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RADIATION RESISTANCE Radiated energy is the useful part of the transmitter's signal. However, it represents as much of a loss to the antenna as the energy lost in heating the antenna wire. In either case, the dissipated power is equal to I^{2}R. In the case of heat losses, the R is real resistance. In the case of radiation, R is an assumed resistance; if this resistance were actually present, it would dissipate the same amount of power that the antenna takes to radiate the energy. This assumed resistance is referred to as the RADIATION RESISTANCE. Radiation resistance varies at different points on the antenna. This resistance is always measured at a current loop. For the antenna in free space, that is, entirely removed from any objects that might affect its operation, the radiation resistance is 73 ohms. A practical antenna located over a ground plane may have any value of radiation resistance from 0 to approximately 100 ohms. The exact value of radiation resistance depends on the height of the antenna above the ground. For most halfwave wire antennas, the radiation resistance is about 65 ohms. It will usually vary between 55 and 600 ohms for antennas constructed of rod or tubing. The actual value of radiation resistance, so long as it is 50 ohms or more, has little effect on the radiation efficiency of the antenna. This is because the ohmic resistance is about 1 ohm for conductors of large diameter. The ohmic resistance does not become important until the radiation resistance drops to a value less than 10 ohms. This may be the case when several antennas are coupled together. The energy radiated from an antenna forms a field having a definite RADIATION PATTERN. A radiation pattern is a plot of the radiated energy from an antenna. This energy is measured at various angles at a constant distance from the antenna. The shape of this pattern depends on the type of antenna used. In this section, we will introduce the basic types of radiation (isotropic and anisotropic) and their radiation patterns. Isotropic Radiation Some antenna sources radiate energy equally in all directions. Radiation of this type is known as ISOTROPIC RADIATION. We all know the Sun radiates energy in all directions. The energy radiated from the Sun measured at any fixed distance and from any angle will be approximately the same. Assume that a measuring device is moved around the Sun and stopped at the points indicated in figure 49 to make a measurement of the amount of radiation. At any point around the circle, the distance from the measuring device to the Sun is the same. The measured radiation will also be the same. The Sun is therefore considered an isotropic radiator. Figure 49.  Isotropic radiator.
To plot this pattern, we will assume that the radiation is measured on a scale of 0 to 10 units and that the measured amount of radiation is 7 units at all points. We will then plot our measurements on two different types of graphs, rectangularand polarcoordinate graphs. The RECTANGULAR COORDINATE GRAPH of the measured radiation, shown in view A of figure 410, is a straight line plotted against positions along the circle. View B shows the POLARCOORDINATE GRAPH for the same isotropic source. Figure 410.  Comparison of rectangular and polarcoordinate graphs for an isotropic source.
In the rectangularcoordinate graph, points are located by projection from a pair of stationary, perpendicular axes. In the polarcoordinate graph, points are located by projection along a rotating axis (radius) to an intersection with one of several concentric, equallyspaced circles. The horizontal axis on the rectangularcoordinate graph corresponds to the circles on the polarcoordinate graph. The vertical axis on the rectangularcoordinate graph corresponds to the rotating axis (radius) on the polarcoordinate graph. RectangularCoordinate Pattern Look at view A of figure 410. The numbered positions around the circle are laid out on the HORIZONTAL AXIS of the graph from 0 to 7 units. The measured radiation is laid out on the VERTICAL AXIS of the graph from 0 to 10 units. The units on both axes are chosen so the pattern occupies a convenient part of the graph. The horizontal and vertical axes are at a right angle to each other. The point where the axes cross each other is known as the ORIGIN. In this case, the origin is 0 on both axes. Now, assume that a radiation value of 7 units view B is measured at position 2. From position 2 on the horizontal axis, a dotted line is projected upwards that runs parallel to the vertical axis. From position 7 on the vertical axis, a line is projected to the right that runs parallel to the horizontal axis. The point where the two lines cross (INTERCEPT) represents a value of 7 radiation units at position 2. This is the only point on the graph that can represent this value. As you can see from the figure, the lines used to plot the point form a rectangle. For this reason, this type of plot is called a rectangularcoordinate graph. A new rectangle is formed for each different point plotted. In this example, the points plotted lie in a straight line extending from 7 units on the vertical scale to the projection of position 7 on the horizontal scale. This is the characteristic pattern in rectangular coordinates of an isotropic source of radiation. PolarCoordinate Pattern The polarcoordinate graph has proved to be of great use in studying radiation patterns. Compare views A and B of figure 410. Note the great difference in the shape of the radiation pattern when it is transferred from the rectangularcoordinate graph in view A to the polarcoordinate graph in view B. The scale of radiation values used in both graphs is identical, and the measurements taken are both the same. However, the shape of the pattern is drastically different. Look at view B of figure 410 and assume that the center of the concentric circles is the Sun. Assume that a radius is drawn from the Sun (center of the circle) to position 0 of the circle. When you move to position 1, the radius moves to position 1; when you move to position 2, the radius also moves to position 2, and so on. The positions where a measurement was taken are marked as 0 through 7 on the graph. Note how the position of the radius indicates the actual direction from the source at which the measurement was taken. This is a distinct advantage over the rectangularcoordinate graph in which the position is indicated along a straightline axis and has no physical relation to the actual direction of measurement. Now that we have a way to indicate the direction of measurement, we must devise a way to indicate the magnitude of the radiation. Notice that the rotating axis is always drawn from the center of the graph to some position on the edge of the graph. As the axis moves toward the edge of the graph, it passes through a set of equallyspaced, concentric circles. In this example view B, they are numbered successively from 1 to 10 from the center out. These circles are used to indicate the magnitude of the radiation. The advantages of the polarcoordinate graph are immediately evident. The source, which is at the center of the observation circles, is also at the center of the graph. By looking at a polarcoordinate plot of a radiation pattern, you can immediately see the direction and strength of radiation put out by the source. Therefore, the polarcoordinate graph is more useful than the rectangularcoordinate graph in plotting radiation patterns. Anisotropic Radiation Most radiators emit (radiate) stronger radiation in one direction than in another. A radiator such as this is referred to as ANISOTROPIC. An example of an anisotropic radiator is an ordinary flashlight. The beam of the flashlight lights only a portion of the space surrounding it. If a circle is drawn with the flashlight as the center, as shown in view B of figure 411, the radiated light can be measured at different positions around the circle. Again, as with the isotropic radiator, all positions are the same distance from the center, but at different angles. However, in this illustration the radiated light is measured at 16 different positions on the circle. Figure 411.  Anisotropic radiator.
Directly behind the flashlight (position 0) the radiation measured is minimum. Accordingly, a 0 value is assigned to this position in the rectangularcoordinate graph (fig. 411, view A). This radiation remains at minimum until position 4 is reached. Between positions 4 and 6, the measuring device enters the flashlight beam. You can see this transition from darkness to brightness easily in view B. Radiation is fairly constant between positions 6 and 10. Maximum brightness occurs at position 8, which is directly in the path of the flashlight beam. From positions 10 to 12, the measuring device leaves the flashlight beam and the radiation measurement falls off sharply. At position 13 the radiation is again at 0 and stays at this value back to position 0. Radiation from a light source and radiation from an antenna are both forms of electromagnetic waves. Therefore, the measurement of radiation of an antenna follows the same basic procedure as that just described for the Sun and the flashlight. Before proceeding further with the study of antenna patterns, you should be sure you understand the methods used to graph the measured radiation (magnitude of the radiation). Study the rectangular and polarcoordinate systems of plotting presented in the following section. Q.13 What is the radiation resistance of a halfwave antenna in free space? 
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