Passivity enforcement via perturbation of Hamiltonian matrices

By Stefano Grivet-Talocia. IEEE Transactions on Circuits and Systems Part 1: Regular Papers, 2004

382 citations recorded by the source corpus.

This paper presents a new technique for the passivity enforcement of linear time-invariant multiport systems in state-space form. This technique is based on a study of the spectral properties of related Hamiltonian matrices. The formulation is applicable in case the system input-output transfer function is in admittance, impedance, hybrid, or scattering form. A standard test for passivity is first performed by checking the existence of imaginary eigenvalues of the associated Hamiltonian matrix. In the presence of imaginary eigenvalues the system is not passive. In such a case, a new result based on first-order perturbation theory is presented for the precise characterization of the frequency bands where passivity violations occur. This characterization is then used for the design of an iterative perturbation scheme of the state matrices, aimed at the displacement of the imaginary eigenvalues of the Hamiltonian matrix. The result is an effective algorithm leading to the compensation of the passivity violations. This procedure is very efficient when the passivity violations are small, so that first-order perturbation is applicable. Several examples illustrate and validate the procedure.

Subfields: Astronomy and Astrophysics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/12308d0d0ccde5fad0e5d7344194cf99c0352145

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Citations in the corpus

Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations (2011, background): “The perturbation theory for structured generic low rank perturbations is dominated by two conflicting effects, the generic structured perturbation trying to destroy the most sensitive part in the Jordan structure (which is the largest Jordan block) and the structure which requires certain Jordan…”
Stability, Causality, and Passivity in Electrical Interconnect Models (2007, methodology): “The models for the “bad” dataset are also convergent, but a passivity check, here performed using [54], shows that also the models are nonpassive.”
Designing and Modeling for Power Integrity (2010, positive): “Fortunately, purely algebraic methods for checking (26c) are available, by means of the Hamiltonian matrix M associated with the model [57], [58].”
Passivity Enforcement With Relative Error Control (2007, methodology): “Detailed derivations can be found in [24].”
Transient analysis of lossy transmission lines: an efficient approach based on the method of Characteristics (2004, neutral): “, one of the procedures detailed in [3], [9], [10], [14], and [22].”
Overview of Signal Integrity and EMC Design Technologies on PCB: Fundamentals and Latest Progress (2013, background): “Approaches for passivity enforcement techniques of macromodeling have also been proposed based on linear or quadratic optimization [18]–[20] or Hamiltonian matrix perturbation [21], [22].”
Fast Passivity Enforcement for Pole-Residue Models by Perturbation of Residue Matrix Eigenvalues (2008, methodology): “fast approach is also achieved by the alternative RP approach in [19], which minimizes the change to the system impulse energy.”
An Adaptive Sampling Technique for Passivity Characterization and Enforcement of Large Interconnect Macromodels (2007, methodology): “[21] and [25] can only be applied to moderate-size macromodels with a reasonable computational cost.”
On the generation of large passive macromodels for complex interconnect structures (2006, positive): “However, the results in [21] and [23] show that a simple first-order perturbation analysis of the Hamiltonian eigenspectrum is sufficient for resolving this ambiguity.”
A Half-Size Singularity Test Matrix for Fast and Reliable Passivity Assessment of Rational Models (2010, background): “It has therefore become accepted practice to assess passivity via a particular Hamiltonian matrix, which is calculated directly from the parameters of the rational model [10], [11].”
A Comparative Study of Passivity Enforcement Schemes for Linear Lumped Macromodels (2008, positive): “926004 bounded real lemma (BRL) [15] constraints [19]–[21], methods for passivity enforcement at discrete frequency samples via linear or quadratic programming [18], [22]–[25], and Hamiltonian-based techniques [17], [26], [27].”