An Efficient Algebraic Method for the Passivity Enforcement of Macromodels

In this paper, an efficient algebraic method for the passivity enforcement of macromodels is presented. The method is based on quadratic programming with equality constraint. The differences between equality constraint and conventional inequality constraint are discussed. Compared with the general quadratic programming-based method, where the passivity violations are compensated via numerical optimization, the presented method is based on the solution of sparse linear equations. With the special sparse structure of macromodels, the passivity compensation is equivalent to the solution of some small size linear equations. This gives large savings for CPU time and memory requirement. Several examples show that the presented method yields accurate passive macromodels in a limited simulation time.