Addressing Load Sensitivity of Rational Macromodels

Behavioral models are effective tools used to relieve the computational burden of large-scale system-level simulations. In electrical and electronic applications, the Vector Fitting (VF) iteration often represents the algorithm of choice for generating low order equivalent circuits for complex multiport components in a data-driven setting. Although accurate and reliable in general, macromodels generated via VF are inherently represented in terms of a rational approximation of one specific input-output transfer function of the structure under modeling, e.g., its scattering matrix. However, accuracy in the scattering representation does not necessarily imply a good accuracy when solving the macromodel in a system-level setting, under different termination conditions. In fact, the sensitivity of the macromodel with respect to its loading conditions may be large and needs to be addressed and controlled. In this work, we present a modified VF scheme that overcomes this issue, by introducing in the rational approximation algorithm the requirement that the macromodel remains accurate when interconnected with a known class of admissible networks. The proposed formulation is based on an augmentation of the cost function minimized at each VF iteration; further, it does not require additional expensive data gathering steps when compared to standard approaches. The effectiveness of the scheme is tested over a set of relevant examples, in particular for Power Integrity applications.