| Model order reduction techniques are proposed to deal with the growing complexity of IC (integrated circuit) interconnect problems, ranging from simple RC trees to complex PEEC (Partial Element Equivalent Circuit) structures. Each type of problem requires specific adjustments in the model reduction methodology, however it is possible to outline the general requirements for use in practice. These include preservation of passivity, extension of accuracy and error control. The passivity property guarantees that the reduced order model will not yield unstable results when combined with other devices or macromodels. The accuracy extension allows models to be solved with only the necessary accuracy, hence optimal efficiency. Finally, an error measure is needed to determine the order of the approximation under certain accuracy and macromodel complexity constraints. In the following work a practical model order reduction algorithm which provides the three essential ingredients is presented. It is based on the passive reduced-order macromodeling algorithm (PRIMA). PRIMA is a double matrix projection framework that provides for robust model order reduction in terms of a proven convergence criterion. Problem specific cases ranging from simple RC circuits to circuits requiring multi point expansions are discussed and results are shown for such examples when analyzed in this framework. |
