r of that given by equation 7.31. Current Element Current Distribution Fig. 7.9 Short dipole. Radiation from a Half-Wavelength Dipole The radiation characteristics of the half-wavelength dipole can be derived on the basis that, for a thin dipole, the current distribution along the antenna is approximately sinusoidal, as shown in Figure 7.10. In this figure the value of the current distribution is given by equation 7.39 and Ee by equation 7.40. I = Im COS BL (7.39) (7.40) Generation of Electromagnetic Waves Current Element d-l Cos 0 Current Distribution Fig. 7.10 Half-wavelength dipole. Using the same system of spherical coordinates defined earlier, the far-field radiation terms in free space are given by equations 7.41 and 7.42. (7.41) Eo=nH (7.42) The average power flux density through the surface of a surrounding sphere is given by the Poynting vector. The total power, P, radiated by the dipole is equal to the total power radiated through the surface of the sphere and is given by equation 7.43. (7.43) Evaluation of this integral is dealt with by Jordan and Balmain (1968) and (for I given by equation 7.45) gives equation 7.44. P 73.11° watts (7.44) (7.45) The radiation resistance of the thin half-wavelength dipole is given by the coefficient of Io in equation 7.46 and is therefore equal to 73.1 ohms. It is now possible to determine the r.m.s. value of the electric field in the direction of maximum radiation by combining equations 7.41, 7.42, and 7.44, with O equal to zero, giving equation 7.46, where E is in volts per meter, with P in watts and d in meters. ==7VP (7.46) Chapter 7 Electromagnetic Waves d-l COS 0 Current Distribution Perfectly Conducting Infinite Plane Image Fig. 7.11 Vertical monople over a ground plane. Radiation from a Short Monopole Figure 7.11 shows a vertical monopole on a perfectly conducting, infinite, flat ground plane. The current distribution (given by equation 7.47), for a thin monopole is approximately sinusoidal and, as a result of the perfect image in the ground plane, the radiation