Free-Space Radiation Patterns from Periodic Straight-Wire Antennas

In deriving the radiation pattern for a periodic straight-wire doublet or dipole antenna, the equation for the radiation from an elementary doublet,³ of such small length that the current in all parts is the same, is used. The next step in determining the radiation pattern of an actual antenna is to assume the actual antenna to be made up of a number of elementary doublets and to determine graphically or mathematically³ the field intensity produced by all the elementary doublets at the various points in space about the antenna under study.

For periodic straight-wire doublets, or dipoles, the free space radiation patterns are³⁶

For a periodic straight-wire antenna an odd number of half wavelengths long:

For a periodic straight-wire antenna an even number of half wavelengths long:

In these equations E is the effective value (r.m.s.) of the field strength in volts per meter at the point under consideration, d is the distance in meters from the point to the antenna, I is the effective value of the current at the point of maximum current flow in the antenna, l is the antenna length in meters, A is the wavelength in meters, and θ is an angle measured as shown in Fig. 13.

Figure 13. Free-space radiation patterns plotted from equations 11 and 12. Relative magnitude of radiated field strength is indicated by 0.5, 1.0, and 1.5. Areas of figures should not be compared. These figures represent radiation in one plane. The complete radiation is a "solid figure" obtained by revolving the pattern about the antenna (at the center) as an axis.

These figures show the shapes of the free-space radiation patterns for several straight-wire antennas. The relative field strength of the signal radiated at any angle is the length of a vector at that angle from the center of the antenna to the pattern edge. Information is available³⁶ for finding the positions and relative magnitudes of the lobes without first plotting the figures. In Fig. 13 is shown the radiation pattern in a plane parallel to the antenna, and in which the antenna lies. The entire radiation is a "solid figure," obtained by "revolving" the patterns shown about the antenna as an axis.