Skip to Main Content
Reduced-order modeling of distributed structures for transient and steady-state circuit simulation transforms discrete frequency-domain network parameters to a set of rational functions. The models are ideally causal and passive with passivity being the most difficult property to assure, especially when the distributed structures incorporate propagation delay effects or the available network parameters have limited bandwidth. Small errors in the frequency-domain network parameters, or out-of-band assumptions, can yield models that result in unstable transient simulations. Here, an inverse singular value method is developed that imposes the smallest perturbation required to simultaneously modify the residues, poles, and coupling coefficients of the rational function-based model to achieve passivity. The process enables selection of the frequency ranges for which the model is required to be most accurate. The method is based on the observation that a macromodel is passive if the singular values of the scattering parameter matrix are less than unity at all frequencies.