Establishment of boundaries for near-field, fresnel and Fraunhofer-field regions

Abstract

The paper establishes boundaries for near-field, Fresnel and Fraunhofer field regions of an antenna using Wave Impedance and Phase difference theory. Spatial phase difference between electric and magnetic fields remain same i.e. E and H fields remain perpendicular to each other in space, however, the temporal phase difference changes. For far-field (Fraunhofer) region, electric and magnetic fields come in-phase with each other and result in 00 temporal phase difference. In far-field the ratio of magnitudes of electric to magnetic field (Wave Impedance) becomes equal to the impedance of the medium (free space impedance; Z 0 = 377Ω), indicating the start of far-field region. Wave impedance and phase difference theories are implemented in NEC (Numerical Electromagnetics Code) and MATLAB, to establish boundaries for field regions with respect to distances from the antenna to get accurate approximations. The approximations developed are closer to the existing approximations of field distances based on the geometry of the antenna. To establish boundary conditions employing wave impedance theory, the far field is expected to start when the impedance of the wave becomes ≥ 357Ω. Wave impedance of Z185Ω indicates the start of radiating near field. Phase difference theory states that for a temporal phase difference of ≤ 37.30 the field can be considered as reactive near field and for a temporal phase difference of ≥ 82.70 the field region can be considered as far-field region. In between these end-points, lies the reactive near field region. Geometrically, the approximations are: far field Distance = [(14m2λ)/(7+m4)] & reactive near field distance = [(3λ)/(5)] [√(8m3)/(7)], where m=scaling factor with λ in the expression of maximum dimension of the antenna.