Black box modeling of passive systems by rational function approximation

As the operation frequency of integrated circuit chips increases, electromagnetic effects of interconnect and packaging structures are no longer negligible and have to be accurately modeled and incorporated into the simulation, which is a challenging issue when simulation speed and accuracy are both required for facilitating the integrated circuit design.;Electromagnetic effects of a passive system can be characterized by measurements or full-wave simulations in the frequency domain. The results are expressed either in the form of input-output responses of a multiport network with a large number of sampled data in frequency domain or in the form of a high-order state-space model. Neither form is compact enough to be incorporated into circuit simulation directly. Various model-order reduction approaches have been developed to generate lower-order macromodels for the latter case, but are not applicable for the former case where a state-space expression is not available.;An efficient black-box modeling approach is proposed to construct rational function macromodels from sampled frequency-domain system responses. Orthogonal polynomials are employed to overcome the ill-conditioning problem associated with the curve fitting procedure. The performance of different polynomials is investigated and compared. Causality and stability of the macromodel are ensured inherently by the proposed method. Passivity enforcement is also discussed.;The modified minimum phase, all pass, and delay (MAD) method for black-box modeling is proposed and validated. Using this method, a black-box system is modeled as three parts, a minimum phase subsystem, an all-pass subsystem, and a delay term. Since this model precisely capture the physical characteristics of complicated networks in a wide frequency range, it significantly improves both the modeling efficiency and accuracy compared to existing rational function approximation methods.