Theoretical aspects of the physical realizability of broad-band equivalent circuits for energy collecting structures

The practical implementation of equivalent circuits that represent the energy delivered to an arbitrary load impedance by an antenna or a port on a scatterer is discussed. Particular attention is paid to the positive-real (PR) function issues associated with the equivalent admittance of the structure when evolved from the point of view of the singularity expansion method (SEM). A proof is given which establishes that the eigenadmittances (reciprocal eigenvalues) of a structure are positive-real functions. The connection between this fact and the positive realness of the admittance associated with individual current eigenmode contributions to total current is discussed. An ad hoc approach to approximating these admittances with simpler pole-pair positive-real admittances is given for high-
Q
structures. A brief survey of the applicable circuit synthesis algorithms and their features is provided. Some fundamental considerations in the implementation of the sources representing the energy coupled from the incident wave are presented.