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As we know, air breakdown would occur if the power of a microwave pulse, which radiates from an aperture antenna, was high enough, the transmission of microwave could be hindered. Based upon this assumption, this paper intends to report on the mathematical deduction of the maximum power radiated from an aperture antenna before air breakdown in the near-field region. It also presents the calculations in the power density enhancement factors corresponding to different kinds of aperture field distributions in the near-field region of a circular cophasal aperture. In addition, this paper also proposes a formula by the field equivalence principle for calculating the normalized power density on axis. The results showed that the air breakdown in the near-field region could be a limiting factor for the maximum power, depending on aperture radius, the field distribution in the aperture plane, the frequency, and the pulse width of a microwave pulse.