Statistical modeling of frequency responses using linear Bayesian vector fitting

Ridder, S. De; Deschrijver, Dirk; Spina, Domenico; Ginste, Dries Vande; Dhaene, Tom

doi:10.1002/jnm.2762

Cited by 3 publications

(5 citation statements)

References 22 publications

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“…The proposed modeling framework is tested on a two microstrip devices: a pair of coupled transmission lines [3] and a folded-stub notch filter [10]. Their responses are computed using the settings in Table 1, via the simulator ADS Momentum [11].…”

Section: Resultsmentioning

confidence: 99%

Evaluation of Generative Modeling Techniques for Frequency Responses

Garbuglia

Spina

Deschrijver

et al. 2020

1st International Electronic Conference—Futuristic Applications on Electronics

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During microwave design, it is of practical interest to obtain insight in the statistical variability of a device’s frequency response with respect to several sources of variation. Unfortunately, the frequency response acquisition can be particularly time-consuming or expensive. This makes uncertainty quantification unfeasible when dealing with complex networks. Generative modeling techniques that are based on machine learning can reduce the computation load by learning the underlying stochastic process from few instances of the device response and generating new ones by executing an inexpensive sampling strategy. This way, an arbitrary number of frequency responses can be obtained that are drawn from a probability distribution that resembles the original one. The use of Gaussian Process Latent Variable Models (GP-LVM) and Variational Autoencoders (VAE) as modeling algorithms will be evaluated in a generative framework. The framework includes a Vector Fitting (VF) pre-processing step which guarantees stability and reciprocity of S-matrices by converting them into a suitable rational model. Both GP-LVM and VAE are tested on the S-parameter responses of two linear multi-port network examples.

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Section: Resultsmentioning

confidence: 99%

Evaluation of Generative Modeling Techniques for Frequency Responses

Garbuglia

Spina

Deschrijver

et al. 2020

1st International Electronic Conference—Futuristic Applications on Electronics

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“…Hence, the magnitude of S 11 is constant and equal to unity for all frequencies. However, as shown in Figure 7A, the magnitude of S 11 calculated from the input data by means of the RectSinc transformation shows a small progressive decay with respect the unitary value according to (9). This is the effect of the discretization at the input time step T IN for which the numerical derivative becomes a rectangular pulse instead of a Dirac delta, as it should be in the continuous time-domain.…”

Section: One-port Capacitormentioning

confidence: 94%

“…Hence, it is possible to express the RectSinc transformation in (9) by adopting a consistent notation with the DFT. From (9), it is also easy to verify that lim…”

Section: Spectrum Calculationmentioning

confidence: 95%

“…In the first case, it can be obtained through measurements of a vector network analyzer (VNA) or by numerical simulations using full-wave field or circuit solvers, while time-domain reflectometry (TDR/TDT) and transient field or circuit solvers can be adopted in the latter case. While there is a vast literature for macromodeling techniques using frequency-domain data, [1][2][3][4][5][6][7][8][9][10] only few techniques have been developed over the years for time-domain macromodeling. For example, the Time-Domain Vector Fitting (TD-VF) technique is introduced in References 11,12 for the identification of the dominant poles of the structure using raw data transient excitations and responses at the ports of the structure.…”

Section: Introductionmentioning

confidence: 99%

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Frequency domain behavior of S‐parameters piecewise‐linear fitting in a digital‐wave framework

Belforte¹,

Spina

Astorino

et al. 2021

Int J Numerical Modelling

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This paper describes PWLFIT+, an extension to the frequency domain of PWLFIT, a new paradigm in time‐domain macromodeling for linear multiport systems, based on a piecewise‐linear (PWL) behavioral representation of the S‐parameters step response. While the impulse response of each S‐parameter is approximated as sum of delayed rectangles (rect) functions, its spectrum is interpolated as sum of the corresponding delayed cardinal sine (sinc) functions. Exploiting this correspondence, the model building is performed by an iterative procedure where the PWL macromodels can be determined in order to meet defined accuracy goals on the spectrum. At runtime, waves at macromodels ports are calculated using the Segment Fast Convolution (SFC) algorithm within the Digital Wave Simulator (DWS) framework. The proposed method is characterized by its simplicity, stability, speed and scalability, all features that are emphasized when it is used in the DWS framework. After an analysis of the excellent numerical features of SFC in the Z‐domain, clearly differentiated with respect conventional macromodeling methods based on poles and residues, two suitable application examples are presented to demonstrate the unique features of PWLFIT+.

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“…The advantages of the method are demonstrated using optical components. De Ridder et al 5 address statistical modeling of frequency responses using linear Bayesian vector fitting. Finally, Hassan et al 6 present computationally efficient microwave design centering using space mapping and a trust‐region framework.…”

mentioning

confidence: 99%

Editorial for the special issue on advances in forward and inverse surrogate modeling for high‐frequency design

Koziel

Pietrenko‐Dabrowska

2020

Int J Numerical Modelling

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The design of modern-day high-frequency devices and circuits, including microwave/RF, antenna and photonic components, historically has relied on full-wave electromagnetic (EM) simulation tools. Initially used for design verification, EM simulations are nowadays used in the design process itself, for example, for finding optimum values of geometry and/or material parameters of the structures of interest. In a growing number of cases, EM-driven design closure is mandatory because alternative ways of evaluating the circuit performance (such as through equivalent network modeling) are grossly inaccurate and unable to account for cross-coupling effects (eg, in densely arranged layouts of compact circuits or antenna arrays), or various environmental components that affect the circuit performance (eg, connectors or housing for antenna structures). Despite being imperative, simulation-based design poses significant challenges, mostly due to the high computational cost of accurate, high-fidelity analysis. Repetitive simulations entailed by conventional optimization routines and even more by uncertainty quantification procedures (eg, Monte Carlo analysis) or toleranceaware design tasks may generate the costs that are unmanageable or at least impractical. The availability of massive computational resources does not always translate into design speedup due to the need to account for interactions between devices and their surroundings as well as multiphysics (eg, EM-thermal) effects. Not surprisingly, traditional design procedures that directly utilize EM-simulated responses often fail or are impractical. Alternatives to full-wave simulation tools, therefore, are increasingly popular among EM designers. Among the many available options, fast surrogate models that accurately capture the electrical characteristics of the components of interest, recently have received significant attention. Replacing or supplementing EM analysis by the surrogates enables execution of simulation-based design tasks at low computational cost. This is especially the case for data-driven (approximation) models, which are by far the most popular ones due to their versatility and widespread availability. Some broadly used methods include polynomial regression, kriging, radial basis function, neural networks, and polynomial chaos expansion. The practical issue here is nonlinearity of high-frequency component outputs, which along with the curse of dimensionality, hinders utilization of this class of techniques for multiparameter components. Physicsbased surrogates (eg, space mapping or various response correction methods) feature improved generalization capability at the expense of being problem specific: rendering the surrogate normally involves an underlying low-fidelity model, for example, equivalent network or coarse-mesh EM simulation. In addition to that, inverse modeling has been recently fostered as a practical alternative to forward models when solving certain types of design tasks, especially dimension scaling or high-frequency structures. The...

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Statistical modeling of frequency responses using linear Bayesian vector fitting

Cited by 3 publications

References 22 publications

Evaluation of Generative Modeling Techniques for Frequency Responses

Evaluation of Generative Modeling Techniques for Frequency Responses

Frequency domain behavior of S‐parameters piecewise‐linear fitting in a digital‐wave framework

Editorial for the special issue on advances in forward and inverse surrogate modeling for high‐frequency design

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