A Novel Framework for Parametric Loewner Matrix Interpolation

Xiao, Yi Qing; Grivet-Talocia, S.; Manfredi, Paolo; Khazaka, Roni

doi:10.1109/tcpmt.2019.2948802

Cited by 12 publications

(14 citation statements)

References 45 publications

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“…The above procedure can be extended by requiring that the macromodel mimics the behavior of the structure for different configurations of a set of design or physical parameters, whose value is not fixed a priori but is known to belong to a prescribed set. In such a case, the network function data are sampled in correspondence of a finite number of parameters configurations, and a multivariate modeling strategy is pursued to obtain a parameterized macromodel that can replace the original structure for all of the parameters configurations of interest [11]- [15].…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Extraction of Uniformly Stable and Passive Parameterized Macromodels

et al. 2022

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A Robust algorithm for the extraction of reduced-order behavioral models from sampled frequency responses is proposed. The system under investigation can be any Linear and Time Invariant structure, although the main emphasis is on devices that are relevant for Signal and Power Integrity and RF design, such as electrical interconnects and integrated passive components. We assume that the device under modeling is parameterized by one or more design variables, which can be related to geometry or materials. Therefore, we seek for multivariate macromodels that reproduce the dynamic behavior over a predefined frequency band, with an explicit embedded dependence of the model equations on these external parameters. Such parameterized macromodels may be used to construct component libraries and prove very useful in fast system-level numerical simulations in time or frequency domain, including optimization, what-if, and sensitivity analysis. The main novel contribution is the formulation of a finite set of convex constraints that are applied during model identification, which provide sufficient conditions for uniform model stability and passivity throughout the parameter space. Such constraints are characterized by an explicit control allowing for a trade-off between model accuracy and runtime, thanks to some special properties of Bernstein polynomials. In summary, we solve the longstanding problem of multivariate stability and passivity enforcement in data-driven model order reduction, which insofar has been tackled only via either overconservative or heuristic and possibly unreliable methods.

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Section: Introductionmentioning

confidence: 99%

Data-Driven Extraction of Uniformly Stable and Passive Parameterized Macromodels

et al. 2022

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“…An original large‐scale circuit or system is first characterized, leading to some first‐principle description of its behavior. This can be in form of partial differential equations or integral equations (PDEs and IEs, e.g., as resulting from Maxwell full‐wave formulations), ordinary differential equations (ODEs) or differential algebraic equations (DAEs), the latter being the common choice in circuit formulations based on the modified nodal analysis (MNA), or even in terms of time‐ 6 or frequency‐domain sampled responses 7–12 . The latter situation occurs when only direct measurements are available or alternatively when a nonintrusive solver is used to retrieve the system responses.…”

Section: Introductionmentioning

confidence: 99%

“…This paper presents a novel dissipativity characterization of LTI models in parameterized descriptor form 12 . The proposed formulation extends spectral characterizations of nonparameterized models based on the associated Hamiltonian matrix 14,20 to the bivariate case, allowing dependence of the transfer function on one external parameter in addition to frequency.…”

Section: Introductionmentioning

confidence: 99%

“…formulations), ordinary differential equations (ODEs) or differential algebraic equations (DAEs), the latter being the common choice in circuit formulations based on the modified nodal analysis (MNA), or even in terms of time- 6 or frequency-domain sampled responses. [7][8][9][10][11][12] The latter situation occurs when only direct measurements are available or alternatively when a nonintrusive solver is used to retrieve the system responses. Irrespective of this first-principle characterization, a plethora of MOR techniques are available to derive compact models that approximate the input-output behavior of the system.…”

mentioning

confidence: 99%

“…This paper presents a novel dissipativity characterization of LTI models in parameterized descriptor form. 12 The proposed formulation extends spectral characterizations of nonparameterized models based on the associated Hamiltonian matrix 14,20 to the bivariate case, allowing dependence of the transfer function on one external parameter in addition to frequency. Based on an orthogonal polynomial parameterization, 32 the proposed method leads to an underdetermined multiparameter eigenvalue problem, 33 whose solutions provide the boundaries between locally active and locally dissipative regions.…”

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confidence: 99%

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On checking dissipativity of parameterized linear and time‐invariant circuits and systems

Zanco

Grivet-Talocia

2022

Circuit Theory & Apps

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A novel dissipativity characterization is proposed for linear time-invariant circuits and systems whose dynamic behavior depends on one external parameter. The proposed formulation extends to the parameterized case standard Hamiltonian-based algebraic dissipativity characterizations and is structured as an underdetermined multiparameter eigenvalue problem. Resulting from a polynomial parameterization, the proposed characterization leads to an effective set of algorithms that are able to determine the regions of local dissipativity and local activity in the frequency-parameter plane, which in turn can be exploited by dissipativity enforcement algorithms to produce uniformly passive models. The reference application of proposed technique is behavioral modeling of complex circuits or systems, whose dynamic behavior can be compressed into a low-order system through dedicated model order-reduction processes. Various examples ranging from integrated components to microstrip filters and networks are used to illustrate the proposed characterization.

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A mesh-free adaptive parametric macromodeling strategy with guaranteed stability

Zanco¹,

Grivet-Talocia²

2020

2020 International Symposium on Electromagnetic Compatibility - EMC EUROPE

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A Novel Framework for Parametric Loewner Matrix Interpolation

Cited by 12 publications

References 45 publications

Data-Driven Extraction of Uniformly Stable and Passive Parameterized Macromodels

Data-Driven Extraction of Uniformly Stable and Passive Parameterized Macromodels

On checking dissipativity of parameterized linear and time‐invariant circuits and systems

A mesh-free adaptive parametric macromodeling strategy with guaranteed stability

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