We describe a new method for determining component values and transistor dimensions for CMOS operational ampli ers (op-amps). We observe that a wide variety of design objectives and constraints have a special form, i.e., they are posynomial functions of the design variables. As a result the ampli er design problem can be expressed as a special form of optimization problem called geometric programming, for which very e cient global optimization methods have been developed. As a consequence we can e ciently determine globally optimal ampli er designs, or globally optimal trade-o s among competing performance measures such aspower, open-loop gain, and bandwidth. Our method therefore yields completely automated synthesis of (globally) optimal CMOS ampli ers, directly from speci cations. In this paper we apply this method to a speci c, widely used operational ampli er architecture, showing in detail how to formulate the design problem as a geometric program. We compute globally optimal trade-o curves relating performance measures such as power dissipation, unity-gain bandwidth, and open-loop gain. We show how the method can be used to synthesize robust designs, i.e., designs guaranteed to meet the speci cations for a

Abstract: In this paper we first considered a maximum likelihood estimation of trip distribution problem and next use primal-dual geometric programming method the said trip distribution problem converted into an entropy maximization trip distribution problem. Here the generalized cost function is assumed in different form, and then the said formulation is equivalent to single or multi-objective entropy maximization trip distribution problem. We use fuzzy mathematical programming method to show this equivalent problem formulation. The present article we use the concept of multi-objective trip distribution problem.

c ○ Cambridge University Press 2004 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without

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c ○ Cambridge University Press 2004 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without

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Optimization of biotechnological systems through geometric programming