The spherical shape in the study of antenna Q

In the study of Q factors for radiating devices, the spherical shape always has played a crucial role. Chu, McLean, and Thal used the spherical shape to derive their lower bounds for Q. In this paper, first a general relation is given between the change of a topology inside the circumscribing sphere and the change of the lower bound for Q. It turns out that any increase of the volume inside the sphere leads to a lower minimal Q. Then, based on this relation, an almost trivial proof is given for the well-known fact that the full sphere provides the absolute minimal Q. Also, the value for this minimal Q is derived analytically.