The Foster reactance theorem for antennas and radiation Q

The calculation of antenna Q has been an interesting and a controversial topic for years. We first give a rigorous study of antenna Q by introducing a complete description of the complex power balance relation for an antenna system. Using the complex Poynting theorem, we have shown that the antenna is essentially equivalent to a one port lossy network. The Foster 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 valid for an antenna. Finally, the Foster reactance theorem for the antenna has been applied to demonstrate the widely held assumption Q≈1/B, provided Q≫1, where B stands for the fractional bandwidth of an arbitrary antenna