### Gain and Directivity

The power gain of a transmitting antenna is the ratio of the maximum effective radiated power (ERP) to the actual RF power applied at the feed point. Power gain is expressed in decibels (dB). Suppose the ERP, in watts, for a given antenna is PERP, and the applied power, also in watts, is P. Then the following equation holds:
Power gain (dB) = 10 log10 (PERP/P)
Power gain is always measured in the favored direction or directions of an antenna. These are the directions in which the antenna performs the best.

For power gain to be defined, a reference antenna must be chosen with a gain that is defined as 0 dB. This reference antenna is usually a λ/2 dipole in free space. Power-gain figures taken with respect to a dipole (in its favored directions) are expressed in units called dBd. The reference antenna for power-gain measurements can also be an isotropic antenna, which theoretically radiates and receives equally well in all directions in three dimensions. In this case, units of power gain are called dBi. For any given antenna, the power gains in dBd and dBi are different by approximately 2.15 dB:
Power gain (dBi) = 2.15 + Power gain (dBd)

#### Directivity Plots

Directivity plots for a dipole antenna. At A, the H plane (horizontal plane) plot; at B, the E plane (elevation plane) plot.
Antenna radiation and response patterns are represented by plots such as those shown in above figure. The location of the antenna is assumed to be at the center (or origin) of a polar coordinate system. The greater the radiation or reception capability of the antenna in a certain direction, the farther from the center the points on the chart are plotted. A dipole antenna, oriented horizontally so that its conductor runs in a north-south direction, has a horizontal plane (or H plane) pattern similar to that in above figure A. The elevation plane (or E plane) pattern depends on the height of the antenna above effective ground at the viewing angle. With the dipole oriented so that its conductor runs perpendicular to the page, and the antenna 1⁄ 4 wavelength above effective ground, the E plane antenna pattern for a half-wave dipole resembles the graph shown at B.

#### Forward Gain

Forward gain is expressed in terms of the ERP in the main lobe (favored direction) of a unidirectional (one-directional) antenna compared with the ERP from a reference antenna, usually a half-wave dipole, in its favored directions. This gain is calculated and defined in dBd at microwave frequencies; large dish antennas can have forward gain upward of 35 dBd. In general, as the wavelength decreases (the frequency gets higher), it becomes easier to obtain high forward gain figures.

#### Front-to-Back Ratio

Directivity plot for a hypothetical antenna. Front-to-back and front-to-side ratios can be determined from such a graph. This plot is in the H plane.
The front-to-back (f/b) ratio of a unidirectional antenna is an expression of the concentration of radiation/response in the main lobe, relative to the direction opposite the center of the main lobe. Above figure shows a hypothetical directivity plot for a unidirectional antenna pointed north. The outer circle depicts the RF field strength in the direction of the center of the main lobe, and represents 0 dB. The next smaller circle represents a field strength 5 dB down with respect to the main lobe. Continuing inward, circles represent 10 dB down, 15 dB down, and 20 dB down. The origin represents 25 dB down, and also shows the location of the antenna. The f/b ratio is found, in this case, by comparing the signal levels between north (azimuth 0°) and south (azimuth 180°).

#### Front-to-Side Ratio

The front-to-side (f/s) ratio is another expression of the directivity of an antenna system. The term applies to unidirectional antennas, and also to bidirectional antennas. The f/s ratio is expressed in decibels (dBd), just as is the f/b ratio. The EM field strength in the favored direction is compared with the field strength at right angles to the favored direction. An example is shown in above figure. The f/s ratios are found, in this case, by comparing the signal levels between north and east (righthand f/s), or between north and west (left-hand f/s). The right-hand and left-hand f/s ratios are usually the same in theory, although they can differ slightly in practice.