SAW filters, etc., are often described and studied in the frequency domain. Models take the form of frequency domain data obtained through measurement or through physical simulation. Usually the available data is sampled, incomplete, noisy, and covers only a finite range of the spectrum. In this paper we present a methodology for generating guaranteed passive time-domain models of frequency-described subsystems. The methodology presented is based on convex programming based algorithms for fixed denominator system identification. The algorithm is guaranteed to produce a passive system model that is optimal in the sense of having minimum weighted square error in the frequency band of interest over all models with a prescribed set of system poles. An incremental-fitting reformulation of the problem is also introduced that trades optimality for efficiency while still guaranteeing passivity. Results of the application of the proposed methodologies to the modeling of a variety of subsystems are presented and discussed.

Passive Constrained Rational Approximation Algorithm Using Nevanlinna-Pick Interpolation

As system integration evolves and tighter design constraints must be met, it becomes necessary to account for the non-ideal behavior of all the elements in a system. For high-speed digital, and microwave systems, it is increasingly important to model previously neglected frequency domain effects. In this paper, results from Nevanlinna-Pick interpolation theory are used to develop a bounded real matrix rational approximation algorithm. A method is presented that allows for the generation of guaranteed passive rational function models of passive systems by approximating their scattering parameter matrices. Since the order of the models may in some cases be high, an incremental fitting strategy is also proposed that allows for the generation of smaller models while still meeting the required passivity and accuracy requirements. Results of the application of the proposed method to several real-world examples are also shown.