Fundamental limitaions of a small VLF antenna for submarines

A submarine requires a small VLF antenna for reception while submerged. Since the propagation in sea water is nearly vertical (downward from the surface), the only operative types are horizontal dipoles, electric and magnetic. The electric dipole is coupled by conduction and the magnetic dipole by induction in a loop. The former has no resonance and nearly unlimited bandwidth, but fails when not submerged. The latter, by resonance, is able to present much greater interception area and available power. The magnetic interception area is determined by the size of the radome and by the radianlength or skin depth in sea water (2 meters at 15 kc). The radiation power factor, which is essential to bandwidth and efficiency, is influenced also by the size of the inductor and by the magnetic permeability of an iron core. Simple formulas illustrate these relations for the idealized spherical shape of radome, coil and core. Omnidirectivity in azimuth requires crossed coils in a two-phase circuit.