Design of pipeline analog-to-digital converters via geometric programming

In this paper we present a method for the design of analog-to-digital converters (ADCs). This method computes the sizes of the different components (transistors, capacitors, etc.) in a predefined ADC topology so that the design specifications are met in the desired process technology. The method is based on formulating the ADC design constraints such as specifications on power, signal-to-noise ratio (SNR), area, and sampling frequency in special convex form in terms of the component sizes of the ADC and intermediate design variables. More specifically, we cast the problem of sizing the components of the ADC as a geometric program. Therefore, all design constraints are formulated as polynomial inequality or monomial equality constraints. Very efficient numerical algorithms are then used to solve the resulting geometric program and to compute the component sizes of an ADC that meets the desired specifications. The synthesis method is fast, and determines the globally optimal design; in particular the final solution is completely independent of the starting point (which can even be infeasible), and infeasible specifications are unambiguously detected. This paper introduces the concept of hierarchical problem formulation within a geometric programming framework. This modular formulation allows a high re-use of the ADC polynomial model.