The complex Poynting theorem: reactive power, radiative Q, and limitations on electrically small antennas

The complex Poynting theorem does not calculate the correct reactive power for all possible field conditions. Upon sub-dividing the fields into their modal constituents, the theorem is valid for all TE or TM field combinations, but it is not valid for all TE and TM combinations. The method needed to find the reactive power under all modal field combinations is reviewed. Proofs that there are severe size limitations on electrically small antennas are based upon the reactive power calculated using the complex Poynting theorem. This commonly believed and significant antenna result is neither proven nor true for fields consisting of mixed modal types. An example is given where it breaks down. The result emphasizes a research direction in which to seek an efficient, electrically small antenna.