Fundamental limits on antenna size: a new limit

In this study, previous theories on the minimum radiation-Q against antenna size are examined, basic assumptions are reviewed and an alternate formulation is presented. The radiation-Q limit varies with the amount of an estimated non-radiating energy, which is directly related to the energy velocity. The classic approximate Q formula of Chu is found to be equivalent to using the group velocity for the energy velocity. Other previous approaches implicitly assumed that the radiated-energy travels in the radial direction at the speed of light from the antenna sphere to the far-field region, which is not true. Based on this observation of the incorrect energy velocity, a time-domain approach is used to derive the fundamental limit on radiation-Q against electrical size of an antenna. A new form of radiation-Q is presented that provides a bound lower than all the previous results. The new limit, which is just below the Chu limit, holds for any antenna size, not just electrically-small antennas. The new radiation-Q limit provides antenna designers with a simple guide to estimate the minimum required antenna size for a given bandwidth and efficiency, thereby avoiding the search for an impractical antenna.