A Systematic Method for the Passivity Enforcement of Delayed Rational Macromodels

In this paper, an efficient least squares norm based method for the passivity enforcement of delayed rational macromodels is presented. The least squares norm based method and the energy norm based method are described and compared. A new formulation for the objective function of energy norm type is also derived, which shows that least squares norm and energy norm are mathematically equivalent. This confirms two important ideas. First, both equality constraint and inequality constraint yield the same results. Second, the algorithms for these two norms based methods are interchangeable. Several examples show that the presented algorithm yield accurate passive macromodels in a limited simulation time.