Fast passivity enforcement of rational macromodels by perturbation of residue matrix eigenvalues

Residue perturbation (RP) is often used a means for enforcing passivity of rational models. One RP version combines a least squares problem with a constraints part and solves via quadratic programming (QP). A major difficulty is that commonly available QP solvers cannot utilize the problem sparsity, leading to lengthy computations. This paper proposes to take the eigenvalues of the residue matrices as free variables. This leads to a more compact problem and thus a fast computation (FRP). The resulting model error is found to be much smaller than when perturbing only the diagonal elements of the residue matrices. It is also shown how to combine the residue matrix eigenvalue perturbation with the recently developed modal perturbation approach (MP), leading to a fast version (FMP). The FMP/MP approaches have the additional advantage of retaining the relative accuracy of the admittance matrix eigenvalues.