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.