Limits...
Graph-based symbolic technique and its application in the frequency response bound analysis of analog integrated circuits.

Tlelo-Cuautle E, Rodriguez-Chavez S, Palma-Rodriguez AA - ScientificWorldJournal (2014)

Bottom Line: The derived H(s) of a given analog IC is used to compute the frequency response bounds (maximum and minimum) associated to the magnitude and phase of H(s), subject to some ranges of process variational parameters, and by performing nonlinear constrained optimization.Our simulations demonstrate the usefulness of the new GBST for deriving the exact symbolic expression for H(s), and the last section highlights the good agreement between the frequency response bounds computed by our variational analysis approach versus traditional Monte Carlo simulations.As a conclusion, performing variational analysis using our proposed GBST for computing the frequency response bounds of analog ICs, shows a gain in computing time of 100x for a differential circuit topology and 50x for a 3-stage amplifier, compared to traditional Monte Carlo simulations.

View Article: PubMed Central - PubMed

Affiliation: INAOE, 72840 Tonantzintla, Puebla, PUE, Mexico.

ABSTRACT
A new graph-based symbolic technique (GBST) for deriving exact analytical expressions like the transfer function H(s) of an analog integrated circuit (IC), is introduced herein. The derived H(s) of a given analog IC is used to compute the frequency response bounds (maximum and minimum) associated to the magnitude and phase of H(s), subject to some ranges of process variational parameters, and by performing nonlinear constrained optimization. Our simulations demonstrate the usefulness of the new GBST for deriving the exact symbolic expression for H(s), and the last section highlights the good agreement between the frequency response bounds computed by our variational analysis approach versus traditional Monte Carlo simulations. As a conclusion, performing variational analysis using our proposed GBST for computing the frequency response bounds of analog ICs, shows a gain in computing time of 100x for a differential circuit topology and 50x for a 3-stage amplifier, compared to traditional Monte Carlo simulations.

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Transfer function description including parameter variations.
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fig5: Transfer function description including parameter variations.

Mentions: where Hl(ω) and Hu(ω) are the lower and upper bounds of the magnitude, respectively, and θl(ω) and θu(ω) are the lower and upper bounds of the phase. The evaluation of (7) gives a complex valued result, where the magnitude H(ω) = /H(jω)/ and the phase angle θ(ω) = ∠H(jω) are real values. The goal is to find the bounds of the magnitude and phase for H(jω), such that one can obtain (8). Henceforth, in the presence of process variations, the signal is perturbed from its nominal behavior, and it is usually bounded between its minimum and maximum limits, as sketched in Figure 5.


Graph-based symbolic technique and its application in the frequency response bound analysis of analog integrated circuits.

Tlelo-Cuautle E, Rodriguez-Chavez S, Palma-Rodriguez AA - ScientificWorldJournal (2014)

Transfer function description including parameter variations.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4127259&req=5

fig5: Transfer function description including parameter variations.
Mentions: where Hl(ω) and Hu(ω) are the lower and upper bounds of the magnitude, respectively, and θl(ω) and θu(ω) are the lower and upper bounds of the phase. The evaluation of (7) gives a complex valued result, where the magnitude H(ω) = /H(jω)/ and the phase angle θ(ω) = ∠H(jω) are real values. The goal is to find the bounds of the magnitude and phase for H(jω), such that one can obtain (8). Henceforth, in the presence of process variations, the signal is perturbed from its nominal behavior, and it is usually bounded between its minimum and maximum limits, as sketched in Figure 5.

Bottom Line: The derived H(s) of a given analog IC is used to compute the frequency response bounds (maximum and minimum) associated to the magnitude and phase of H(s), subject to some ranges of process variational parameters, and by performing nonlinear constrained optimization.Our simulations demonstrate the usefulness of the new GBST for deriving the exact symbolic expression for H(s), and the last section highlights the good agreement between the frequency response bounds computed by our variational analysis approach versus traditional Monte Carlo simulations.As a conclusion, performing variational analysis using our proposed GBST for computing the frequency response bounds of analog ICs, shows a gain in computing time of 100x for a differential circuit topology and 50x for a 3-stage amplifier, compared to traditional Monte Carlo simulations.

View Article: PubMed Central - PubMed

Affiliation: INAOE, 72840 Tonantzintla, Puebla, PUE, Mexico.

ABSTRACT
A new graph-based symbolic technique (GBST) for deriving exact analytical expressions like the transfer function H(s) of an analog integrated circuit (IC), is introduced herein. The derived H(s) of a given analog IC is used to compute the frequency response bounds (maximum and minimum) associated to the magnitude and phase of H(s), subject to some ranges of process variational parameters, and by performing nonlinear constrained optimization. Our simulations demonstrate the usefulness of the new GBST for deriving the exact symbolic expression for H(s), and the last section highlights the good agreement between the frequency response bounds computed by our variational analysis approach versus traditional Monte Carlo simulations. As a conclusion, performing variational analysis using our proposed GBST for computing the frequency response bounds of analog ICs, shows a gain in computing time of 100x for a differential circuit topology and 50x for a 3-stage amplifier, compared to traditional Monte Carlo simulations.

Show MeSH