Passive Modeling of Interconnects Using Sum of Squares Partial Fraction Expansions

Vector fitting has been successfully applied for signal and power integrity design of interconnects and power distribution networks. It is based on a partial fraction expansion of rational functions, resulting in a well-conditioned algorithm applicable to large size problems. A major shortcoming of vector fitting is that the resulting model in many cases will not be passive. In this paper we introduce a sum-of-squares (SOS) partial fraction passivity enforcement algorithm for fitting residues of a passive network. We demonstrate that this new algorithm provides a necessary and sufficient condition for passivity enforcement of scalar networks.