Inductor-capacitor one-ports and inverse eigenvalue problems

Abstract

The newly discovered canonicity theorem for LC one-ports, which states conditions for such one-ports to be able to realize arbitrary, positive-real-odd impedance functions with the minimum number of components, is shown to provide conditions for the existence of a solution to a special, inverse-eigenvalue problem for matrices. Certain recent results in matrix theory are proved to be particular solutions of this inverse-eigenvalue problem, and these solutions are then shown to provide new and independent canonicity proofs for the Foster and Cauer forms. The results derived herein may prove useful in developing numerical design methods for the general class of canonic LC one-ports.