The pseudo McMillan degree of implicit transfer functions of RLC networks

We study the structure of a given RLC network without sources. Since the McMillan degree of the implicit transfer function is not a suitable measure of complexity of the network, we introduce the pseudo McMillan degree to overcome these shortcomings.Using modified nodal analysis models, which are linked directly to the natural network topology, we shaw that the pseudo-McMillan degree equals the sum of the number of capacitors and inductors minus the number of fundamental loops of capacitors and fundamental cutsets of inductors; this is the number of independent dynamic elements in the network. Exploiting this representation we derive a minimal realization of the given RLC network, that is one where the number of independent differential equations equals the pseudo McMillan degree