According to the antenna theory, the maximum available power W_m of a receiving antenna for a matched load is proportional to the product of λ^２, |Ｅ|^２, and  D.

  Where

       W_m： Maximum available power of receiving antenna with a matched load.

        λ: Wavelength.

        Ｅ: Electric field.

        D : Directivity (Directive gain) of the receiving antenna.

   Accordingly, the received power “W_m” decreases to smaller values with increasing frequencies in inverse proportion to the square of the frequency when its directivity “D” remains unchanged. This is a definite fault of the “Frequency-independent” antenna as an extremely broadband antenna. Such a property is really unimaginable from its nomenclature.

   Therefore, the directivity “D” must be enhanced to higher values with increasing frequencies in proportion to the square of the frequency by narrowing the beam width of the radiation pattern if the power “W_m” is to be kept constant. In such a case, the receiving antenna should be “Frequency-characterized” antenna with constant input impedance.

   Besides, there are always the upper and the lower limits in the actual operating frequencies for the practical antennas.

  By taking into account of the facts mentioned above, the broadband derivatives of the self-complementary antennas with such “Frequency-characterized” properties should be investigated in practice, instead of clinging indiscriminately to the “Frequency-independent” antenna, though it is a very interesting concept for reasonably broadband antennas.

  Incidentally, it should be mentioned here that the usefulness of the Principle of Similitude has been well recognized since the Newton's time. (See: e.g. Electromagnetic Theory by J. A. Stratton, 1941.)