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

Automatic Synthesis of CMOS Digital/Analog Converters by Robert McKinstry Robinson Neff Doctor of Philosophy in Engineering -- Electrical Engineering and Computer Sciences University of California at Berkeley Professor Paul R. Gray, Chair Synthesis of analog functional blocks in integrated circuits offers promise for improved designer productivity. By developing module generators for commonly used analog circuit elements, a synthesis methodology may be matched to a particular application, with approaches and algorithms determined by the particular needs of target circuit type. An analog circuit designer should be able to input design specifications and underlying technology information, and a synthesis methodology should determine circuit parameter values and dimensions, creating the required mask layouts. Slow, tedious design and redesign methods should be replaced by one in which the computer finds minimum cost designs which meet performance requirements. This work implements synthesis methods for a widely used analog block, the digital/analog converter (DAC).

We present a method for optimizing and automating component and transistor sizing in CMOS operational amplifiers. We observe that a wide variety of performance measures can be formulated as posynomial functions of the design variables. As a result, amplifier design problems can be expressed as geometric programs, as special type of convex problems for which very efficient global optimization methods exist. A side benefit of using convex optimization is that a sensitivity analysis is obtained with the final solution with no additional computation. This information is of great interest to analog circuit designers. The method we present can be applied to a wide variety of amplifier architectures, but in this paper we apply the method to a specific two-stage amplifier architecture.