Compressed Passive Macromodeling

Abstract

This paper presents an approach for the extraction of passive macromodels of large-scale interconnects from their frequency-domain scattering responses. Here, large-scale is intended both in terms of number of electrical interface ports and required dynamic model order. For such structures, standard approaches based on rational approximation via Vector Fitting and passivity enforcement via model perturbation may fail due to excessive computational requirements, both in terms of memory occupation and runtime. Our approach addresses this complexity by first reducing the redundancy in the raw scattering responses through a projection and approximation process based on a truncated Singular Value Decomposition. Then, we formulate a compressed rational fitting and passivity enforcement framework, that is able to obtain speedup factors up to 2-3 orders of magnitude with respect to standard approaches, with full control over the approximation errors. Numerical results on a large set of benchmark cases demonstrate the effectiveness of the proposed technique.

Vector Fitting

“…Several other ideas were proposed to increase VF scalability for large input and output counts. 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.…”

Passivity verification and enforcement—A review paper

“…Afterwards, in the novel works of previous studies, [16][17][18][19][20][21][23][24][25] notable extension with necessary modifications have been proposed for improving the performance and integration for different area of applications. Although passivity of VF algorithm has been ensured in Gustavsen and Semlyen 26,27 but in Olivadese and Grivet-Talocia, 28 it has been cited that due to the band limited nature of the practical data, beyond the measurement bandwidth where there is no fitting restriction to minimal errors in the frequency domain data, may end up in generating a nonpassive model. To alleviate the problem, substantial research efforts have been given to passivity verification and enforcement techniques in macromodeling community.…”

High-Performance Passive Macromodeling Algorithms for Parallel Computing Platforms

“…Two main attempts towards the reduction of this cost have been reported. In [13], a preprocessing data reduction step is applied to the samples (1), resulting in a small number ρ P 2 of frequency-dependent "basis" functions ϕ ν (ω k ). With a full control over the approximation error, each response Ĥi,j (ω k ) in the original dataset is expressed as a linear combination of these basis functions.…”

“…Therefore, a macromodel is obtained by applying VF to the reduced basis, with a cost reduction by a factor ρ/P 2 , plus an overhead due to the initial data compression stage. Full details on this procedure are available in [13].…”