5.3.2 Effective Aperture

The power received by an antenna can be associated with a collecting area—the power density incident upon the antenna (in watts per square meter) is converted into a received power (in watts) by multiplying the power density of the received signal by the effective receiving area of the antenna). Every antenna may be considered to have such a collecting area that is called the effective aperture A_e. It can be shown that an antenna with power gain G has an effective aperture A_e at the operating wavelength λ that is given by:

A_{e} = \frac{G λ^{2}}{4 π} (m^{2})

(5.7)

The effective aperture may be associated with a physical aperture, as in the case of a horn antenna, although it is usually smaller. However, even a linear antenna such as the dipole can be associated with an effective aperture even though it has no physical aperture. That is, for a given power density incident upon the antenna, the effective aperture is a measure of how much power is collected by the antenna—an antenna with a larger effective aperture will collect more power.

5.3.3 Beamwidth

Figure 5.4 also illustrates another important feature of a gain function: the beamwidth. The beamwidth of a gain function is normally defined as the width of the beam at the half-power points—that is, at the points where the gain is the maximum gain less 3 dB (G minus 3 dB). This half-power beamwidth, θ_b, is a measure of the angle over which most of the gain occurs. When the beam is not symmetrical in both the E and H planes, the beamwidth is usually given separately for both planes.

For example, for uniformly illuminated circular apertures, the half-power beamwidth (or 3-dB beamwidth), θ_b, in radians can be approximated by:

θ_{b} ≅ \frac{λ}{D \sqrt{η}} (r a d)

(5.8)

where D is the cross-sectional diameter.

It should be noted that the gain and beamwidth are related in that, as should be expected, a higher gain results when the beamwidth is narrowed. It is also important to note the frequency dependence of the two properties. The antenna gain is proportional to the square of the frequency of operation—that is, if the frequency is doubled, the gain is increased by a factor of four for a fixed antenna size. On the other hand, the beamwidth is halved as the frequency is doubled. For a given frequency, therefore, the gain increases by a factor of four when the diameter of the antenna is doubled, while the beamwidth is halved. Because of the impact of the ratio of the size of the antenna to the frequency of operation, the ratio D/λ is often used to describe a reflector antenna—ratios up to 800 are in use.

We should also note here that a compromise must normally be made in any communications system saving transmitter power by making use of a high-gain antenna and requiring high alignment accuracy due to the consequent narrow beamwidth of the antenna. In some cases, such as mobile transmitters, the two issues are at considerable odds—a high-gain antenna would be preferred because of the subsequent savings in battery life, but an omni-directional antenna (with its attendant low gain) is essential to avoid having to point the transmit and receive antennas toward each other.