A Perturbation Scheme for Passivity Verification and Enforcement of Parameterized Macromodels

This paper presents an algorithm for checking and enforcing passivity of behavioral reduced-order macromodels of LTI systems, whose frequency-domain (scattering) responses depend on external parameters. Such models, which are typically extracted from sampled input-output responses obtained from numerical solution of first-principle physical models, usually expressed as Partial Differential Equations, prove extremely useful in design flows, since they allow optimization, what-if or sensitivity analyses, and design centering. Starting from an implicit parameterization of both poles and residues of the model, as resulting from well-known model identification schemes based on the Generalized Sanathanan-Koerner iteration, we construct a parameter-dependent Skew-Hamiltonian/Hamiltonian matrix pencil. The iterative extraction of purely imaginary eigenvalues ot fhe pencil, combined with an adaptive sampling scheme in the parameter space, is able to identify all regions in the frequency-parameter plane where local passivity violations occur. Then, a singular value perturbation scheme is setup to iteratively correct the model coefficients, until all local passivity violations are eliminated. The final result is a corrected model, which is uniformly passive throughout the parameter range. Several numerical examples denomstrate the effectiveness of the proposed approach.Comment: Submitted to the IEEE Transactions on Components, Packaging and Manufacturing Technology on 13-Apr-201

Bivariate macromodeling with guaranteed uniform stability and passivity

This paper extends the well-established macromod- eling flows based on rational fitting and passivity enforcement to the bivariate case, where the model response depends on frequency and on some additional design parameter. We propose a black-box model identification algorithm that is able to guarantee uniform stability and passivity throughout the parameter range. The resulting models, which can be cast as parameterized SPICE subnetworks, may be used to construct parameterized component libraries for design optimization, what-if analyses and fast parametric sweeps in frequency or time domain

Wavelet-based numerical methods for the solution of the Nonuniform Multiconductor Transmission Lines

This work presents a new Time-Domain Space Expansion (TDSE) method for the numerical solution of the Nonuniform Multiconductor Transmission Lines (NMTL). This method is based on a weak formulation of the NMTL equations, which leads to a class of numerical schemes of different approximation order according to the particular choice of some trial and test functions. The core of this work is devoted to the definition of trial and test functions that can be used to produce accurate representations of the solution by keeping the computational effort as small as possible. It is shown that bases of wavelets are a good choice

A Multivariate Adaptive Sampling Scheme for Passivity Characterization of Parameterized Macromodels

We introduce a multivariate adaptive sampling algorithm for the passivity characterization of parameterized macromodels. The proposed approach builds on existing sampling methods based on adaptive frequency warping for tracking pole-induced variability of passivity metrics, which however are available only for univariate (non-parameterized) models. Here, we extend this approach to the more challenging parameterized setting, where model poles hence passivity violations depend on possibly several external parameters embedded in the macro-model. Numerical examples show excellent performance and speedup with respect to competing approaches

Passive Macromodeling: Theory and Applications

Offers an overview of state of the art passive macromodeling techniques with an emphasis on black-box approaches This book offers coverage of developments in linear macromodeling, with a focus on effective, proven methods. After starting with a definition of the fundamental properties that must characterize models of physical systems, the authors discuss several prominent passive macromodeling algorithms for lumped and distributed systems and compare them under accuracy, efficiency, and robustness standpoints. The book includes chapters with standard background material (such as linear time-invariant circuits and systems, basic discretization of field equations, state-space systems), as well as appendices collecting basic facts from linear algebra, optimization templates, and signals and transforms. The text also covers more technical and advanced topics, intended for the specialist, which may be skipped at first reading. Provides coverage of black-box passive macromodeling, an approach developed by the authors. Elaborates on main concepts and results in a mathematically precise way using easy-to-understand language. Illustrates macromodeling concepts through dedicated examples. Includes a comprehensive set of end-of-chapter problems and exercises. Passive Macromodeling: Theory and Applications serves as a reference for senior or graduate level courses in electrical engineering programs, and to engineers in the fields of numerical modeling, simulation, design, and optimization of electrical/electronic systems

Compact Parameterized Black-Box Modeling via Fourier-Rational Approximations

We present a novel black-box modeling approach for frequency responses that depend on additional parameters with periodic behavior. The methodology is appropriate for representing with compact low-order equivalent models the behavior of electromagnetic systems observed at well-defined ports and/or locations, including dependence on geometrical parameters with rotational symmetry. Examples can be polarization or incidence angles of a plane wave, or stirrer rotation in reverberation chambers. The proposed approach is based on fitting a Fourier-rational model to sampled frequency responses, where frequency dependence is represented through rational functions and parameter dependence through a Fourier series. Several examples from different applications are used to validate and demonstrate the approach

A rational polynomial chaos formulation for the uncertainty quantification of linear circuits in the frequency domain

This paper discusses the general form of the transfer functions of linear lumped circuits. It is shown that an arbitrary transfer function defined on such circuits has a functional dependence on individual circuit parameters that is rational, with multi-linear numerator and denominator. This result is then used to introduce a suitable model for the uncertainty quantification of this class of circuits, namely a rational polynomial chaos expansion in place of the conventional single expansion

On the Exactness of Rational Polynomial Chaos Formulation for the Uncertainty Quantification of Linear Circuits in the Frequency Domain

We discuss the general form of the transfer functions of linear lumped circuits. We show that an arbitrary transfer function defined on such circuits has a functional dependence on individual circuit parameters that is rational, with multi-linear numerator and denominator. This result demonstrates that rational polynomial chaos expansions provide more suitable models than standard polynomial chaos for the uncertainty quantification of this class of circuits