Fundamental Efficiency Limits for Small Metallic Antennas
  Both the radiation efficiency and bandwidth of electrically small antennas are dramatically reduced as the size decreases. Fundamental limitations on the bandwidth of small antennas have been thoroughly treated in the past. However, upper bounds on radiation efficiency have not been established even though it is also of significant importance. Here, radiation from a thin metallic shell is rigorously analyzed to establish fundamental limits on the radiation efficiency of resonant, electrically small antennas in terms of the size and the metal conductivity. Metallic losses are systematically introduced into the circuit model proposed by Chu, and several resonant antennas with maximum radiation efficiencies are analyzed. Resonant electric and magnetic dipole antennas both have maximum radiation efficiencies near 100% until the size is reduced below a critical value, at which point the efficiency scales as electrical size to the fourth power ((ka)^4 ). It is also shown that a helix antenna that resonantly couples the TM10 mode to the TE10 mode has a maximum radiation efficiency, and is about twice that of a resonant dipole or loop antenna. The closed form expressions reported here provide valuable insight into the design of small antennas with optimal efficiencies. 
Carl Pfeiffer
physics.ins-det physics.class-ph