How Affine Arithmetic Helps Beat Uncertainties in Electrical Systems


The ever-increasing impact of uncertainties in electronic circuits and systems is requiring the development of robust design tools capable of taking this inherent variability under consideration. Because of the computational inefficiency of repeated design trials, there was a growing demand for sensible simulation tools that can inherently and effectively capture the results of parameter variations on the system responses. To boost product performance, improve yield and scale back design price, it is particularly relevant for the designer to be ready to estimate worst-case responses. At intervals this framework, the article addresses the worst-case simulation of lumped and distributed electrical circuits. The application of interval-based methods, like interval analysis, Taylor models and affine arithmetic, is mentioned and compared. The article reviews in particular the appliance of the affine arithmetic to complex algebra and basic matrix operations for the numerical frequency-domain simulation. A comprehensive and unambiguous discussion appears of course to be missing within the out there literature. The affine arithmetic turns out to be correct and a lot of economical than traditional solutions based on Monte Carlo analysis. A choice of relevant examples, starting from linear lumped circuits to distributed transmission-line structures, is used to illustrate this technique.

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