Fast passivity enforcement for pole-residue models by perturbation of residue matrix eigenvalues

Rational models must be passive in order to avoid unstable time domain simulations. This paper introduces a fast approach for passivity enforcement of pole-residue models. This is achieved by perturbing the eigenvalues of the residue matrices, as opposed to the existing approach of perturbing matrix elements. This leads to large savings in computation time with only a small increase of the modeling error. This fast residue perturbation (FRP) approach is merged with the Modal Perturbation technique, leading to fast modal perturbation (FMP). Usage of FMP over FRP achieves to retain the relative accuracy of the admittance matrix eigenvalues. A complete approach is obtained by combining the passivity enforcement step with passivity assessment via the Hamiltonian matrix eigenvalues and a robust iteration scheme, giving a guaranteed passive model. Application of FMP to a six-port power transformer shows that the approach is able to remove large out-of band passivity violations without corrupting the in-band behavior. This is shown to mitigate an unstable simulation. The approach is also demonstrated for a high-speed interconnect and a transmission line.