Kirchoff Law Markov Fields for Analog Circuit Design

Part of Advances in Neural Information Processing Systems 12 (NIPS 1999)

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Richard Golden


Three contributions to developing an algorithm for assisting engi(cid:173) neers in designing analog circuits are provided in this paper. First, a method for representing highly nonlinear and non-continuous analog circuits using Kirchoff current law potential functions within the context of a Markov field is described. Second, a relatively effi(cid:173) cient algorithm for optimizing the Markov field objective function is briefly described and the convergence proof is briefly sketched. And third, empirical results illustrating the strengths and limita(cid:173) tions of the approach are provided within the context of a JFET transistor design problem. The proposed algorithm generated a set of circuit components for the JFET circuit model that accurately generated the desired characteristic curves.

1 Analog circuit design using Markov random fields

1.1 Markov random field models

A Markov random field (MRF) is a generalization of the concept of a Markov chain. In a Markov field one begins with a set of random variables and a neighborhood re(cid:173) lation which is represented by a graph. Each random variable will be assumed in this paper to be a discrete random variable which takes on one of a finite number of possible values. Each node of the graph indexs a specific random variable. A link from the jth node to the ith node indicates that the conditional probability distribution of the ith random variable in the field is functionally dependent upon the jth random variable. That is, random variable j is a neighbor of random vari(cid:173) able i. The only restriction upon the definition of a Markov field (Le., the positivity condition) is that the probability of every realization of the field is strictly posi(cid:173) tive. The essential idea behind Markov field design is that one specifies a potential (energy) function for every clique in the neighborhood graph such that the subset of random variables associated with that clique obtain their optimal values when that clique'S potential function obtains its minimal value (for reviews see [1]-[2]) .

• Associate Professor at University of Texas at Dallas (www.utdallas.eduj-901den)