The ellipsoidal technique for design centering and region approximation

Abdel-Malek, H.L.; Hassan, Ali

doi:10.1109/43.85738

Cited by 74 publications

(22 citation statements)

References 12 publications

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“…The polyhedral approximation technique (PAT) is implemented and the results are given in Table II and Figure 3. Also the results of the implementation of the single-cut ellipsoidal technique [7,13] are given in Table II and Figure 4, for comparison.…”

Section: A Two-section Transmission Line Transformermentioning

confidence: 99%

“…Numerical and practical examples are given in Section 4. The results are compared with those obtained by using the single-cut ellipsoidal technique [7,13]. …”

Section: Introductionmentioning

confidence: 98%

“…These methods are computationally expensive. Another group of methods treats the problem geometrically [7][8][9][10][11][12][13][14][15][16]. In this approach, the feasible region in the parameter space where the design specifications are satisfied is approximated assuming it to be convex and bounded.…”

Section: Introductionmentioning

confidence: 99%

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Design centering and polyhedral region approximation via parallel-cuts ellipsoidal technique

Hassan¹,

Abdel-Malek²,

Rabie³

2004

Engineering Optimization

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A new technique for constructing a polyhedral approximation of the feasible region and finding the associated design center through a parallel-cuts ellipsoidal technique is presented. The linearizations of the feasible region boundary required to implement the parallel-cuts ellipsoidal technique are saved from one iteration to another in a non-redundant form. These linearizations are used in the construction of the parallel cuts as well as in the generation of an exterior polyhedral approximation of the feasible region at no additional cost. Numerical and practical examples are given to demonstrate the effectiveness of the new technique.

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Section: A Two-section Transmission Line Transformermentioning

confidence: 99%

“…Numerical and practical examples are given in Section 4. The results are compared with those obtained by using the single-cut ellipsoidal technique [7,13]. …”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Design centering and polyhedral region approximation via parallel-cuts ellipsoidal technique

Hassan¹,

Abdel-Malek²,

Rabie³

2004

Engineering Optimization

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“…Therefore, there is a fair chance of very low yield due to process variation. To avoid this consequence, design centering method [23,24] for yield improvement has been incorporated in the proposed ISGP based technique.…”

Section: Practical Aspects Considered In Isgpmentioning

confidence: 99%

ISGP: Iterative sequential geometric programming for precise and robust CMOS analog circuit sizing

Kundu

Mandal

2014

Integration

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“…The problem of seeking nominal parameter values x 0 that maximize the yield is usually known as design centering (Abdel-Malek and Hassan 1991, Antreich et al 1994, Sapatnekar et al 1994, Abdel-Malek et al 1999, Hassan et al 2004, Wojciechowski et al 2004). This problem can be formulated as the unconstrained maximization problem…”

Section: Introductionmentioning

confidence: 99%

Non-derivative design centering algorithm using trust region optimization and variance reduction

Hassan

Abdel-Malek

Rabie

2006

Engineering Optimization

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Fluctuations in manufactured integrated circuit parameters may dramatically reduce the parametric yield. Yield maximization can be formulated as an unconstrained optimization problem in nominal parameter values, which is known as design centering. The high expense of yield evaluations, the absence of any gradient information, and the presence of some numerical noise obstruct the use of the traditional derivative-based optimization methods. In this article, a novel design centering algorithm is presented, which consists of a non-derivative unconstrained optimizer coupled with a variance reduction estimator. The used optimizer combines a trust region mechanism with quadratic interpolation and provides efficient use of yield evaluations. The stratified sampling technique is used to develop a lower variance yield estimator that reduces the number of circuit simulations required to reach a desired accuracy level. Numerical and practical circuit examples are used to demonstrate the efficiency of the proposed algorithm with respect to other methods in the same field.

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The ellipsoidal technique for design centering and region approximation

Cited by 74 publications

References 12 publications

Design centering and polyhedral region approximation via parallel-cuts ellipsoidal technique

Design centering and polyhedral region approximation via parallel-cuts ellipsoidal technique

ISGP: Iterative sequential geometric programming for precise and robust CMOS analog circuit sizing

Non-derivative design centering algorithm using trust region optimization and variance reduction

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