On the Generation of Large Passive Macromodels for Complex Interconnect Structures

Abstract

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.

Numerical modeling of a linear photonic system for accurate and efficient time-domain simulations

“…Then, the rational model (2) can be transformed to state-space form by a simple rearrangement [17,21] …”

“…In particular, A is a diagonal matrix with all the poles as diagonal elements while C contains all the residues, and they can be always converted to real matrices as long as the poles and residues are real or complex conjugate pairs [17]. Now, it is straightforward to convert (3) to an equivalent state-space representation in the time domain [21] as…”

“…Note that the eigenvalues of (22) can be obtained directly from the eigenvalues of the corresponding bandpass system (21). According to (17), by replacing l , B l ,Ĉ l ,D l in (22) witĥ…”

Spectral characterization and enforcement of negative imaginariness for descriptor systems

“…We will give a more detailed motivation and explanation in mathematical terms in Section 4. There is a huge list of papers concerning restoring dissipativity of dynamical systems such as [20,21,43] and more recently [10]. All of them rely on perturbing certain eigenvalues of Hamiltonian matrices or even matrix pencils.…”

“…All of them rely on perturbing certain eigenvalues of Hamiltonian matrices or even matrix pencils. The paper [33] about the restoration of the negative imaginary property is also based on [20,21]. In our paper we will adapt this strategy for descriptor system using the eigenvalue characterization for even pencils.…”