Simple Procedure to Derive Lower Bounds for Radiation $Q$ of Electrically Small Devices of Arbitrary Topology

A new and simple technique is presented to derive absolute lower bounds for the radiation Q of electrically small radiating devices. In contrast to many other techniques available in open literature, the new technique is applicable to any topology. It does not rely on defining a canonical volume, like for example a sphere or an ellipsoide, around the antenna, nor is it based on the scattering properties of the topology or any efficiency, but it takes into account possible currents actually flowing on the real device. It yields values for the lower bound strongly depending on the topology. Moreover, it allows to prove several well-known minimum radiation Q´s for basic topologies, such as the spherical TM mode, and the spherical inductor.