 Fig. 9.6 Dipole and radiation pattern: (a) dipole; (b) monopole; (c) polar pattern of dipole. Chapter 9 Antennas (9.9) The electric field is plotted in polar form in Figure 9.6. The radiation resistance is cal- culated by evaluating the radiated power and using P = I2R to give equation 9.10. R = 2072(9)2 (9.10) A dipole of length a = 2/10 has a radiation resistance of 2.0 ohms. 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 9.11. (9.11) This gives a slightly narrower pattern than that of the short dipole and has a half-beamwidth of 78 degrees. The radiation resistance must be evaluated numerically. For an infinitely thin dipole it has a value of 73 + j42.5 ohms. For finite thickness the imaginary part can become zero, in which case the dipole is easily matched to a coaxial cable of impedance 75 ohms. The half-wave dipole has a gain of 2.15 dB. A monopole is a dipole divided in half at its center feed point and fed against a ground plane, as shown in Figure 9.6. The ground plane acts as a mirror, and consequently the image of the monopole appears below the ground. Because the fields extend over a hemi- sphere, the power radiated and the radiation resistance are half those of the equivalent dipole with the same current. The gain of a monopole is twice that of a dipole. The radiation pattern above the ground plane is the same as that of the dipole. Radiation from Arrays Array antennas consist of a number of discrete elements that are usually small in size. Typical elements are horns, dipoles, and microstrip patches. The discrete sources radiate individually, but the pattern of the array is largely determined by the relative amplitude and phase of the excitation currents on each element and the geometric spacing apart from the elements. The total radiation pattern is the multiplication of the pattern of an individual element 