The foster reactance theorem for antennas and radiation Q

The calculation of antenna Q has been an interesting and a controversial to pic for years. In this paper, we first give a rigorous study of antenna Q b y introducing a complete description of the complex power balance relation for an antenna system, Using the complex Poynting theorem, we have shown th at the antenna is essentially equivalent to a one port lossy network. The F oster reactance theorem is usually stated for a lossless network. The main purpose of this paper is to determine whether the Foster reactance theorem holds for antennas. By making use of a complex frequency domain version of the Poynting theorem, we have shown that the Foster reactance theorem is va lid for an antenna. Finally, the Foster reactance theorem for the antenna h as been applied to demonstrate the widely held assumption Q approximate to 1/B, provided Q much greater than 1, where B stands for the fractional band width of an arbitrary antenna.