ITU-R P.684-6 PDF

Introduction

Two methods are available for theoretically calculating the field strength of ELF, VLF and LF signals.

It may be noted that the information in this Recommendation includes values of f cos i exceeding 150 kHz. The use of this information for frequencies exceeding 150 kHz is not recommended. Recommendation ITU-R P.1147 gives information for frequencies above 150 kHz.

The wave-hop method is that in which electromagnetic energy paths between a given transmitter and receiver are represented geometrically as is done in the case of HF.

This method should be used at LF and, for distances less than 1 000 km, at VLF. The method treats radio transmission as taking place along certain paths defined by one or more ionospheric reflections, depending on whether the propagation in question involves one or more hops, as well as a ground wave. The total field is then the vectorial resultant of the fields due to each path. In view of the long wavelengths concerned, the diffraction of the waves by the Earth's surface must be taken into account, which is not the case for HF. The wave-hop method may be justified by the fact that, with oblique incidence, the dimensions of the section of altitude in which propagation takes place are equal to or greater than several wavelengths.

With this method it is necessary to know the values of the reflection coefficients of the incident wave on the ionosphere. These vary greatly with frequency, length and geographic and geomagnetic coordinates of transmission path, time of day, season, and epoch of the solar cycle. It is also necessary to know the electrical characteristics (conductivity and permittivity) of the ground at the transmitting and receiving sites, since the finite conductivity of the Earth affects the vertical radiation patterns of the terminal antennas.

The waveguide mode method should be used at VLF for distances greater than 1 000 km. In this method, the propagation is analysed as the sum of the waves corresponding to each of the different types of propagation in the Earth-ionosphere waveguide, analogous to a mode as defined for waveguides in the microwave region. The selection of the method to be used for field calculation depends on practical consideration of numerical calculations.

In the case of VLF at distances of less than 1 000 km and for LF in general, the series of modes are slightly convergent and the calculations then require adding together vectorially a large number of components. The wave-hop theory, on the other hand, requires only a limited number of paths, including the ground wave, and it is particularly convenient for the long-distance propagation of LF, taking into account, if possible, the diffraction.

For VLF at distances of more than 1 000 km, the wave-hop theory requires the vectorial addition of the field due to a large number of paths whereas, since the series of modes converge rapidly, sufficient accuracy can be obtained by adding together only a small number of modes. But in many cases for calculation with sufficient accuracy it is possible to use the wave-hop model at large distances for frequencies down to 10 kHz, and it is possible to limit the number of paths to be taken into account to three or in rare cases to four. Propagation at ELF also may be described in terms of a single waveguide mode.