ncy, T. The reduction in field strength for the real path relative to that for a perfectly conducting flat plane. This is taken into account by the path attenuation factor, A. Chapter 7 Electromagnetic Waves Fig. 7.27 Relative power gain of a monopole antenna. Length of Monopole in Wavelengths The quantity P' given by equation 7.93 is the Effective Monopole Radiated Power (EMRP) in kilowatts, which is analogous to the ERP defined previously for the space wave. P'=Pkwgt (7.93) Thus, an EMRP of 1 kW gives a field strength of 0.3 volts/meter at 1 km on a perfectly con- ducting ground. Monopole antennas that are longer than 0.1 wavelength have gains given by the graph of Figure 7.27. A practical antenna can obtain additional gain, in a given direction, by many means. This can be allowed for, as with the space wave, by the use of a Horizontal Radiation Pattern (HRP). The field strength for the practical case now becomes as in equation 7.94. E-300(Payst) volts/meter (7.94) The Sommerfeld-Norton Theory The Sommerfeld-Norton theory (Jordan & Balmain, 1986; Terman, 1943) gives a method for prediction of attenuation over a homogeneous smooth earth. This method will not be fully described here, but for a vertical antenna it is convenient to define this calculation via the surface impedance concept. Thus, for ground conductivity O, relative permittivity Er, and wave of length, A, the relative surface impedance at grazing incidence can be given by equa- tion 7.95. (7.95) j60ol Ground Waves and Surface Waves 908 kHz 1214 kHz 1457kHz Fig. 7.28 Attenuations of MF signals through a built-up area. Distance from Transmitter (km) For a given distance, d, a parameter, W, can be defined by equation 7.96. w=-jm (7.96) From this, the complex surface wave attenuation factor, A, is given by equation 7.97, where erfc denotes the complementary error function (Abramowitz & Stegun, 1964). (7.97) The Realistic Terrain-A Solution via an Integral Equation A realistic terrain is covered by clutter of human-made and natural objects that significan