Limitations for the radiation quality factor, Q, of a lossless linearly polarised structure which fits a spheroidal volume are searched for. The Q is evaluated by numerical integration of the evanescent energy outside the spheroid for the axially polarised field. The minimum Q for a prolate spheroid is found for a narrower radiation pattern than the sin θ-figure characteristic for an elementary dipole, while for the oblate, the minimum turns out for a broader pattern than that of an elementary dipole. The results agree with the previous theory, stating that the Q of a linearly polarised antenna can not be smaller than (ka)-3+ka
-1, k being the wave number and a the radius of the smallest circumscribed sphere. The graphs showing the influence of the axial ratio on the radiation Q should be of practical interest in the design of wide band antennae of small electrical size as not only the maximum dimension of the antenna, but also its shape and polarisation is taken into account.
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