Guaranteed passive parameterized model order reduction of the partial element equivalent circuit (PEEC) method

The decrease of IC feature size and the increase of operating frequencies require 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D electromagnetic methods. During the circuit synthesis of large-scale digital or analog applications, it is important to predict the response of the system under study as a function of design parameters, such as geometrical and substrate features, in addition to frequency (or time). Parameterized model order reduction (PMOR) methods become necessary to reduce large systems of equations with respect to frequency and other design parameters. We propose an innovative PMOR technique applicable to PEEC analysis, which combines traditional passivity-preserving model order reduction methods and positive interpolation schemes. It is able to provide parametric reduced-order models, stable, and passive by construction over a user-defined range of design parameter values. Numerical examples validate the proposed approach

Stability-preserving model order reduction for nonlinear time delay systems

Delay elements are needed to model physical, industrial and engineering systems as action and reaction always come with latency. In this paper, we present an algorithm to obtain the reduced-order models (ROMs) while preserving the stability of nonlinear time delay systems (TDSs), which are approximated first by the piecewise-linear TDSs. One contribution is the derivation of the input-output stability of piecewise-linear TDSs, for the first time. The other is the preservation of the input-output stability of the ROMs. The system matrices are obtained by the left projection matrix from the solution of linear matrix inequalities (LMIs) for the input-output stability test of the original piecewise-linear TDSs and the right projection matrix from matching the estimated moments. An application example then verifies the effectiveness of the proposed method.published_or_final_versio

Physics-based passivity-preserving parameterized model order reduction for PEEC circuit analysis

The decrease of integrated circuit feature size and the increase of operating frequencies require 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D electromagnetic methods, and model order reduction (MOR) methods have proven to be very effective in combating such high complexity. During the circuit synthesis of large-scale digital or analog applications, it is important to predict the response of the circuit under study as a function of design parameters such as geometrical and substrate features. Traditional MOR techniques perform order reduction only with respect to frequency, and therefore the computation of a new electromagnetic model and the corresponding reduced model are needed each time a design parameter is modified, reducing the CPU efficiency. Parameterized model order reduction (PMOR) methods become necessary to reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as geometrical layout or substrate characteristics. We propose a novel PMOR technique applicable to PEEC analysis which is based on a parameterization process of matrices generated by the PEEC method and the projection subspace generated by a passivity-preserving MOR method. The proposed PMOR technique guarantees overall stability and passivity of parameterized reduced order models over a user-defined range of design parameter values. Pertinent numerical examples validate the proposed PMOR approach

Steady-state matching and model reduction for systems of differential-algebraic equations

The problem of model reduction for nonlinear differential-algebraic systems is addressed using the notions of moment and of steady-state response. These notions are formally introduced for this class of systems and families of nonlinear differential-algebraic reduced order models achieving moment matching with additional properties are presented. Stronger results for the special class of linear singular systems are provided. Two simple examples illustrate the proposed technique

A moment-matching scheme for the passivity-preserving model order reduction of indefinite descriptor systems with possible polynomial parts

Passivity-preserving model order reduction (MOR) of descriptor systems (DSs) is highly desired in the simulation of VLSI interconnects and on-chip passives. One popular method is PRIMA, a Krylov-subspace projection approach which preserves the passivity of positive semidefinite (PSD) structured DSs. However, system passivity is not guaranteed by PRIMA when the system is indefinite. Furthermore, the possible polynomial parts of singular systems are normally not captured. For indefinite DSs, positive-real balanced truncation (PRBT) can generate passive reduced-order models (ROMs), whose main bottleneck lies in solving the dual expensive generalized algebraic Riccati equations (GAREs). This paper presents a novel moment-matching MORfor indefinite DSs, which preserves both the system passivity and, if present, also the improper polynomial part. This method only requires solving one GARE, therefore it is cheaper than existing PRBT schemes. On the other hand, the proposed algorithm is capable of preserving the passivity of indefinite DSs, which is not guaranteed by traditional moment-matching MORs. Examples are finally presented showing that our method is superior to PRIMA in terms of accuracy. ©2011 IEEE.published_or_final_versionThe 16th Asia and South Pacific Design Automation Conference (ASP-DAC 2011), Yokohama, Japan, 25-28 January 2011. In Proceedings of the 16th ASP-DAC, 2011, p. 49-54, paper 1C-

Stability-preserving model reduction for linear and nonlinear systems arising in analog circuit applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 221-229).Despite the increasing presence of RF and analog components in personal wireless electronics, such as mobile communication devices, the automated design and optimization of such systems is still an extremely challenging task. This is primarily due to the presence of both parasitic elements and highly nonlinear elements, which makes simulation computationally expensive and slow. The ability to generate parameterized reduced order models of analog systems could serve as a first step toward the automatic and accurate characterization of geometrically complex components and subcircuits, eventually enabling their synthesis and optimization. This thesis presents techniques for reduced order modeling of linear and nonlinear systems arising in analog applications. Emphasis is placed on developing techniques capable of preserving important system properties, such as stability, and parameter dependence in the reduced models. The first technique is a projection-based model reduction approach for linear systems aimed at generating stable and passive models from large linear systems described by indefinite, and possibly even mildly unstable, matrices. For such systems, existing techniques are either prohibitively computationally expensive or incapable of guaranteeing stability and passivity. By forcing the reduced model to be described by definite matrices, we are able to derive a pair of stability constraints that are linear in terms of projection matrices.(cont.) These constraints can be used to formulate a semidefinite optimization problem whose solution is an optimal stabilizing projection framework. The second technique is a projection-based model reduction approach for highly nonlinear systems that is based on the trajectory piecewise linear (TPWL) method. Enforcing stability in nonlinear reduced models is an extremely difficult task that is typically ignored in most existing techniques. Our approach utilizes a new nonlinear projection in order to ensure stability in each of the local models used to describe the nonlinear reduced model. The TPWL approach is also extended to handle parameterized models, and a sensitivity-based training system is presented that allows us to efficiently select inputs and parameter values for training. Lastly, we present a system identification approach to model reduction for both linear and nonlinear systems. This approach utilizes given time-domain data, such as input/output samples generated from transient simulation, in order to identify a compact stable model that best fits the given data. Our procedure is based on minimization of a quantity referred to as the 'robust equation error', which, provided the model is incrementally stable, serves as up upper bound for a measure of the accuracy of the identified model termed 'linearized output error'. Minimization of this bound, subject to an incremental stability constraint, can be cast as a semidefinite optimization problem.by Bradley Neil Bond.Ph.D