Passivity Enforcement for Admittance Models of Distributed Networks Using an Inverse Eigenvalue Method

Most transient circuit simulators are based on admittance representations of the constituent circuit elements. It is therefore natural to use admittance parameter descriptions of linear networks, preferably in the form of rational transfer functions that can be directly implemented in the analysis. A problem arises when the measured or calculated frequency-domain response of a linear distributed network must be derived from data that has inherent error, is of limited bandwidth, or is not in the appropriate rational form. A reduced-order rational model that is causal, stable, and passive must be developed. Previous methods of deriving rational functions for the admittance parameters of a network do guarantee stability and causality, but passivity of the model must be assured through subsequent post-processing. Enforcing passivity requires modification of the state-space parameters of the model with consequent introduction of errors. This paper reports on a procedure to simultaneously achieve passivity, accuracy, causality, and stability in the development of an admittance macromodel described using a matrix of rational functions. An iterative inverse eigenvalue algorithm enforces passivity, and is applied by conjoining sets of eigenvalue and admittance constraints. These constraints form a monolithic projection matrix, which simultaneously addresses both passivity and accuracy of the model.