Extended subspace identification of improper linear systems

The modeling of linear transfer functions is often required prior to the simulation of electronic systems. An example is the modeling of on-chip inductors starting from 2-port measurements. The modeling is often done using state-space models that can only represent proper systems. This leads to modeling problems in the case of improper systems such as in the case of 2-port modeling of the admittance matrix of an on-chip inductor. This paper first describes an extended state-space model to represent improper systems. Afterwards, the paper introduces an extension to classical frequency-domain subspace identification methods. The usefulness of both the extended state-space model and the extended subspace modeling technique are illustrated by comparing them with commercially available solutions. This includes a comparison on measurements of an on-chip inductor and on simulations of a coplanar waveguide.