Radiation Q of dipole-generated fields

The radiation Q of several dipole fields in free space are determined using the time-dependent Poynting theorem. Earlier works on this subject, recently summarized by McLean [1996], are based upon the complex Poynting theorem. It was previously shown [Grimes and Grimes, 1997] that the full complex Poynting theorem is correct only for single-mode radiation fields. The time-dependent theorem shows that three numbers are necessary to completely specify time-varying power, and complex numbers supply but two; the third piece of information, a phase, is discarded when complex notation is formed. Omissions inherent in the complex Poynting theorem affect the calculated value of standing energy about an antenna and hence the calculated value of Q. To avoid such omissions, we develop a method of determining Q based upon the time-dependent Poynting theorem that builds upon and extends our earlier work [Grimes and Grimes, 1997]. The purposes of this paper are to (1) provide a time domain basis for calculating IS in mixed modal radiation fields, (2) determine the Q of electric and magnetic dipoles, alone and in combination, and (3) demonstrate how source structure and relative phasing affect the physics of several combinations of electric and magnetic dipole radiation fields. The primary conclusion of this work is that the minimum possible Q of a radiation source established by Chu [1948] does not extend to properly mixed and phased multimodal radiation fields. A radiation source is presented for which, by our analysis, the radiation Q is zero.