No abstract

SUMMARYA new complete approach to the multiport formulation of the state-space equations of uniquely solvable regular or strictly topologically degenerate linear lumped time-invariant networks is presented. It is based on a Gedankenexperiment during which the topological structure of the original network is manipulated in various ways. The ÿnal method requires one to calculate the describing matrices of three homogeneous multiports (i.e. a capacitive, an inductive and a resistive one), which are obtained from the network of interest in a very simple manner. As a by-product, the equivalent partitioned network is also derived. As an example of application, the state-space equations of a fourth-order strictly topologically degenerate network are provided.

No abstract

The energy behavior of first-order linear lumped time-invariant one-ports is thoroughly investigated, starting from the definition of available energy introduced by Wyatt et al. in 1981 and exploiting the calculus of variations approach. First, all the extrema of the energy delivered from these components over finite time intervals are identified and evaluated. Then, available energy and passivity are inferred by comparing these results on the nonnegative time half-axis. The case of reducible one-ports, which is beyond the traditional criterion based on the theory of positive-real rational functions, is also treated. Two numerical circuital examples are used throughout this paper to illustrate the theoretical results obtained. Index Terms-Available energy, calculus of variations, passivity.

A rigorous and complete analysis of the inductive two-ports that are linear lumped time-invariant, duly-controlled and non-trivial, reciprocally coupled and passive is carried out. It is based on the use of the flux/current transmission matrix, which permits pursuing a straightforward unified investigation. It clarifies some important features concerning the perfect coupling mode of operation, and shows the existence of another mode of operation that in some sense is the counterpart of the perfect coupling one