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The objective of this work is to determine the orders of magnitude of the band width available from a cavity antenna. Fcr simplicity of calculation a piece of shorted square wave guide of side a, opening into a half‐space, is considered, and the resonance frequency and band width (1/Q) are calculated from transmission‐line theory. The analysis depends on an equivalent aperture admittance which is defined for the lowest‐order wave guide mode. This type of antenna has a minimum Q which is equal to 0.424(a/λ)-3 when (a/λ)≪0.35. The cavity depth required for the minimum Q is of the order of 0.4a. The required dielectric constant increases rapidly as a/λ decreases. The effect of dielectric loss is considered. Some experimental results which agree well with theory are presented.