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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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Symbolic determinant from a graph.
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Related In: Results  -  Collection


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alg2: Symbolic determinant from a graph.

Mentions: From these structures, nz + 1 nodes are created. The row and column fields are used to evaluate the sign by (2) as well as to determine which nodes are to be skipped. The graph is generated starting with a trivial node named 0 with term value of 1; then the multiplication of terms is codified as the depth in the graph, and nodes are linked accordingly. The algorithm to build the graph structure for the representation of /A/ is sketched by Algorithm 1. Algorithm 2 computes the expression for the determinant. That way, the graph associated to the determinant in (1) is shown in Figure 2.


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)

Symbolic determinant from a graph.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

alg2: Symbolic determinant from a graph.
Mentions: From these structures, nz + 1 nodes are created. The row and column fields are used to evaluate the sign by (2) as well as to determine which nodes are to be skipped. The graph is generated starting with a trivial node named 0 with term value of 1; then the multiplication of terms is codified as the depth in the graph, and nodes are linked accordingly. The algorithm to build the graph structure for the representation of /A/ is sketched by Algorithm 1. Algorithm 2 computes the expression for the determinant. That way, the graph associated to the determinant in (1) is shown in Figure 2.

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