Comparative Study of Convolution and Order Reduction Techniques for Blackbox Macromodeling Using Scattering Parameters

Schutt-Ainé, José E.; Goh, Patrick; Mekonnen, Yidnekachew S.; Tan, Jilin; Al‐Hawari, Feras; Liu, Ping; Dai, Wujiao

doi:10.1109/tcpmt.2011.2163308

Cited by 16 publications

(6 citation statements)

References 32 publications

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“…Convolution with an input function a ( p ) then gives

h false(p false) = (][, \sum_{k = 1}^{L} c_{k} δ false(p - k false)) * a false(p false) = \sum_{k = 1}^{L} c_{k} a false(p - k false)

which is the overall transient response. It has been shown that when S ‐parameters are used as the transfer function, the impulse response decays rapidly and most of the c k s will be negligibly small [4]. Thus, only a few points will need to be retained for an accurate solution.…”

Section: Fast S‐parameter Convolutionmentioning

confidence: 99%

“…Thus, only a few points will need to be retained for an accurate solution. Readers are referred to [4] for the full formulation.…”

Section: Fast S‐parameter Convolutionmentioning

confidence: 99%

“…Presently, the state-of-the-art on interconnect simulations relies on finding a macromodel, often in the form of a rational function, which is then used to speed up the time-domain convolution to obtain the overall transient response of the circuit [2,3]. However, recently, it has been shown that when S-parameters are used to represent the interconnects, taking a regular inverse fast Fourier transform (IFFT) and performing the convolution can be even faster, since the impulse response decays rapidly and thus only a small number of points needs to be retained in the convolution [4]. In this Letter, we show that this fast S-parameter convolution method can be further improved by first optimising the choice of reference impedance used in the S-parameters.…”

mentioning

confidence: 99%

“…which is the overall transient response. It has been shown that when S-parameters are used as the transfer function, the impulse response decays rapidly and most of the c k s will be negligibly small [4]. Thus, only a few points will need to be retained for an accurate solution.…”

mentioning

confidence: 99%

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Improving fast S ‐parameter convolution by optimising reference impedance

Goh¹,

Schutt-Ainé

2014

Electron. lett.

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A method to perform fast transient simulations of interconnects by modelling the impulse responses of the S-parameters as discrete impulses, and then retaining only those with significant magnitudes has recently been shown to be faster than the present state-of-the-art method of curve fitting to a rational function model. An improvement to the fast convolution method by first optimising the choice of reference impedance used in the dataset is proposed. The method is seen to yield computational savings while retaining the accuracy.Introduction: The increase in signal frequency in high-speed electronics has placed signal integrity analysis at the forefront of the design of modern devices. At the same time, an increase in the density and complexity of the interconnects has made their analysis more challenging [1]. Presently, the state-of-the-art on interconnect simulations relies on finding a macromodel, often in the form of a rational function, which is then used to speed up the time-domain convolution to obtain the overall transient response of the circuit [2, 3]. However, recently, it has been shown that when S-parameters are used to represent the interconnects, taking a regular inverse fast Fourier transform (IFFT) and performing the convolution can be even faster, since the impulse response decays rapidly and thus only a small number of points needs to be retained in the convolution [4]. In this Letter, we show that this fast S-parameter convolution method can be further improved by first optimising the choice of reference impedance used in the S-parameters.

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“…Convolution with an input function a ( p ) then gives

h false(p false) = (][, \sum_{k = 1}^{L} c_{k} δ false(p - k false)) * a false(p false) = \sum_{k = 1}^{L} c_{k} a false(p - k false)

Section: Fast S‐parameter Convolutionmentioning

confidence: 99%

“…Thus, only a few points will need to be retained for an accurate solution. Readers are referred to [4] for the full formulation.…”

Section: Fast S‐parameter Convolutionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Improving fast S ‐parameter convolution by optimising reference impedance

Goh¹,

Schutt-Ainé

2014

Electron. lett.

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“…The rational approximation for a passive system must also be passive; therefore, several methods such as those in Gustavsen and Semlyen, Saraswat, Grivet‐Talocia, Triverio et al, Gustavsen and Semlyen, Gustavsen, Hu et al are introduced to enforce the passivity of the generated model. Consequently, the produced poles and residues are used to define the state‐space equation that is needed to generate a time‐domain (TD) macromodel for the system. Such a model enables performing TD analysis of the system in SPICE like circuit simulators.…”

Section: Introductionmentioning

confidence: 99%

Automatic and multithreaded method for determining the number of vector fitting poles based on empirical data

Al‐Hawari

2018

Int J Numerical Modelling

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The vector fitting method has been largely used to generate accurate and passive time-domain macromodels for circuits or structures characterized by frequencydomain data such as scattering parameters. Nevertheless, very few approaches to determine the vector fitting order were discussed in the literature. In this paper, an iterative method to automatically identify the number of vector fitting poles is proposed. It can achieve acceptable performance and accuracy by capitalizing on the fact that the number of vector fitting poles lies in the range that spans the number of resonance peaks in the model and double that number as deduced from the empirical data that was acquired by experimentation on different types of models. Therefore, the algorithm's awareness of the frequency response of the model and confining the search for an acceptable order within the aforementioned range proved to be key factors to enable it to mostly outperform its MATLAB counterpart as shown in the experimental results. Furthermore, a multithreaded implementation of the proposed method is introduced to distribute the vector fitting passes on multicore processors in order to obtain a better speedup factor. The experiments that demonstrate the positive effect of the multithreaded version on performance are also presented.

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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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Comparative Study of Convolution and Order Reduction Techniques for Blackbox Macromodeling Using Scattering Parameters

Cited by 16 publications

References 32 publications

Improving fast S ‐parameter convolution by optimising reference impedance

Improving fast S ‐parameter convolution by optimising reference impedance

Automatic and multithreaded method for determining the number of vector fitting poles based on empirical data

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

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