On the Equivalence of Network Representations in Relation to Stability Analysis

The precise relations between number of RHP zeros and poles of the characteristic determinants in the three main representations (impedance, admittance and scattering) are derived. Given one inherently-stable representation, formulas are provided to predict the numbers of RHP zeros and poles of the characteristic determinants in the other representations. Finally, it is shown that, if at least one out the impedance and admittance representations fulfills the proviso, then some inherently-stable scattering representation also exists.