of the shape E = E1 + (17.12) and thickness of the rod. Many studies have been addressed towards obtaining accurate results (King, 1956; King, 1968). For most cases this has to be done by numerical integration. A simple case is a short dipole with a length a 102 the current distribution may be assumed to be triangular. This results in radiated fields of the form given in Equation 17.9. (17.9) The electric field is plotted in polar form in Figure 17.6. The radiation resistance is calculated by evaluating the radiated power and using P = I2R to give Equation 17.10. R - 20m2(4) (17.10) dipole of length a = has a radiation resistance of 2.0ohms. This is low by comparison with standard transmission lines and indicates the problem of matching to the transmission line. The half wave dipole is widely used. Assuming a sinusoidal current distribution the far fields are given by Equation 17.11. (17.11) E=j607 COS 0 COS This gives a slightly narrower pattern than that of the short dipole Figure 17.7 Two element array and radiation pattern: (a) and has a half beamwidth of 78 degrees. The radiation resistance two elements with equal amplitudes; (b) half wavelength must be evaluated numerically. For an infinitely thin dipole it has a spacing; (c) 180° phase difference value of 73 42.5 ohms. For finite thickness the imaginary part 17/8 Antennas of the energy radiated into the main beam and very low sidelobes can be designed. Specific antenna types 17.4.1 Prime focus symmetric reflector antennas 17.4.1.1 Parabolic reflectors The axi-symmetric parabolic reflector with a feed at the focus of the paraboloid is the simplest type of reflector antenna. The geometry is shown in Figure 17.8. The paraboloid has the property that energy from the feed at F goes to the point P on the surface where it is reflected parallel to the axis to arrive at a point A on the imaginary aperture plane. The equation describing the surface is given by Equation 17.15, where F is the focal length. 2=4F(F-z) (17.15) At the edge of the reflector, of diameter D,