A Fast Implementation for Passivity Enforcement of Hybrid Macromodels

The hybrid macromodels of high-speed digital systems fitted by the Modal Vector Fitting (MVF) approach have the advantages of accurate fitness and easy to be simulated with equivalent circuits, but the initial-built models may violate the system passivity in partial-band. To solve this problem, a method of passivity enforcement of hybrid macromodels based on modal components is presented. Firstly, it proposes a new formulation for the objective function, wherein the eigenpairs of the macromodel are included. The relative accuracy of the model is controlled with weighting by the eigenpairs in the process of the parameter perturbation. Then the relevant passivity constrain function is also discussed and united with the above objective function. According to the analysis of the equations set, it is essentially that the passivity compensation is equivalent to the solution of a least-square-based optimization problem, which is able to be solved using the analysis method. This proposed method can effectively enforce the passivity of hybrid macromodel and be satisfactory with arbitrary terminal conditions. Compared with the reported methods such as Residue Perturbation (RP) and Modal Perbation (MP), experimental results demonstrate that the presented method has a certain advantage on the model accuracy or computational efficiency.