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—This paper presents an implementation of a decoupled optimization technique for design of switching regulators using genetic algorithms (GAs). The optimization process entails the selection of component values in a switching regulator, in order to meet the static and dynamic requirements. Although the proposed method inherits characteristics of evolutionary computations that involve randomness, recombination, and survival of the fittest, it does not perform a whole-circuit optimization. Thus, intensive computations that are usually found in stochastic optimization techniques can be avoided. Similar to many design approaches for power electronics circuits, a regulator is decoupled into two components, namely the power conversion stage (PCS) and the feedback network (FN). The PCS is optimized with the required static characteristics, whilst the FN is optimized with the required static and dynamic behaviors of the whole system. Systematic optimization procedures will be described and the technique is illustrated with the design of a buck regulator with overcurrent protection. The predicted results are compared with the published results available in the literature and are verified with experimental measurements. Index Terms—Circuit optimization, circuit simulation, computer-aided design, genetic algorithms, power electronics. I.