Discussion on the definition of the antenna radiation Q

According to the classical theories developed by Chu, Wheeler and subsequent authors, there exists a fundamental law which restricts the performances of antennas enclosed in a given volume. This law states that the antenna radiation quality factor Q (proportional to the ratio of time-average non-propagating energy to radiated power) cannot be smaller than the one obtained if only the lowest spherical order mode is excited out of the minimal sphere containing the antenna. However, some authors have recently contradicted this lower limit of Q, exhibiting antennas overcoming this bound. This paper shows that the contradiction mainly relies on a problem of formulation of the quality factor, resulting in a different definition of Q, compared with the classical one. Nevertheless, this raises the question of the interest of using other expressions of Q, depending on the parameters of the problem to be optimized. In fact, it is shown that, if the goal is to obtain the largest matching bandwidth or efficiency, then the Q factor should not be considered at the frequency point of balance between the electric and magnetic stored energies, as it is classically done. It would rather be calculated at the frequency where the reactive power is null (the antenna is matched) which is generally not equivalent to the stored energies balance for complex multi-mode antennas.