Optimal design of a CMOS op-amp via geometric programming

Hershenson, M.delM.; Boyd, Stephen; Lee, T.H.

doi:10.1109/43.905671

Cited by 435 publications

(276 citation statements)

References 75 publications

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“…Geometric programming has been used in various fields since the late 1960s; early applications of geometric programming can be found in the books Avriel (1980), Duffin et al (1967), Zener (1971) and the survey papers Ecker (1980), Peterson (1976), Boyd et al (2007). More recent applications can be found in various fields including circuit design Chen et al 2000;Dawson et al 2001;Daems et al 2003;Hershenson 2002;Hershenson et al 2001;Mohan et al 2000;Sapatnekar 1996;Singh et al 2005;Sapatnekar et al 1993;Young et al 2001), chemical process control (Wall et al 1986), environment quality control (Greenberg 1995), resource allocation in communication systems (Dutta and Rama 1992), information theory (Chiang and Boyd 2004;Karlof and Chang 1997), power control of wireless communication networks (Kandukuri and Boyd 2002;O'Neill et al 2006), queue proportional scheduling in fading broadcast channels (Seong et al 2006), and statistics (Mazumdar and Jefferson 1983).…”

Section: Geometric Programmingmentioning

confidence: 99%

Tractable approximate robust geometric programming

2007

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The optimal solution of a geometric program (GP) can be sensitive to variations in the problem data. Robust geometric programming can systematically alleviate the sensitivity problem by explicitly incorporating a model of data uncertainty in a GP and optimizing for the worst-case scenario under this model. However, it is not known whether a general robust GP can be reformulated as a tractable optimization problem that interior-point or other algorithms can efficiently solve. In this paper we propose an approximation method that seeks a compromise between solution accuracy and computational efficiency.The method is based on approximating the robust GP as a robust linear program (LP), by replacing each nonlinear constraint function with a piecewise-linear (PWL) convex approximation. With a polyhedral or ellipsoidal description of the uncertain data, the resulting robust LP can be formulated as a standard convex optimization problem that interior-point methods can solve. The drawback of this basic method is that the number of terms in the PWL approximations required to obtain an acceptable approximation error can be very large. To overcome the "curse of dimensionality" that arises in directly approximating the nonlinear constraint functions in the original robust GP, we form a conservative approximation of the original robust GP, which contains only bivariate constraint functions. We show how to find globally optimal PWL approximations of these bivariate constraint functions.

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Section: Geometric Programmingmentioning

confidence: 99%

Tractable approximate robust geometric programming

2007

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“…The only disadvantage and limitation is that the design problem has to be carefully formatted first to make it suitable for the treatment of the geometric programming algorithm. However, all the above approaches are based on the assumption that the structures of the cell elements are relatively fixed and subject to no radical topology changes [9]. A multi-objective evolutionary algorithm approach is reported for automatic synthesis of topology and sizing of a MEMS 2-D meandering spring structure with desired stiffnesses in certain directions [10].…”

Section: Extensionsmentioning

confidence: 99%

System-Level Synthesis of MEMS via Genetic Programming and Bond Graphs

Fan

Seo

et al. 2003

Genetic and Evolutionary Computation — GECCO 2003

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Abstract. Initial results have been achieved for automatic synthesis of MEMS system-level lumped parameter models using genetic programming and bond graphs. This paper first discusses the necessity of narrowing the problem of MEMS synthesis into a certain specific application domain, e.g., RF MEM devices. Then the paper briefly introduces the flow of a structured MEMS design process and points out that system-level lumped-parameter model synthesis is the first step of the MEMS synthesis process. Bond graphs can be used to represent a system-level model of a MEM system. As an example, building blocks of RF MEM devices are selected carefully and their bond graph representations are obtained. After a proper and realizable function set to operate on that category of building blocks is defined, genetic programming can evolve both the topologies and parameters of corresponding RF MEM devices to meet predefined design specifications. Adaptive fitness definition is used to better direct the search process of genetic programming. Experimental results demonstrate the feasibility of the approach as a first step of an automated MEMS synthesis process. Some methods to extend the approach are also discussed.

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“…Previous works have been done in the field of analog design automation to enable fast design at the block level. Different strategies and approaches have been proposed during the evolution of analog design automation, such as simulation-based optimization [5,9,17], symbolic simulation [10], artificial intelligence [6], manually derived design equations [4,21], hierarchy and topology selection [11], geometric programming [12,16] and memetic algorithms [15]. The main difficulty encountered for wide spread usage of these tools is that they require appropriate modeling of both devices (technology dependent) and circuit topologies in order to achieve the design objectives in a reasonable processing time.…”

Section: Introductionmentioning

confidence: 99%