Modified Half-Size Test Matrix for Robust Passivity Assessment of $S$ -Parameter Macromodels

This letter presents a modified algebraic passivity test to check if an S-parameter based macromodel with symmetric scattering matrix is passive or not. To construct the passivity test matrix, the inversion of another matrix is required that can possibly be singular. If this is the case, such methods will fail since they cannot be applied directly. This letter proposes an elegant solution to deal with this problem. The effectiveness of the approach is illustrated by two numerical examples.