The Foster reactance theorem and quality factor for antennas

The validity of the Foster reactance theorem for the general lossless or lossy antenna is considered for the straight-wire monopole and half-loop antennas. The finite diameter, lossy or lossless monopole, and half-loop behave as either a series RLC circuit near resonance or a parallel RLC circuit near antiresonance. For the Foster reactance theorem to be valid for the general antenna, the frequency derivative of the antenna´s feed point reactance, X´(/spl omega/), must be positive for all values of frequency. This behavior is not consistent with that of a parallel RLC circuit near antiresonance and, therefore, the Foster reactance theorem is not valid for either the lossy or the lossless finite diameter antenna. Simulated and measured reactances of the finite diameter monopole and half-loop are shown to be in good agreement and are shown not to obey the Foster reactance theorem in frequency ranges near antiresonance. It is shown that the commonly used relationship between quality factor and |X´(/spl omega/)| is not valid in frequency ranges near antiresonance.