Black-box macromodeling and its EMC applications

The main idea of black-box macromodeling is to approximate the dynamic behavior of complex systems in terms of lowcomplexity models or equivalent circuits. Such compact models can be derived through robust numerical algorithms, such as the Vector Fitting scheme, starting from frequency- or time-domain responses of the system, and without any specific knowledge of its internal structure. The excellent accuracy that can be achieved, combined with the reduced size of the models, has led to a widespread adoption of this approach in several electrical and electronic applications, allowing designers to perform numerical simulations at the system level with high efficiency. This paper reviews the basics of black-box macromodeling and illustrates several application scenarios that are relevant for the EMC community, including Signal and Power Integrity, lossy transmission line modeling, electromagnetic full-wave simulation, network equivalencing and transformer modeling.