The Physical Meaning of Compactness

A lossless twoport N, whose impedances , and possess poles at the complex frequencies , is considered. It is shown that the algebraic alternatives of compactness, or lack of compactness, for the at correspond directly to the physical alternatives of whether or not a pair of N\´s natural oscillations at the frequency are scaled replicas of one another throughout N. A secondary result of the paper is called the Energy Theorem. This theorem assumes that the natural oscillations of a lossless oneport have been excited by a unit impulse of current, and states that each impedance residue of the oneport is proportional to the energy stored in the corresponding one of these oscillations.