Existing approaches for modeling mismatch effects in matching-critical circuits are based upon models derived under the widely accepted premise that distributed parameter devices can be modeled with lumped parameter models. It is shown in this dissertation that the lumped parameter models do not consistently reflect device performance and introduce substantial errors in matching-critical circuits if either systematic or random parameter variations occur in the channel. A new approach for characterizing the effects of both systematic and random variations in semiconductor device properties on device matching is introduced. This approach circumvents the introduction of model errors inherent in the existing approaches. A CAD tool, MOSGRAD, was developed to simulate the effects of distributed two-dimensional systematic and random variations in device parameters on the performance of matching-critical circuits. The tool is capable of predicting the performance of non-conventional circuit structures in which multiple drain and/or source regions that may or may not be rectangular and/or multiply segmented. Through the use of the tool, new current mirror layout strategies have been developed that exhibit reduced sensitivity to matching in the presence of linear parameter gradients.