“Crossed-Field” and “EH” Antennas Including Radiation from the Feed Lines and Reflection from the Earth’s Surface

An ongoing challenge in electrical engineering is the design of antennas whose size is small compared to the broadcast wavelength λ. One difficulty is that the radiation resistance of a small antenna is small compared to that of the typical transmission lines that feed the antenna, so that much of the power in the feed line is reflected off the antenna rather than radiated unless a matching network is used at the antenna terminals (with a large inductance for a small dipole antenna and a large capacitance for a small loop antenna). The radiation resistance of an antenna that emits dipole radiation is proportional to the square of the peak (electric or magnetic) dipole moment of the antenna. This dipole moment is roughly the product of the peak charge times the length of the antenna in the case of a linear (electric) antenna, and is the product of the peak current times the area of the antenna in the case of a loop (magnetic) antenna. Hence, it is hard to increase the radiation resistance of small linear or loop antennas by altering their shapes. One suggestion for a small antenna is the so-called “crossed-field” antenna [2]. Its proponents are not very explicit as to the design of this antenna, so this problem is based on a conjecture as to its motivation. It is well known that in the far zone of a dipole antenna the electric and magnetic fields have equal magnitudes (in Gaussian units), and their directions are at right angles to each other and to the direction of propagation of the radiation. Furthermore, the far zone electric and magnetic fields are in phase. The argument is, I believe, that it is desirable if these conditions could also be met in the near zone of the antenna. The proponents appear to argue that in the near zone the magnetic field B is in phase with the current in a simple, small antenna, while the electric field E is in phase with the charge, but the charge and current have a 90◦ phase difference. Hence, they imply, the electric and magnetic fields are 90◦ out of phase in the near zone, so that the radiation (which is proportional to E×B) is weak. The concept of the “crossed-field” antenna seems to be based on the use of two small antennas driven 90◦ out of phase. The expectation is that the electric field of one of the A center-fed linear dipole antenna of total length l λ has radiation resistance Rlinear = (l/λ) 197Ω, while a circular loop antenna of diameter d λ has Rloop = (d/λ) 1948Ω. For example, if l = d = 0.1λ then Rlinear = 2Ω and Rloop = 0.2Ω. That there is little advantage to so-called small fractal antennas is explored in [1]. A variant based on combining a small electric dipole antenna with a small magnetic dipole (loop) antenna has been proposed by [3].