POWER IN MODAL RADIATION-FIELDS - LIMITATIONS OF THE COMPLEX POYNTINGTHEOREM AND THE POTENTIAL FOR ELECTRICALLY SMALL ANTENNAS

Analyses of power in radiation fields are nearly universally based upo n the complex Poynting theorem, CPT, yet the scientific basis for its use is not well established. The time dependent Poynting theorem, TDPT , is seldom used yet its scientific basis is well established. We use Hansen's method to obtain a generalized modal expansion for all possib le electromagnetic fields that can originate within a confined volume and travel infinitely outward, combine the modal expansions and both P oynting theorems to determine the power expressions, and contrast resu lts. The TDPT shows that the characterization of power in a sinusoidal field requires three numbers. Therefore it cannot be fully described by only real and reactive values. We conclude that the CPT is intrinsi cally an insufficient basis for a full description of power in a radia tion field. We compare TDPT and CPT solutions for several idealized an tenna designs. Comparative analyses show that the TDPT provides soluti ons that correspond to reality in all cases and the CPT does not. Proo fs that electrically small antennas cannot be efficient are based upon the CPT; we re-examine these proofs using the TDPT and find that cert ain mixed modal configurations may surpass the generally accepted smal l antenna rules.