The gain or directivity of an antenna is the ratio of the radiation intensity in a given direction to the radiation intensity averaged over all directions. Quite often directivity and gain are used interchangeably. The difference is that directivity neglects antenna losses such as dielectric, resistance, polarization, and VSWR losses. Normalizing a radiation pattern by the integrated total power yields the directivity of the antenna. Real antennas are different, however, and do not have an ideal radiation distribution.
Energy varies with angular displacement and losses occur due to sidelobes.
The elliptical model has about one dB difference from the ideal calculation, but will yield the same real antenna gain when appropriate efficiencies are assumed. The upper plot of Figure 4 shows the gain for an ideal antenna pattern using the elliptical model. The middle plot shows the gain for an ideal antenna using the rectangular model. Conversely, nulls to either side of the main lobe will occur when the waves radiating from the antenna cancel each other. To aid in visualizing what happens, consider each point in the antenna aperture, from A to C in Figure 5, as a point source of a spherical wave front.