A New Perspective on the Reactive Electromagnetic Energies and Q factors of Antennas

Abstract

It is required to calculate the stored reactive energy of an antenna in order to evaluate its Q factor. Although it has been investigated for a long time, some issues still need further clarification. The main difficulty involved is that the reactive energy of an antenna tends to become infinitely large when integrating the conventionally defined energy density in the whole space outside a small sphere containing the antenna. The reactive energy is usually made to be bounded by subtracting an additional term associated with the radiation fields. However, there exists no well-accepted accurate definition for this additional term that is valid for all cases. By rechecking the definition of reactive energies, an alternative formulation is proposed in this paper which can separate the reactive energy and the radiation energy explicitly based on source-potentials. The clearly defined reactive energy is bounded without necessity to subtract that additional term, and the resultant formulae are easy to implement.

A Theory for Analysis of Pulse Electromagnetic Radiation

“…Note that the observation surface is not required to approach infinity for evaluating the radiative power with the radiative power flux density vector. It can be checked that the result is in consistent with that obtained using the Poynting vector, as has been shown in [14] that 1 1R e 0 4 4…”

“…For electromagnetic pulse sources, the surface integrals are zeros since we can always put the observation surface outside the region containing the fields. For harmonic waves, it can be proved that the surface integral at S  in (21) approaches zero, while that in (22) may be a nonzero but finite value [14].…”

“…The electromagnetic radiation problems have been intensively investigated for more than a hundred years. It is a little bit strange that there is still no widely accepted formulation for evaluating the stored reactive energies and Q factors of radiators [1]- [14]. The main difficulty may come from the fact that there is no clear definition in macroscopic electromagnetic theory for the reactive electromagnetic energy.…”

“…For harmonic fields, the total electromagnetic energy obtained by integrating the conventional energy densities of   0.5  D E and   0.5  B H over the whole space is infinite because the conventionally defined electric and magnetic energy densities generally account for the total fields consisting of the radiative fields and the reactive fields. The radiative energy occupies the whole space and is infinitely large [14]. Some researchers suggested that those fields associated with the propagating waves should not contribute to the stored reactive energies, and the results can become finite by subtracting from the energy density an additional term associated with the radiation power.…”

A Theory for Electromagnetic Radiation and Coupling

“…For harmonic fields, the total electromagnetic energy obtained by integrating the conventional energy densities of   0.5  D E and   0.5  B H over the infinite three-dimensional volume is infinite because they account for the total energy consisting of the radiative energy and the reactive energy. For harmonic fields over the time interval ( t     ), the radiative energy occupies the whole space and is infinitely large [14]. Some researchers suggested that those fields associated with the propagating waves should not contribute to the stored reactive energies.…”