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

High-Performance Passive Macromodeling Algorithms for Parallel Computing Platforms

This paper presents a comprehensive strategy for fast generation of passive macromodels of linear devices and interconnects on parallel computing hardware. Starting from a raw characterization of the structure in terms of frequency-domain tabulated scattering responses, we perform a rational curve fitting and a postprocessing passivity enforcement. Both algorithms are parallelized and cast in a form that is suitable for deployment on shared-memory multicore platforms. Particular emphasis is placed on the passivity characterization step, which is performed using two complementary strategies. The first uses an iterative restarted and deflated rational Arnoldi process to extract the imaginary Hamiltonian eigenvalues associated with the model. The second is based on an accuracy-controlled adaptive sampling. Various parallelization strategies are discussed for both schemes, with particular care on load balancing between different computing threads and memory occupation. The resulting parallel macromodeling flow is demonstrated on a number of medium- and large-scale structures, showing good scalability up to 16 computational core

Numerical methods for rectangular multiparameter eigenvalue problems, with applications to finding optimal ARMA and LTI models

Standard multiparameter eigenvalue problems (MEPs) are systems of $k\ge 2$ linear $k$-parameter square matrix pencils. Recently, a new form of multiparameter eigenvalue problems has emerged: a rectangular MEP (RMEP) with only one multivariate rectangular matrix pencil, where we are looking for combinations of the parameters for which the rank of the pencil is not full. Applications include finding the optimal least squares autoregressive moving average (ARMA) model and the optimal least squares realization of autonomous linear time-invariant (LTI) dynamical system. For linear and polynomial RMEPs, we give the number of solutions and show how these problems can be solved numerically by a transformation into a standard MEP. For the transformation we provide new linearizations for quadratic multivariate matrix polynomials with a specific structure of monomials and consider mixed systems of rectangular and square multivariate matrix polynomials. This numerical approach seems computationally considerably more attractive than the block Macaulay method, the only other currently available numerical method for polynomial RMEPs.Comment: 26 page