Passive Reduced Order Macromodeling Based on Loewner Matrix Interpolation

This paper presents the modeling of high speed distributed networks characterized by S-parameters frequency data using the rational Krylov fitting (RKFIT) algorithm. Numerical examples illustrate the effectiveness of the method to compute stable rational approximation that fit given S-parameters data. In addition, it is shown that RKFIT has some advantages when compared to the well-established Vector Fitting (VF) method, such as more accurate fitting, less dependence on the choice of the initial poles of the algorithm, and faster convergence. Numerical examples are implemented using RKFIT and the results are compared with VF and the Loewner Matrix (LM) algorithm.

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“…. , A m b} (13) where q m ∈ P m is a polynomial with no roots in the spectrum of A and K m+1 is a Krylov subspace associated with A and b.…”

Section: Review Of the Rkfit Algorithmmentioning

confidence: 99%

“…However, unlike VF, which builds stable models by construction, LM models may not always be stable. To tackle this problem, in [13], the unstable part of the LM model is fitted using a low order polynomial, however this increases the error of the LM approximation.…”

Section: Introductionmentioning

confidence: 99%

Macromodeling High-Speed Circuit Data Using Rational Krylov Fitting Method

Sahouli

Dounavis

2021

Energies

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“…In VF with compression, samples H k are "compressed" with a singular value decomposition reducing the cost of the subsequent fitting [37] and passivity enforcement steps [63]. The Loewner method [52,46], which is an alternative to VF for the data-driven modeling of linear systems, was also shown to scale favorably with respect to the number of inputs and outputs. This class of techniques is the subject of chapter ?…”

Section: The Fast Vector Fitting Algorithmmentioning

confidence: 99%

Vector Fitting

Triverio

2019

Preprint

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We introduce the Vector Fitting algorithm for the creation of reduced-order models from the sampled response of a linear time-invariant system. This data-driven approach to reduction is particularly useful when the system under modeling is known only through experimental measurements. The theory behind Vector Fitting is presented for single-and multiple-input systems, together with numerical details, pseudocodes, and an open-source implementation. We discuss how the reduced model can be made stable and converted to a variety of forms for use in virtually any modeling context. Finally, we survey recent extensions of the Vector Fitting algorithm geared towards time-domain, parametric and distributed systems modeling. This work is a draft of the book chapter P. Triverio, "Vector Fitting" that will be part of the "Handbook on Model Order Reduction" edited by P.

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