Automatic Stage-form Circuit Reduction for Multistage Opamp Design Equation Generation

Abstract

An automatic stage-form circuit reduction method for multistage operational amplifiers (opamps) is proposed. A tool based on this method can reduce a multistage opamp into a condensed stage-form macromodel, from which design equations can be generated automatically by another existing symbolic program. The proposed model generation method is fully symbolic; namely, it does not make reference to any numerical device values with a circuit, hence it does not require circuit biasing and sizing at an early design stage. The parameters coming with the generated models are dominant-effect approximation of the stage-related characteristics of the original circuits and thus are visually readable for design reasoning. Compensations in the original circuits are extracted automatically and reserved in the macromodel circuits. The user of this tool is only required to input the circuit stage information by identifying several key devices in the original circuits. As design equations can also be automatically generated from stage-form macromodels by a purely symbolic method, the proposed model generation method completes the path from a transistor-level opamp circuit to its characteristic design equations in a completely formal way. Examples are provided to demonstrate the effectiveness of the proposed model generation method, and numerical validation is further carried out to verify that the reduced symbolic models can successfully capture the key circuit behavior in the frequency domain for multistage opamps.