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Stochastic modeling of nonlinear circuits via SPICE-compatible spectral equivalents

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Abstract
This paper presents a systematic approach for the statistical simulation of nonlinear networks with uncertain circuit elements. The proposed technique is based on spectral expansions of the elements' constitutive equations (I-V characteristics) into polynomial chaos series and applies to arbitrary circuit components, both linear and nonlinear. By application of a stochastic Galerkin method, the stochastic problem is cast in terms of an augmented set of deterministic constitutive equations relating the voltage and current spectral coefficients. These new equations are given a circuit interpretation in terms of equivalent models that can be readily implemented in SPICE-type simulators, as such allowing to take full advantage of existing algorithms and available built-in models for complex devices, like diodes and MOSFETs. The pertinent statistical information of the entire nonlinear network is retrieved via a single simulation. This approach is both accurate and efficient with respect to traditional techniques, such as Monte Carlo sampling. Application examples, including the analysis of a diode rectifier, a CMOS logic gate and a low-noise amplifier, validate the methodology and conclude the paper.
Keywords
UNCERTAINTY QUANTIFICATION, uncertainty, POLYNOMIAL CHAOS, Circuit design, circuit simulation, nonlinear circuits, polynomial chaos, SPICE, statistical analysis

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Citation

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MLA
Manfredi, Paolo, et al. “Stochastic Modeling of Nonlinear Circuits via SPICE-Compatible Spectral Equivalents.” IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, vol. 61, no. 7, 2014, pp. 2057–65, doi:10.1109/TCSI.2014.2304667.
APA
Manfredi, P., Vande Ginste, D., De Zutter, D., & Canavero, F. (2014). Stochastic modeling of nonlinear circuits via SPICE-compatible spectral equivalents. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 61(7), 2057–2065. https://doi.org/10.1109/TCSI.2014.2304667
Chicago author-date
Manfredi, Paolo, Dries Vande Ginste, Daniël De Zutter, and Flavio Canavero. 2014. “Stochastic Modeling of Nonlinear Circuits via SPICE-Compatible Spectral Equivalents.” IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 61 (7): 2057–65. https://doi.org/10.1109/TCSI.2014.2304667.
Chicago author-date (all authors)
Manfredi, Paolo, Dries Vande Ginste, Daniël De Zutter, and Flavio Canavero. 2014. “Stochastic Modeling of Nonlinear Circuits via SPICE-Compatible Spectral Equivalents.” IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 61 (7): 2057–2065. doi:10.1109/TCSI.2014.2304667.
Vancouver
1.
Manfredi P, Vande Ginste D, De Zutter D, Canavero F. Stochastic modeling of nonlinear circuits via SPICE-compatible spectral equivalents. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS. 2014;61(7):2057–65.
IEEE
[1]
P. Manfredi, D. Vande Ginste, D. De Zutter, and F. Canavero, “Stochastic modeling of nonlinear circuits via SPICE-compatible spectral equivalents,” IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, vol. 61, no. 7, pp. 2057–2065, 2014.
@article{5697417,
  abstract     = {{This paper presents a systematic approach for the statistical simulation of nonlinear networks with uncertain circuit elements. The proposed technique is based on spectral expansions of the elements' constitutive equations (I-V characteristics) into polynomial chaos series and applies to arbitrary circuit components, both linear and nonlinear. By application of a stochastic Galerkin method, the stochastic problem is cast in terms of an augmented set of deterministic constitutive equations relating the voltage and current spectral coefficients. These new equations are given a circuit interpretation in terms of equivalent models that can be readily implemented in SPICE-type simulators, as such allowing to take full advantage of existing algorithms and available built-in models for complex devices, like diodes and MOSFETs. The pertinent statistical information of the entire nonlinear network is retrieved via a single simulation. This approach is both accurate and efficient with respect to traditional techniques, such as Monte Carlo sampling. Application examples, including the analysis of a diode rectifier, a CMOS logic gate and a low-noise amplifier, validate the methodology and conclude the paper.}},
  author       = {{Manfredi, Paolo and Vande Ginste, Dries and De Zutter, Daniël and Canavero, Flavio}},
  issn         = {{1549-8328}},
  journal      = {{IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS}},
  keywords     = {{UNCERTAINTY QUANTIFICATION,uncertainty,POLYNOMIAL CHAOS,Circuit design,circuit simulation,nonlinear circuits,polynomial chaos,SPICE,statistical analysis}},
  language     = {{eng}},
  number       = {{7}},
  pages        = {{2057--2065}},
  title        = {{Stochastic modeling of nonlinear circuits via SPICE-compatible spectral equivalents}},
  url          = {{http://dx.doi.org/10.1109/TCSI.2014.2304667}},
  volume       = {{61}},
  year         = {{2014}},
}

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