The Antenna Current Green´s Function Formalism—Part I

This paper generalizes the familiar concept of system function in electrical engineering from the time domain (one dimension) to the spatial domain (three dimensions) for the analysis and design of arbitrary electromagnetic systems, including both radiating structures and circuits elements interacting with each other in the near-field zone. The key concept in the formalism is the antenna current Green´s function, which can be considered an exact transfer function in space. We provide a conceptual view of electromagnetic systems framed in terms of three operational modes: Mode A is the excitation of a given antenna element by an externally applied field; Mode B is the radiation of the excited current into the medium surrounding the antenna; and finally Mode C as the receiving mode of antennas immersed in the near-field zone of a nearby antenna or circuit element or the far field of another antenna. It is shown that the antenna current Green´s function of Mode A can be obtained in terms of a 2D tensor that depends on the local geometry of the general antenna surface. The core of Part I resides in a distributional construction of the antenna current Green´s tensor and its relation to differential manifolds in order to deal with arbitrary antennas and to relate the local and global aspects of their geometrical shape to the electromagnetic performance of the system.