Radiation Efficiency Limits for Elementary Antenna Shapes

Both the bandwidth and efficiency of antennas decrease as the physical size decreases. Bounds on the <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula>-factor, inversely related to bandwidth, have been studied rigorously and reported extensively, but published investigations of efficiency limits are much less common. In this paper, expressions for the minimum dissipation ratio, and hence maximum efficiency, are derived using circuits that represent the six lowest order radiating modes. Examples consisting of a wide range of elementary shapes demonstrate that even though an antenna may approach its <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula>-bound quite closely, it typically has dissipation well above the new lower bounds due to higher order modes.