Abstract: This dissertation shows that analog design problems can be formulated analytically and solved numerically, without sacrificing accuracy and reliability. More specifically, the thesis describes a methodology which contains two complementary components. The first component is a set of numerical algorithms for design exploration and optimization. The second component is a collection of circuit and device models, which are sufficiently accurate and efficient for automated circuit design in deep sub-micron technologies. This thesis presents an optimization technique which is a combination of a branch-and-bound algorithm and an interior-point algorithm. The technique is used to solve reversed geometric programs, a non-convex extension of geometric programming. The combined algorithm can handle highly non-linear problems encountered in optimizing analog circuits. A software framework implementing these algorithms has been developed and has been used for the design of a power-efficient pipelined analog-to-digital converter. The device models provide small-signal and large-signal characteristics in a form which fits into the reversed geometric programming framework. The MOS transistor models are based on existing charge-sheet models using continuous expressions valid from weak inversion to strong inversion. These design models can be fit to either simulation models or to measured device data. An approximation error smaller than 10% can be obtained over a wide range of bias conditions and transistor sizes for 0.18 μm and 0.13 μm CMOS technologies. The circuit models describe various analog blocks such as operational transconductance amplifiers, comparators, and switches, as well as their interaction, including the effect of the switch resistance on the settling time and the noise of switched-capacitor amplifiers. Simplified model equations are developed use mathematical techniques such as perturbation methods for differential equations. Finally, the methodology is illustrated using several examples: gain-bandwidth optimization of operational transconductance amplifiers, dynamic range optimization of integrated filters, power optimization of pipelined analog-to-digital converters, and the complete design of an analog-to-digital converter.