3 Diffraction over a spherical Earth The additional transmission loss due to diffraction over a spherical Earth can be computed by the classical residue series formula. A computer program GRWAVE, available from the ITU, provides the complete method. A subset of the outputs from this program (for antennas close to the ground and at lower frequencies) is presented in Recommendation ITU-R P.368. The following subsections describe numerical and nomogram methods which may be used for frequencies 10 MHz and above. For frequencies below 10 MHz, GRWAVE should always be used. Section 3.1 gives methods for over-the-horizon paths. Section 3.1.1 is a numerical method. Section 3.1.2 is a nomogram method. Section 3.2 is a method applicable for the smooth earth case for any distance and for frequencies 10 MHz and above. This utilizes the numerical method in § 3.1.1. 3.1 Diffraction loss for over-the-horizon paths At long distances over the horizon, only the term of the residue series is important. Even near or at the horizon this approximation can be used with a maximum error around 2 dB in most cases. This first term can be written as the product of a distance term, and two height gain terms, F, GT and Sections 3.1.1 and § 3.1.2 describe how these terms can be obtained from simple formula GR. or from nomograms. 3.1.1 Numerical calculation 3.1.1.1 Influence of the electrical characteristics of the surface of the Earth The extent to which the electrical characteristics of the surface of the Earth influence the diffraction loss can be determined by calculating a normalized factor for surface admittance, given by the K, formulae: in self-consistent units: for horizontal polarization (11) and for vertical polarization (12) or, in practical units: (11a) (12a) where: : effective radius of the Earth (km); ae : effective relative permittivity; ε : effective conductivity (S/m);  : frequency (MHz). f Typical values of are shown in Fig 2. K
3 Diffraction over a spherical Earth The additional transmission loss due to diffraction over a spherical Earth can be computed by the classical residue series formula. A computer program GRWAVE, available from the ITU, provides the complete method. A subset of the outputs from this program (for antennas close to the ground and at lower frequencies) is presented in Recommendation ITU-R P.368. The following subsections describe numerical and nomogram methods which may be used for frequencies 10 MHz and above. For frequencies below 10 MHz, GRWAVE should always be used. Section 3.1 gives methods for over-the-horizon paths. Section 3.1.1 is a numerical method. Section 3.1.2 is a nomogram method. Section 3.2 is a method applicable for the smooth earth case for any distance and for frequencies 10 MHz and above. This utilizes the numerical method in § 3.1.1. 3.1 Diffraction loss for over-the-horizon paths At long distances over the horizon, only the term of the residue series is important. Even near or at the horizon this approximation can be used with a maximum error around 2 dB in most cases. This first term can be written as the product of a distance term, F, and two height gain terms, GT and GR. Sections 3.1.1 and § 3.1.2 describe how these terms can be obtained from simple formula or from nomograms. 3.1.1 Numerical calculation 3.1.1.1 Influence of the electrical characteristics of the surface of the Earth The extent to which the electrical characteristics of the surface of the Earth influence the diffraction loss can be determined by calculating a normalized factor for surface admittance, K, given by the formulae: in self-consistent units: for horizontal polarization (11) and for vertical polarization (12) or, in practical units: (11a) (12a) where: ae : effective radius of the Earth (km); ε : effective relative permittivity;  : effective conductivity (S/m); f : frequency (MHz). Typical values of K are shown in Fig 2.
R-REC-P.526-13201309-P!!MSW-E.docx