On the Generation of Large Passive Macromodels for Complex Interconnect Structures

This paper addresses some issues related to the passivity of interconnect macromodels computed from measured or simulated port responses. The generation of such macromodels is usually performed via suitable least squares fitting algorithms. When the number of ports and the dynamic order of the macromodel is large, the inclusion of passivity constraints in the fitting process is cumbersome and results in excessive computational and storage requirements. Therefore, we consider in this work a post-processing approach for passivity enforcement, aimed at the detection and compensation of passivity violations without compromising the model accuracy. Two complementary issues are addressed. First, we consider the enforcement of asymptotic passivity at high frequencies based on the perturbation of the direct coupling term in the transfer matrix. We show how potential problems may arise when off-band poles are present in the model. Second, the enforcement of uniform passivity throughout the entire frequency axis is performed via an iterative perturbation scheme on the purely imaginary eigenvalues of associated Hamiltonian matrices. A special formulation of this spectral perturbation using possibly large but sparse matrices allows the passivity compensation to be performed at a cost which scales only linearly with the order of the system. This formulation involves a restarted Arnoldi iteration combined with a complex frequency hopping algorithm for the selective computation of the imaginary eigenvalues to be perturbed. Some examples of interconnect models are used to illustrate the performance of the proposed technique

Weighting Strategies for Passivity Enforcement Schemes

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On the Generation of Large Passive Macromodels for Complex Interconnect Structures

This paper addresses some issues related to the passivity of interconnect macromodels computed from measured or simulated port responses. The generation of such macromodels is usually performed via suitable least squares fitting algorithms. When the number of ports and the dynamic order of the macromodel is large, the inclusion of passivity constraints in the fitting process is cumbersome and results in excessive computational and storage requirements. Therefore, we consider in this work a post-processing approach for passivity enforcement, aimed at the detection and compensation of passivity violations without compromising the model accuracy. Two complementary issues are addressed. First, we consider the enforcement of asymptotic passivity at high frequencies based on the perturbation of the direct coupling term in the transfer matrix. We show how potential problems may arise when off-band poles are present in the model. Second, the enforcement of uniform passivity throughout the entire frequency axis is performed via an iterative perturbation scheme on the purely imaginary eigenvalues of associated Hamiltonian matrices. A special formulation of this spectral perturbation using possibly large but sparse matrices allows the passivity compensation to be performed at a cost which scales only linearly with the order of the system. This formulation involves a restarted Arnoldi iteration combined with a complex frequency hopping algorithm for the selective computation of the imaginary eigenvalues to be perturbed. Some examples of interconnect models are used to illustrate the performance of the proposed techniques

An iterative reweighting process for macromodel extraction of power distribution networks

This paper introduces a new algorithm for the generation of optimal time-domain macromodels of power distribution networks, starting from a set of tabulated scattering responses and given a nominal termination scheme for active blocks, decoupling capacitors, and voltage regulator module. The new concept being introduced is a modified metric to characterize and optimize the accuracy of the macromodel, which takes into account the operation conditions that will be applied to run transient simulations for power integrity assessment. This metric is applied through an iterative frequency-dependent reweighting scheme in a fully automated flow. Two examples illustrate the performance of the proposed algorith

Tuning the accuracy of rational macromodels to nominal load conditions

We address the generation of broadband macromodels of complex linear systems via rational curve fitting. We show that standard approaches may not ensure that the macromodel accuracy is preserved in system-level simulations, under loading conditions that are different from the adopted identification settings. Our main contribution is an automated procedure for the definition of a frequency-dependent norm weighting strategy that tunes the macromodel accuracy for a specific nominal termination network, thus improving model robustness under realistic operation

Le Centenaire de Meyerbeer (30 novembre 1891)

Transcript of LE CENTENAIRE DE MEYERBEER signed "Ch. G.", appearing in L’ART MUSICAL, 30 novembre 1891, pp. 169-170